NATX INST. OF STAND & TECH R.I.C. J

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PUBLICATIONS

United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

N/ST Technical Note 1504
DATE DUE

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TJU- IsO^

GAYLORD 'HINTED IN USA.
N/ST Technical Note 1 504

Precision Spectroscopy, Diode Lasers, and Optical

Frequency IVIeasurement Technology

Selected publications of the Optical Frequency Measurement Group

of the Time and Frequency Division

Edited by

Leo Hollberg

Richard Fox

Steve Waltman

Hugh Robinson

Time and Frequency Division

Physics Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

Supported in part by

Air Force Office of Scientific Research

and

National Aeronautics and Space Administration

May 1998

''^TES O*

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY. Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1504, 292 pages (May 1998)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Precision Spectroscopy, Diode Lasers, and

Optical Frequency Measurement Technology

Preface

This compilation is a selected set of reprints from the Optical Frequency Measurement

Group of the Time and Frequency Division of the National Institute of Standards and

Technology, and consists of work published between 1987 and 1997. The two main

programs represented here are (1) development of tunable diode-laser technology for

scientific applications and precision measurements, and (2) research toward the goal of

realizing optical-frequency measurements and synthesis. The papers are organized

chronologically in five, somewhat arbitrarily chosen categories: Diode Laser Technology,

Tunable Laser Systems, Laser Spectroscopy, Optical Synthesis and Extended

Wavelength Coverage, and Multi-Photon Interactions and Optical Coherences.

Additional publications mentioned in Section Vl are not included here, but are available

from the Time and Frequency Division Office. For more information, visit our website at http://www.bldroc.gov/timefreq/orphone: 303-497-3276, Fax: 303-497-6461.

Other NIST Publications may be purchased from the U.S. Government Printing Office

(GPO). The GPO website is http://v^ww.access.gpo.gov/ or phone: 202-512-1800.

Older publications may be purchased from the National Technical Information Service

whose website is http://www.ntis.gov/ or phone: 703-487-4650.

Acknowledgments: A number of people have worked with our group during this time

period and the results presented here are due in large part to their efforts. Special

recognition goes to the many important contributions of F. Bondu, J. Kitching, N. Mackie,

J. Magyar, J. Marquardt, C. Gates, M. Stephens, C.S. Weimer, J.S. Wells, A.S. Zibrov,

and T.P. Zibrova. We have also benefited greatly from collaborations with guest

researchers from around the world, including A. Dax, L. D'Evelyn, M.D. Lukin, M. Mjrtz,

D.E. Nikonov, K.P. Petrov, O. Pfister, U. Simon, G. Tino, D.A. Van Baak, V.V. Vasiliev,

and L Zink. Particularly important to our research program have been our long-term

collaborations with V.L Velichansky et al. from the Lebedev Institute, Moscow, Russia;

F.K. Tittel and R.F. Curl et al. from Rice Univ.; M.O. Scully et al. from Texas A&M Univ.;

M. Inguscio et al. from Firenze, Italy; D. Welch et al. from SDL Company; and A.R.

Ravishhankara et al. from NOAA. We gratefully acknowledge the continual guidance

and help provided by J.C. Bergquist and J.L. Hall. Our special thanks to Anna Dillon and

Wendy Ortega for their diligence and organization in the tedious task of bringing all these papers together into a coherent package. We also acknowledge the partial

support of this work from the Air Force Office of Scientific Research, and NASA.

Leo Hollberg

Richard Fox

Steve Waltman

Hugh Robinson

Time and Frequency Division

National Institute of Standards and Technology

325 Broadway, Boulder, CO 80303

December 1997

CONTENTS

PART I DIODE LASER TECHNOLOGY

"Frequency Stabilization of Semiconductor Lasers by Resonant Optical Feedback,"

B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876-878 (1987) IN 1

"Modulatable Narrow-Linewidth Semiconductor Lasers," L. Hollberg and M. Ohtsu,

Appl. Phys. Lett. 52, 944-946 (1988) IN 4

"Using Diode Lasers for Atomic Physics," C.E. Wieman and L. Hollberg, Rev. Sci.

Instrum. 62, 1-20 (1991) IN 7

"High-Sensitivity Spectroscopy with Diode Lasers," R.W. Fox, H.G. Robinson,

A.S. Zibrov, N. Mackie, J. Marquardt, J. Magyar, and L.W. Hollberg, Proc. SPIE

Conf. on Frequency Stabilized Lasers and Their Applications, 1837

(ed. Y.C. Chung) 360-365 (1992) TN 27

"The Diode Laser as a Spectroscopic Tool," R.W. Fox, C.S. Weimer, L. Hollberg,

and G.C. Turk, Spectrochim. Acta Rev. 15, 291-299 (1993) TN 33

"A CPW Phase-Locked Loop for Diode-Laser Stabilization," L. D'Evelyn,

L. Hollberg, and Z.B. Popovic, Proc. 1994 IEEE MTT-S Intl. Microwave Symp.,

San Diego, CA (1994) TN 42

"Amplitude Modulation on Frequency Locked Extended Cavity Diode Lasers,"

R.W. Fox, L. D'Evelyn, H.G. Robinson, C.S. Weimer, and L. Hollberg, Proc.

SPIE Conference, 2378, 58-62 (1995) TN 46

"High-Accuracy Spectroscopy with Semiconductor Lasers: Application to LaserFrequency Stabilization," L. Hollberg, V.L. Velichansky, C.S. Weimer, and

R.W. Fox, in Chapter 3 of Frequency Control of Semiconductor Lasers , (ed. M. Ohtsu, John Wiley and Sons) 73-93 (1996) TN 51

"Grating-Tuned Semiconductor MOPA Lasers for Precision Spectroscopy,"

J.H. Marquardt, F.C. Cruz, M. Stephens, C.W. Gates, L.W. Hollberg, J.C. Bergquist,

D.F. Welch, D. Mehuys, and S. Sanders, Proc. SPIE Conf. 2834 34-40 (1996) TN 71

"Semiconductor Diode Lasers," R.W. Fox, L. Hollberg, and A.S. Zibrov, in Atomic, Molecular, and Optical Physics: Electromagnetic Radiation , (ed. F.B. Dunning and R.G. Hulet, Academic Press) 77-102 (1997) of 29C series

Experimental Methods in the Physical Sciences TN 78

PART II TUNABLE LASER SYSTEMS

"CW Dye Lasers," L. Hollberg, Chapter 5 in Dye Laser Principles: With Applications

(ed. F.J. Duarteand Lloyd W. Hillman, Academic Press) 185-238(1990) TN 105
PART III LASER SPECTROSCOPY

"Hyperfine Structure of the Metastable ^82 State of ^^O Using an AIGaAs Diode

Laser at 777 nm," G.M. Tino, L. Hollberg, A. Sasso, and M. Inguscio, Phys. Rev.

Lett. 64, 2999-3002 (1990) IN 159

"High-Resolution Diode-Laser Spectroscopy of Calcium," A.S. Zibrov, R.W. Fox,

R. Ellingsen, C.S. Weimer, V.L. Velichansky, G.M. Tino, and L. Hollberg, Appl.

Phys. B 59, 327-331 (1994) TN 163

"Sub-Doppler Frequency Measurements on OCS at 87 THz (3.4 ^im) with the CO

Overtone Laser," A. Dax, J.S. Wells, L. Hollberg, A.G. Maki, and W. Urban, J. Mol. Spectrosc. 168, 416-428 (1994) TN 168

"Sub-Doppler Frequency Measurements on OCS near 1689 and 1885 CM"\"

J.S. Wells, A. Dax, L. Hollberg, and A.G. Maki, J. Mol. Spectrosc.

170,75-81 (1995) TN 181

"Detection of Methane in Air Using Diode-Laser Pumped Difference-Frequency

Generation near 3.2 lam," K.P. Petrov, S. Waltman, U. Simon, R.F. Curl, F.K. Tittel, E.J. DIugokencky, and L. Hollberg, Appl. Phys. B 61, 553-558 (1995) TN 188

"Precise Measurement of Methane in Air Using Diode-Pumped 3.4-^m DifferenceFrequency Generation in PPLN," K.P. Petrov, S. Waltman, E.J. DIugokencky,

M. Arbore, M.M. Fejer, F.K. Tittel, and L.W. Hollberg, Appl. Phys. B 64,

567-572(1997) TN 194

"Reactive Uptake of NO3 on Pure Water and Ionic Solutions," Y. Rudich,

R.K. Talukdar, and A.R. Ravishhankara, J. Geophys. Res. 101, 21,023-21,031

(1996) TN200

"An All-Diode-Laser Optical Frequency Reference Using Laser-Trapped Calcium,"

C.W. Gates, M. Stephens, and L. Hollberg, Proc. 1997 Intl. Frequency Control Symp.,

219-224(1997) TN 209

PART IV OPTICAL SYNTHESIS AND EXTENDED WAVE LENGTH COVERAGE

"Precise Optical Frequency References and Difference Frequency Measurements

with Diode Lasers," S. Waltman, A. Romanovsky, J. Wells, R.W. Fox, L. Hollberg,

M.P. Sassi, and H.G. Robinson, Proc. SPIE Conf. on Frequency Stabilized Lasers and

TheirApplications(ed. Y.C. Chung) 1837 , 386-391 (1992) TN215

"Proposed Sum-and-Difference Method for Optical-Frequency Measurements in the Near Infrared," D.A. Van Baak and L. Hollberg, Opt. Lett. 19,

1586-1588(1994) TN 221

"External-Cavity Difference-Frequency Source Near 3.2 ^im Based on Combining a Tunable Diode Laser with a Diode-Pumped Nd:YAG Laser in AgGaS2," U. Simon,

S. Waltman, I. Loa, F.K. Tittel, and L. Hollberg, J. Opt. Soc. Am. B 12, 323-327

(1995) TN224
"Division by 3 of Optical Frequencies by Use of Difference-Frequency Generation

in Noncritically Phase-Matched RbTiOAs04," O. Pfister, M. Murtz, J.S. Wells,

L Hollberg, and J.T. Murray, Opt. Lett. 21, 1387-1389 (1996) TN 229

"Demonstration of a Phase-Lockable Microwave to Submillimeter-Wave Sweeper,"

S.B. Waltman, L.W. Hollberg, K.A. Mcintosh, and E.R. Brown, Proc. SPIE 2842 . 55-58

(1996) TN232

"A 1 GHz Optical-Delay-Line Oscillator Driven by a Diode Laser," J. Kitching,

L. Hollberg, and F.L. Walls, Proc. 1996 Intl. IEEE Freq. Control Synnp., 807-814

(1996) TN236

"Continuous-Wave Frequency Tripling and Quadrupling by Simultaneous ThreeWave Mixings in Periodically Poled Crystals: Application to a Two-Step 1.19-

10.71-^m Frequency Bridge," O. Pfister, J.S. Wells, L. Hollberg, L. Zink,

D.A. Van Baak, M.D. Levenson, and W.R. Bosenberg, Opt. Lett. 22, 1211-1213

(1997) TN244

PART V MULTIPHOTON INTERACTONS AND OPTICAL COHERENCES

"Optical Probing of Cold Trapped Atoms," R.W. Fox, S.L. Gilbert, L. Hollberg,

J.H. Marquardt, and H.G. Robinson, Opt. Lett. 18, 1456-1458 (1993) TN 247

"Experimental Demonstration of Laser Oscillation without Population Inversion

via Quantum Interference in Rb," A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg,

M.O. Scully, V.L. Velichansky, and H.G. Robinson, Phys. Rev. Lett. 75, 1499-1502

(1995) TN250

"Line Shapes of Cascade Two-Photon Transitions in a Cesium Magneto-Optic

Trap," J.H. Marquardt, H.G. Robinson, and L. Hollberg, J. Opt. Soc. Am. B

13, 1384-1393(1996) TN 254

"Population- and Coherence-Induced Gain and Self-Oscillations in Alkali Vapor,"

A.S. Zibrov, H.G. Robinson, V.L. Velichansky, V.V. Vasiliev, L. Hollberg,

E. Arimondo, M.D. Lukin, and M.O. Scully, Proc. Fifth Symp. on Frequency

Standards and Metrology (ed. J.C. Bergquist, World Scientific) 490-492 (1995) TN 264

"Experimental Demonstration of Enhanced Index of Refraction via Quantum

Coherence in Rb," A.S. Zibrov, M.D. Lukin, L. Hollberg, D.E. Nikonov,

M.O. Scully, H.G. Robinson, and V.L. Velichansky, Phys. Rev. Lett. 76,3935-3938(1996) TN 267

"Spectroscopy in Dense Coherent Media: Line Narrowing and Interference Effects,"

M.D. Lukin, M. Fleischhauer, A.S. Zibrov, H.G. Robinson, V.L. Velichansky,

L Hollberg, and M.O. Scully, Phys. Rev. Lett. 79, 2959-2962 (1997) TN 271
PART VI ADDITIONAL PUBLICATIONS (see preface for additional information)

"Diode Lasers and Spectroscopic Applications," L. Hollberg, R. Fox, N. Mackie, A.S. Zibrov, V.L. Velichansky, R. Ellingsen, and H.G. Robinson, Proc. 10th Intl. Conf. on Laser Spectroscopy

(TENICOLS) (eds. M. Ducloy, E. Giacobino, and G. Carry) 347-352 (1991).

"Nonlinear Optics for Optical Frequency Synthesis and an Optical Divide by 3," M. Murtz, O.

Pfister, J.H. Marquardt, M. Stephens, and J.S. Wells, Proc. Fifth Symp. on Frequency Standards,

171-178(1995).

Diode Lasers and their Application to Spectroscopy," L. Hollberg, in Applied Laser Spectroscopy

(ed. W. Demtroder and M. Inguscio, Plenum Press, New York) 1 17-125 (1990).

"Diode Lasers and Metrology," R. Fox, G. Turk, N. Mackie, T. Zibrova, M.P. Sassi, J. Marquardt,

A.S. Zibrov, C. Weimer, and L. Hollberg, Solid State Lasers: New Developments and

Applications (ed. M. Ignuscio and R. Wallenstein, Plenum Press, New York), 279-286 (1993).

"Diode Lasers for Frequency Standards and Precision Spectroscopy," L. Hollberg, J. Aman, S. Waltman, J.H. Marquardt, M. Stephens, R.W. Fox, D.A. Van Baak, C.S. Weimer, H.G. Robinson,

A.S. Zibrov, N. Mackie, T.P. Zibrova, and L. Pendrill, Proc. 1995 Intl. Frequency Control Symp.,

185-190(1995).

"Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,"

A.S. Zibrov, M.D. Lukin, L. Hollberg, D.E. Nikonov, M.O. Scully, H.G. Robinson, and V.L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).

"Lasing without Inversion: The Road to New Short Wavelength Lasers," M.D. Lukin, M.O. Scully,

G.R. Welch, E.S. Fry, L. Hollberg, G.G. Padmabandu, H.G. Robinson, and A.S. Zibrov, Laser

Phys. 6, 436-447(1996).

"High-Coherence Diode Laser with Optical Feedback via a Microcavity with 'Whispering Gallery'

Modes," V.V. Vasil'ev, V.L. Velichanskii, M.L. Gorodetskii, V.S. Il'chenko, L. Hollberg, and A.V.

Yarovitskii, Quant. Electron. 26, 657-658 (1996).

"Absorption Cross Sections and Self-Reaction Kinetics of the lO Radical," M.H. Harwood, J.B. Burkholder, M. Hunter, R.W. Fox, and A.R. Ravishankara, J. Phys. Chem. A 101, 353-363

(1997).
Parti

Diode Laser Technology

Reprinted from Optics Letters, Vol. 12, page 876, November 1987. Copyright © 1987 by the Optical Society of America and reprinted by permission of the copyright owner.

Frequency stabilization of semiconductor lasers by resonant

optical feedback

B. Dahmani,* L. HoIIberg, and R. Drullinger

National Bureau of Standards, Boulder, Colorado 80303

Received May 20, 1987; accepted August 12, 1987 With simple optical geometries a separate resonant Fabry-Perot cavity can serve as an optical feedback element

that forces a semiconductor laser automatically to lock its frequency optically to the cavity resonance. This method

is used to stabilize laser frequencies and reduce linewidths by a factor of 1000 from 20 MHz to approximately 20 kHz.

The high sensitivity of diode lasers to opticeJ feedback

is a well-known phenomenon^ that generally has a

disruptive effect on the lasers' output frequency and

amplitude stability. Under certain circumstances

this sensitivity to feedback can be put to advantageous

use. We have discovered an unconventional method

that uses a low level of optical feedback to narrow

semiconductor-laser linewidths substantially and also

automatically to stabilize the laser's oscillation fre- quency. With the appropriate optical geometry the

laser optically self-locks to the resonance of a separate

Fabry-Perot reference cavity. The method relies on

having optical feedback occur only at the resonance of a high-Q reference cavity. In this case the cavity

serves two functions. It provides the optical feedback, which narrows the laser's spectral width, and it provides the center-frequency stabilization to the cavity resonance. A growing need for lasers with high spectral purity

has stimulated the development of a number of semiconductor-laser frequency-stabilization techniques.

Methods have been developed based on the techniques of optical feedback,^'^ external cavities,^-^ injection locking,^ and electronic servo control.^-^ Another

interesting and related system for diode-laser frequency stabilization is a hybrid method that uses electronic

as well as optical feedback from a fiber-optic cavity.^

Because of the spectral characteristics of semiconductor-laser frequency noise, the only systems that are able to achieve substantial linewidth reduction are those that incorporate some form of optical feedback

or use very fast electronic servos^'^'^^ (typically requiring servo bandwidths >20 MHz).

Our laser locking system contrasts with the previous

systems in that the laser sees optical feedback only

when its frequency matches the resonant frequency of

the reference cavity. We have tested a variety of optical locking geometries; Fig. 1 diagrams a particularly

simple and effective version. As shown here, when the

confocal reference cavity (mirror separation equal to mirror radius) is operated off axis, it should be viewed

as a four-port device. It is important to note that the

two ports on the input mirror side (labeled I and II) have different output characteristics. The output

beam of type I is a combination of the reflected portion

of the input beam with the transmitted portion of the

resonant field inside the cavity. This beam has a power minimum when the laser frequency matches a

cavity resonance. In contrast, the three outputs of

type II contain only the transmitted portion of the

cavity resonant field and hence have the desired cheir- acteristic of a power maximum on resonance. The

geometry of Fig. 1 is one possible method of arranging

to have the resonant optical feedback of type II (maximum feedback on resonance) while avoiding the complications inherent in the directly reflected beam con- tained in output I. For a wide range of feedback

conditions this system tends to self-lock stably, thus

forcing the laser frequency to match that of the cavity resonance. Our experiments have been carried out using commercial, single-mode, 850-nm, GaAlAs lasers^^ without any special preparation of these devices. The

free-running, unperturbed laser linewidths were measured to be approximately 20-50 MHz. A variety of

reference cavities was used for the optical locking sys- tem. These had free spectral ranges varying from 250

MHz to 7.5 GHz and resonance widths ranging from 4

to 75 MHz. As an additional laser diagnostic we monDiode

Laser _^v~

Confocal Cavity

Variable Attenuator

Aperture

PZT-C PZT-0

Fig. 1. Schematic of one version of the optical feedback

locking system. Lens L2 is used to mode match the laser into the confocal reference cavity. The aperture blocks the unwanted feedback of type I while passing the desired feed- back of type II. The variable attenuator is used to study the feedback power dependence of the locking process. The

piezoelectric translator PZT-0 is used to optimize the feed- back phase relative to the undisturbed laser. PZT-C is used

to scan the reference cavity and in turn the optically locked

laser frequency. A photodetector (Det.) monitors the trans- mitted power.

0146-9592/87/1 10876-03$2.00/0 © 1987, Optical Society of America

TN-1
November 1987 / Vol. 12, No. 11 / OPTICS LETTERS 877

[•»- 500 MHz-*-

1 1 1 1 1 1 1 1 1 Laser CurrentFig. 2. The lower trace displays the power transmitted

through the reference cavity as a function of the laser current. The upper trace, taken simultaneously, shows the

fluorescence from a cesium cell as the laser scans from left to

right across the 852-nm cesium resonance. The flat portion on the side of the fluorescence signal and on the peak of the

cavity resonance occurs when the laser frequency locks to the cavity resonance and no longer scans with the laser current. The indicated locking range =5:^ 500 MHz corre- sponds to the frequency range that the laser would normally

scan without the optical self-locking.

itor the resonance fluorescence from an atomic-cesium

vapor cell. With type II feedback if the laser frequency is far from matching a reference cavity resonance there is no

optical feedback and the laser frequency scans as usual

with changes in the injection current. However, as the

laser frequency approaches a cavity resonance, reso- nant feedback occurs and the laser frequency locks to the cavity resonance, even if the laser current contin- ues to scan. The actual frequency range over which

the diode laser locks is a function of the feedback

power level and the phase of the feedback light relative to that of the unperturbed laser. The optical locking

of the laser frequency to the reference cavity reso- nance is observed directly with a photodiode, which

monitors the power transmitted through the cavity as a function of the laser current. This signal is dis- played as the lower trace in Fig. 2. Here we see an

unusual Fabry-Perot transmission function, which

has a flat top and a width approximately 10 times

larger than the actual cavity resonance width of 50

MHz. This shape is a manifestation of the fact that

the laser frequency is not scanning with the laser cur- rent but is locking to the frequency of peak transmission of the cavity resonance. The frequency locking is further demonstrated in the upper trace of Fig. 2, which shows a simultaneous record of the fluorescence

from a cesium cell as the laser scans over the 852-nm

cesium resonance line. This trace shows that when

the laser frequency is far from the peak of the cavity resonance (shown in the lower trace) it scans smoothly

over the cesium resonance as the laser current is varied. The self-locking, which stabilizes the laser fre- quency, is evidenced by the abrupt flattening in the scan of the fluorescence signal as well as the cavity

transmission function. At the end of the 500-MHz

locking range the laser abruptly drops out of lock and

continues to scan over the cesium resonance.

For low levels of optical feedback the locking range

depends on the feedback power ratio. This is the ratio

of the external feedback power, coupled into the laser mode, to the power reflected internally by the output

facet. Locking ranges of a few hundred megahertz

were observed with feedback power ratios typically in

the range of 10~^ to 10~=, with a large uncertainty in the coupUng efficiency of the feedback power into the

laser mode.

In order to determine unambiguously the spectral

characteristics of the optically locked semiconductor

lasers, we measured the beat note between two lasers independently locked to separate reference cavities. Direct observation of the beat-note spectra avoids

many of the uncertainties and errors that plague measurements of laser frequency stability and linewidth

using delayed-self-heterodyne and electronic residualerror-signal techniques. Figure 3 shows the beat note

detected with a fast photodiode and displayed on a rf spectrum analyzer. The upper trace shows the beat

note when one of the lasers is free running without

feedback while the other laser is optically locked. The

sharply peaked trace is obtained when both of the

lasers are optically locked to their independent refer- ence cavities and indicates the dramatic linewidth re- duction that is instantly achieved. In the locked case, the width of the displayed beat note is limited not by

the laser linewidth but rather by the rf spectrum analyzer's resolution bandwidth of 300 kHz. Higher-resolution measurements show that the actual spectral

width of the beat note can be less than 20 kHz (Fig. 4). This narrowing of the semiconductor linewdith by a

factor of about 1000 (from 20 MHz to 20 kHz) is obtained by purely optical means without any electronic

control.

>

Q

S

•ao

/ 'x

jA^^ \^^«^ .

a35 ^4^-^

/

\ Lav- -^ O^AA-^

vyTv-v

^

Diode Laser Beat Note 20 MUz/Div

Fig. 3. The beat note between two semiconductor lasers is shown on a rf spectrum analyzer with a sensitivity of 10 dB/

division vertically and 20 MHz/division horizontally and a resolution bandwidth of 300 kHz. The upper trace shows

the broad beat-note peak that is observed when one of the two lasers is free running and unstabilized. The other,

sharply peaked, trace shows the beat note when both of the

lasers are optically self-locked to separate Fabry-Perot ref- erence cavities. In the locked case the peak width is limited by the 300-kHz resolution of the spectrum analyzer.

TN-2
878 OPTICS LETTERS / Vol. 12, No. 11 / November 1987

Diode Laser Beat Note 1 MHz/Div

Fig. 4. Diode-laser beat note displayed with higher resolu- tion now shows a very narrow width as measured on a rf spectrum analyzer. The approximately 20-kHz width is inferred from the two markers on the central peak (which are separated by —16 dB and 13 kHz), the spectrum-analyzer

resolution of 10 kHz, the sweep rate of 30 msec/division, and

the repeatability of the measurement.

One advantage of the optically self-locked laser sys- tem is that it shows some reduction in sensitivity to other sources of optical feedback. In addition, we find

that the excess intensity noise (=s:30 dB above the

expected photodetection shot noise) that we measure

on the light from the semiconductor laser is reduced

by roughly 10 dB when the laser is optically locked to the cavity.

For many applications it is important to be able to scan the laser frequency as well as to have a stable

long-term frequency lock. Continuous, narrowlinewidth scans of the laser frequency can be made by

synchronizing the sweep of the laser current with that

of the reference cavity length (PZT-C, Fig. 1) and the

feedback phase (PZT-</)). With this synchronization we have made continuous scans of more than 4 GHz;

these were limited only by the range of our present

PZT-0. We note that it is necessary to control the

laser current only accurately enough that the free- running laser frequency is within the !^ 500-MHz optical-self-locking range. To avoid the inevitable drifts and to ensure long-term locking stability, it is useful to servo control the appropriate feedback phase and laser current relative to the reference cavity. Low-speed

electronic feedback circuits are sufficient to accomplish this. The actual physics that determines the spectral

characteristics of semiconductor lasers is a topic of

active research and is reviewed in Ref. 13. Initial theoretical analyis^^ of the self-locking process based on optical feedback theory^-^^"^' gives reasonable

agreement with experimental results, at least in terms

of linewidth reduction, locking range, and the phase

dependence of the cavity locking.

The optical self-locking system described here has

several advantages relative to conventional locking

techniques. It is a relatively simple method that provides a vast improvement in the linewidth and direct

control of the semiconductor-laser frequency. When

the system is locked, the laser's linewidth is reduced

dramatically, from 20 MHz to approximately 20 kHz,

and the laser's oscillation frequency is stabilized to the

cavity resonance frequency. Even narrower spectral

widths could be expected with better-quality refer- ence cavities. Long-term stability of the reference

cavity resonance can be quite high.^^ We observe that

the laser's intensity noise is reduced, as is its sensitivity to other sources of optical feedback. The system is also attractive because it does not require any modification of commercial laser diodes or any extremely fast electronic servo systems. With the increasing interest

in semiconductor lasers with high spectral purity and

precision optical measurements in general, this optical-self-locking method has the potential for numerous applications.

*Permanent address, Laboratoire Primaire du

Temps et des Frequences, 61 avenue de I'Observatoire,

75014 Paris, France.

References

1. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).

2. K. R. Preston, K. C. Woollard, and K. H. Cameron,

Electron. Lett. 17, 931 (1981).

3. J. Mark, E. Bodtker, and B. Tromborg, Electron. Lett. 2L 1008 (1985).

4. R. Wyatt and W. J. DevHn, Electron. Lett. 19, 110

(1983).

5. M. Fleming and A. Mooradian, IEEE J. Quantum Electron. QE-17, 44 (1981).

6. S. Kobayashi and T. Kimura, IEEE J. Quantum Electron. QE-17, 681 (1981).

7. Yu. A. Bykovskii, V. L. Velichanskii, I. G. Goncharov,

and V. A. Maslov, Sov. Phys. Semicond. 4, 580 (1970).

8. J.-L. Picque and S. Roizen, Appl. Phys. Lett. 27, 340

(1975).

9. F. Favre and D. Le Guen, IEEE J. Quantum Electron. QE-21, 1937 (1985), and references therein.

10. M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. QE-21, 1905 (1985).

11. Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).

12. For technical reference, the lasers used were Hitachi

HLP 1400's. This mention does not constitute an en- dorsement, and we expect that other lasers will also be

suitable.

13. M. Osinski and J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).

14. D. Hjelme, A. Mickelson, L. Hollberg, and B. Dahmani,

in Digest of Topical Meeting on Semiconductor Lasers

(Optical Society of America, Washington, D.C., 1987), p.

15.

15. C. H. Henry, IEEE J. Lightwave Technol. LT-4, 298

(1986).

16. R. J. Lang and A. Yariv, IEEE J. Quantum Electron. QE-22, 436 (1986).

17. H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).

18. Drift rates of Av/vAt ^ 10"''*/sec have been reported for gas lasers electronically locked to optical cavities: D.

Hils and J. L. Hall, in Digest of XV International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1987), p. 102.

TN-3
Modulatable narrow-linewidth semiconductor lasers

L Hollberg and M. Ohtsu^*

National Bureau ofStandards, Boulder, Colorado 80303

(Received 28 March 1988; accepted for publication 5 July 1988)

We find that using the technique of optical feedback locking, to narrow semiconductor

linewidths, does not sacrifice the ability to modulate the laser's frequency via the injection current. The frequency of a laser is stabilized to a separate Fabry-Perot reference cavity using resonant optical feedback and can be modulated efficiently at frequencies related by rational

fractions to the free-spectral range of the reference cavity. This system can provide an array of

narrow-linewidth, frequency-stable laser lines and shows promise for applications in frequency-division-multiplexed coherent communications, as well as laser frequency control

and precision measurement systems.

Optical feedback locking of semiconductor lasers provides a powerful means for stabilizing the frequency and nar- rowing the linewidth of diode lasers.'"' This optical tech- nique can reduce laser linewidths by more than a factor of

1000, thus achieving linewidths of a few kilohertz. We consider here the interesting and useful modulation characteristics of these optically stabilized rcmiconductor lasers (OSSL). Direct modulation of the injection current of these

lasers can provide a high FM modulation index while the very narrow linewidth and frequency stabilization produced

by the optical feedback lock is maintained.

The high-speed frequency and amplitude modulation

capabilities of semiconductor lasers are important attributes of these lasers relative to other optical sources. Unfortunately, the FM capabilities are usually sacrificed when the laser linewidths are reduced by optical means. "* With most fre- quency stabilization schemes there is a trade-off between the diode laser's linewidth and its FM modulation capabilities.

Usually a one-to-one correspondence exists between these

quantities; that is, if the laser linewidth is reduced by a factor of 10, its FM sensitivity to injection current (typically ~3

GHz/mA) is also reduced by roughly this same factor of 10. In the case of the OSSL the modulation characteristics are

definitely altered by the optical locking process, but we find that the modulation sensitivity is not necessarily reduced

when the linewidth is narrow. In fact, we find that the modulation characteristics of the OSSL have a predictable reso- nant frequency dependence.

The concept behind the optical feedback locking tech- nique is to establish weak resonant feedback from a high Q

( relative to the ^ of the diode laser cavity ) optical resonator. Figure 1 is a diagram of a system which gives enhanced optical feedback when the laser frequency matches the cavity resonance and effectively zero-feedback off resonance. Here

a beamsplitter picks off a small amount of the laser output

( ~ 4% ) and couples it off axis into a confocal optical reso- nator. This geometrical arrangement ensures that the laser sees positive optical feedback precisely when the laser fre- quency matches the cavity resonance frequency. The optical lock usually operates in the low feedback limit and typically

requires an optical feedback power ofabout 10 ~ '* of the laser

output power. ^ At resonance the spectrally cleaned laser

field which has built up in the reference cavity leaks back

through the cavity input mirror and returns to the laser where it increases the laser gain at that frequency. This fre- quency-selective gain enhancement forces the laser to lock to the cavity resonance frequency. The result is that the semiconductor laser's frequency is stabilized to the cavity reso- nance, and its 20 MHz linewidth is reduced to less than 10 kHz. Related work has also been reported for semiconductor

laser frequency control using optical feedback from optical

waveguides' and fiber cavities.* We have used a variety of optical geometries and refer- ence cavities for these optical locking systems. The free-spectral ranges (FSR) of the reference cavities were between 7.5 GHz and 250 MHz with cavity resonance widths varying

from 75 MHz to 20 kHz. The commercial lasers were singlemode AlGaAs lasers operating near 850 nm and were not modified in any way. For applications requiring higher spectral purity and low residual phase noise at high frequencies,

it is useful to send all of the laser power into and through the

high-efficiency reference cavity. The cavity then acts as a

' Permanent adress: Tokyo Institute of Technology, Graduate School at Nagatsuta, Midori-ku, Yokohama, Kanagawa 227, Japan.

FIG. 1. Experimental diagram of an optically stabilized semiconductor la- ser (OSSL). Approximately 4% of the laser output power is coupled off- axis into the confocal optical locking cavity. In this geometry resonant optical feedback returns to the laser and automatically locks the laser frequency

to the cavity resonance. Piezoelectric ceramics PZT-C and PZT^ are used

to control the cavity frequency and optimize the feedback phase, respectively. An additional monitor cavity is used for spectral analysis and is separat- ed from the laser by an optical isolator, rf modulation is added to the dc

injection current through the modulation port (mod.). Photodiode detectors (det. ) monitor the transmission and reflection signals from the cavities.

944 Appl. Phys. Lett. 53 (1 1

), 1 2 September 1 988 0003-6951 /88/370944-03$01 .00 © 1 988 American Institute of Physics

TN-4

944
bandpass filter and removes the excess laser phase noise at very high frequencies. This scheme uses the reference cavity

as a spectral and spatial filter as well as the frequency discri- minator for the optical feedback lock using the weak reflec- tion.Modulation of the injection current of nonstabilized

semiconductor lasers results in both amplitude and frequen- cy modulation of the laser output. At least in the limit of low

modulation index the temporal characteristics of the laser

electric field can be represented by

E{t) =A[\ + m cos{o)„t)]sin[(ot + P cosico^t + 0)] . (1)

Here A is the field amplitude, (o/{lv) is the laser carrier frequency, (o„/i2ir) is the modulation frequency, and m

and P represent the amplitude and frequency modulation

indices, respectively.^* The resulting frequency-domain

spectra can be described by the usual sum of AM plus FM

sidebands (with Bessel function amplitudes) except that the

relative phase 6 between AM and FM is frequency dependent. When a diode laser is operating well above threshold, a

small modulation of the injection current results in a modulation of the laser field that is predominantly FM with the

ratio of ^ to m typically in the range of 10 to 20. However,

when the modulation index is large (/3>2), the situation can be considerably more complicated.

When the OSSL is modulated at low frequencies, typically ci)„ <200 MHz, the frequency modulation is suppressed by the optical lock relative to that of an unstabilized

laser.^ On the other hand, there are special modulation fre- quencies that strongly affect the frequency modulation characteristics of the OSSL. With certain modulation conditions some or all of the modulation sidebands can resonate with

the reference cavity (with or without the carrier), in which

case they return to the laser and reinforce the optical lock. In

particular optical sidebands at frequencies that correspond

to the FSR (or its harmonics) of the reference cavity are simultaneously resonant with the cavity and are fed back to the laser with the carrier. In this way it is possible to modulate the laser current with a high modulation index (3 and

generate many sidebands without disrupting the frequency

stabilization and linewidth narrowing provided by the opti- cal feedback lock. Figure 2 shows the resonances in the optical locking

process that one observes as a function of the applied rf modulation frequency. The tallest, evenly spaced, sharp reson- ances in this figure occur when the modulation is at frequencies integrally related to the cavity FSR of 245 MHz. Good

optical locking is observed at the modulation frequencies

corresponding to these resonances. Also, the power trans- mitted through the cavity is maximized because the laser carrier and the sidebands match cavity resonances.

All of the cavity transmission resonances shown in Fig. 2 correspond to modulation frequencies that are related to the reference cavity FSR by rational numbers, that is, when

the modulation frequency is (o„/{lTr)^{a/b){¥SK), a,6 = 1,2,3,...

(2)

The smaller resonances shown in Fig. 2 occur when the ratio {a/b) is not an integer. This rational relationship between

Tmax —

s.a

>

CO O

290 530 770 1010 Modulation Frequency (MHz)

125

FIG. 2. Power transmitted through the optical locking cavity ( FSR = 245 MHz, finesse = 10) as seen by detector 2 (Fig. 1) as a function of the frequency of the modulation applied to the injection current. The modulation frequency is swept slowly from 50 to 1250 MHz. Points of zero and maximum transmission are indicated on the vertical axis. The sharp peaks

indicate the resonant natureof the stability of the optical lock as a function of modulation frequency. The large evenly spaced peaks correspond to modulation at the frequency of the cavity free-spectral range (245 MHz)

and its harmonics. The smaller resonant peaks occur when the modulation

frequency is related to the cavity FSR by a noninteger rational number. A

modulation current of ~ 5 mA was added to the dc current of 95 mA ( ~ 1.7 times threshold).

the modulation frequency and the cavity FSR for stable optical locking is easily understood: that is, under the conditions

of Eq. (2) every bxh sideband can resonate with every oth

cavity mode. For example, modulation at 367 MHz corre- sponds to a/b = l/l and means that when the carrier is reso- nant with a cavity mode, every other sideband will be simultaneously resonant with every third cavity mode. This

situation gives stable optical locking with roughly half of the

available power resonant with the cavity. We have observed

these resonant enhancements in the optical lock for many

modulation frequency to FSR ratios, including those with

a = 1-9 and b = 1-5. In principle, some optical locking oc- curs for any modulation frequency that is related to the cavity FSR by a rational number {a/b), but in general as the denominator b gets larger, less and less of the available opti- cal power is resonant with the cavity modes and hence the

optical lock is less effective. The strength of a particular reso- nance depends on the number and size of the sidebands that are resonant with cavity modes and thus depends strongly on

the modulation index 13 and the value of b. The frequency domain power spectra of an optically

locked laser that is modulated at one of the resonances [consistent with Eq. (2) ] consist of an array of frequency stabilized, narrow-linewidth laser lines separated by the modulation frequency. Figure 3 shows sideband spectra of a modulated OSSL taken with an optical spectrum analyzer

(see Fig. 1 ). The optical spectrum analyzer that is used to

rlisplay the modulation sidebands is not capable of measur- mg the very narrow laser linewidth because of the limited

resolving power when a large FSR (7.5 GHz) is required. In order to measure the laser linewidth we use heterodyne

methods to detect the beat note between two OSSL's.^ We

find that the locked laser linewidths are less than 10 kHz and

945 Appl. Phys. Lett., Vol. 53, No. 11 , 12 September 1988 L. Hollberg and M. Ohtsu TN-5945
sively from 10 kHz to 20 MHz as the modulation index is increased.

A good optical lock occurs when the laser is modulated

at a resonance frequency consistent with Eq. (2). However,

these resonances are fairly narrow in modulation frequency

and depend directly on the Q of the cavity, the modulation

index, and the optical feedback level. For example, with a locking cavity Q—\0^ (corresponding to a cavity finesse of

10 and a FSR of 245 MHz) and an optical feedback power

ratio of about 10""*, the modulation frequency range for good optical locking is approximately 6 MHz wide (centered at the modulation resonance frequency at 245 MHz;

see Fig. 2). This range is for a modulation index y9~8 and

increases, as we might expect with smaller modulation in- dex. This resonant character of the laser's FM modulation

response limits the modulation formats that can be employed with the OSSL.

Using the technique of optical feedback locking, we find that it is possible to simultaneously have a narrow-linewidth

semiconductor laser with a high-sensitivity frequency modulation capability. Frequency modulation induced via the

injection current is compatible with the optical stabilization (and narrow hnewidth) when the ratio of the modulation

frequency to cavity FSR is a rational number. One of the promising applications is to use the modulated OSSL to provide an array of frequency-stabilized local oscillators for fre- quency-division-multiplexed coherent communication sys- tems. There is also the potential for measuring optical

absorption and dispersion with high sensitivity using the techniques of optical heterodyne spectroscopy'" as well as applications in precision laser measurements and frequency

control."''

We would Hke to thank J. L. Hall, R. Drullinger, B. Dahmani, and A. Clairon for constructive discussions, and

J. L. Hall and the Joint Institute for Laboratory Astrophysics for making this collaboration possible.

Optical Spectrum

FIG. 3, Sideband structure of a modulated, optically locked, semiconductor

laser taken with an optical spectrum analyzer (FSR = 7,5 GHz, fin- esse = 150) for three of the resonant modulation frequencies. In all of these cases a high-modulation index is obtained while maintaining the narrow

laser linewidth and center frequency stabilization. In (a) the modulation

frequency is equal to the locking cavity FSR of 245 MHz. Here a modulation current of ~ 7 mA is added to the dc bias of 97 mA. We see that more

than 20 narrow-linewidth, frequency stable, sidebands are produced. In ^b) the 4 mA of modulation current is at a frequency of 367 MHz which is 3/2

the cavity FSR. In (c) the laser is modulated with ~ 10 mA at 980 MHz

(four times the FSR), and the laser generates more than ten useful side- bands covering a total frequency range of more than 10 GHz (in this case

the overlapping sidebands from the adjacent 7.5 GHz FSR have been re- moved for clarity).

that the linewidth is unchanged when the laser is modulated

at frequencies that correspond to the locking resonances that are shown in Fig. 2. This is to be compared with linewidths

that are measured to be 20 MHz when the laser is not locked

or is strongly modulated at a frequency that is not an optical

locking resonance frequency. When modulated at such nonlocking frequencies the OSSL's linewidth degrades progres-

'D. Hjelme, A. Mickelson, L. HoUberg, and B. Dahmani, in Digest of Topi- cal meetingon Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), p 15. -B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).

'H. R. Telle and H. Li, IEEE J. Quantum Electron, (to be published). 'M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 ( 1985). ^N. A. Olsson, C. H. Henry, R. F. Kazarinov, H. J. Lee, B. H. Johnson, and

K. J. Orlowsky, Appl. Phys. Lett. 51, 1 141 ( 1987); R. F. Kazarinov and

C. H. Henry, IEEE J. Quantum Electron. 23 1401 (1987); R. F. Kazarinov, C. H. Henry, and N. A. Olsson, IEEE J. Quantum Electron. 23, 1419

(1987).

"F. Favre and D. Le Guen, IEEE J. Quantum Electron. 21, 1937 (1985).

^S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, IEEE J. Quantum

Electron. 18,582 (1982). "W. Lenth, Opt. Lett. 8, 575 (1983).

''A. Clairon, B. Dahmani, Ph. Laurent, and Ch. Breant, in Proceedings of

the 2nd European Frequency and Time Forum, Neuchatel, Switzerland,

1988; and Ph. Laurent, A. Clairon, and Ch. Breant (unpublished).

'"J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, Appl. Phys. Lett. 39, 680(1981). "R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 ( 1983). '-R.G. Devoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer,

Phys. Rev. A 37, 1802 (1988).

946 Appl. Phys. Lett., Vol. 53, No. 11 , 12 September 1988 L. Hollberg and M. Ohtsu TN-6

946
Using diode lasers for atomic physics

Carl E. Wieman

Joint Institute for Laboratory Astrophysics, University of Colorado and National Institute ofStandards

and Technology, and Physics Department, University of Colorado, Boulder, Colorado 80309-0440

Leo Hollberg

National Institute ofStandards and Technology, Boulder, Colorado 80303

(Received 20 April 1990; accepted for publication 2 August 1990)

We present a review of the use of diode lasers in atomic physics with an extensive list of

references. We discuss the relevant characteristics of diode lasers and explain how to purchase

and use them. We also review the various techniques that have been used to control and

narrow the spectral outputs of diode lasers. Finally we present a number of examples

illustrating the use of diode lasers in atomic physics experiments.

I. INTRODUCTION

Much of current atomic physics research involves the

interaction of atoms and light in some way. Laser sources

that can be tuned to particular atomic transitions are now a standard tool in most atomic physics laboratories. Traditionally this source has been a tunable dye laser. However,

semiconductor diode lasers have been steadily improving in

reliability, power, and wavelength coverage, while steadily

decreasing in cost. It is now possible to have a diode laser system that will produce more than 10 mW of tunable light

with a bandwidth of 100 kHz for a cost of less than $1000.

Furthermore, the diode laser and power supply will fit in a

I-/ box, require very little power or cooling water, and, under the right conditions, will be within a few MHz of the desired wavelength as soon as it is turned on. A further vir- tue is that the amplitude is very stable compared to most

other laser sources so that it is relatively simple to make

sensitive absorption or fluorescence measurements. These

features make diode lasers increasingly attractive alternatives for a variety of uses. In this review we present something of a users' guide

aimed at atomic physicists who might want to start using

diode lasers in their work. In this spirit we present the advantages of diode lasers as well as their negative features (there are several serious ones ) and the best ways to deal with them.

We begin in Sec. II by discussing relevant basic laser characteristics. Section III addresses some of the most important

issues involved in actually setting up and using diode lasers

in atomic physics experiments, such as purchasing the correct laser, tuning it to the desired frequency, and how to avoid destroying it. Section IV discusses optical and elec- tronic feedback to control the laser output frequency. In the

past, one of the main drawbacks to using diode lasers in atomic physics was the difficulty in obtaining narrowband,

easily tunable output. However, the developments covered

in Sec. IV have improved this situation considerably. Section

V then discusses a selected set of applications of diode lasers

in atomic physics, focusing primarily on work that has been

made possible by these new wavelength control techniques.

To keep this article to a reasonable length there are necessarily many things we do not discuss. For example, we do

not cover progress made on producing special diode lasers that work in marvelous ways, because these developmental

lasers are not available to most atomic physicists. We restrict ourselves to lasers that are standard commercial devices. Another notable omission is the extensive work in molecular

spectroscopy that has been done using lead salt diode lasers

in the middle and far infrared regions of the spectrum.

Camparo' completed an extensive review on the use of

diode lasers in atomic physics in 1985. That review covered

much of the basic physics and characteristics of diode lasers, and the various uses that had been made of them. At that time most devices were simple free-running lasers without

feedback, and they had been used principally for optical

pumping and low resolution spectroscopy. In the present

review, although there will necessarily be some overlap of

that discussion, we will emphasize the recent developments

including "stabilized lasers" (ones with feedback for fre- quency control), and new types of applications. There is also an excellent review entitled "Coherence in Semiconductor

Lasers" by Ohtsu and Tako^ that discusses applications in a

variety of areas.

II. BASIC LASER CHARACTERISTICS

The basic physics of diode lasers is presented in many

references^ and will not be repeated here. However, we do

wish to single out a few features that are relevant to much of

the later discussion. The construction of a typical semiconductor diode laser is shown in Fig. 1. The devices are ex- tremely small and yet are capable of reasonable cw output

powers with high electrical to optical efficiency. The laser

light is generated by sending a current (the "injection cur- rent" ) through the active region of the diode between the n- and ;?-type cladding layers. This produces electrons and

holes, which in turn recombine and emit photons. The laser's emission wavelength is determined by the band gap of the semiconductor material and is very broadband relative to atomic transitions. The spatial mode of the laser is defined by

a narrow channel in the active region that confines the light.

This confinement of the transverse laser mode is achieved

either through the spatial variation of injection current density (gain guided) or by spatial variations in the index of

Rev. Scj. Instrum. 62 (1), January 1991 0034-6748/91/01 0001 -20$02.00

TN-7
(300 |im)

Note: Chip size may be varied

Al electrode - p-type electrode Substrate Current blocking layer Cladding layer Active layer Cladding layer Cap layer n-type electrode

e//

Radiation pattern ' 6 X

FIG. I . Illustration of the different layers of semiconductor and the typical dimensions of a diode laser. The rectangular shape of the gain region leads

to the oval radiation pattern. (Figure adapted from Ref 4, with permission. )

refraction due to changes in the materials used in the laser's construction ( index guided )

.

A wide variety of laser designs have been used. Most of

the atomic physics done with diode lasers has been carried out using index-guided GaAlAs lasers in the near infrared

region of the spectrum. Unless otherwise noted, this type

will be assumed in the subsequent discussion. These lasers typically produce single-mode (spatial and longitudinal)

output powers of 5-1 5 mW with just the cleaved facets of the semiconductor serving as the laser's mirrors. Output powers

up to ~ 50 mW are commercially available from what are

essentially the same devices with the addition of a high re10

5 8 Eo

Q.3

Q.3

O

o

roo

Q. O

6 —

i 1

/

/

o ' ' i e / lO / O / O j rw / ml

" / " /

II 1 ^ ^ '"/

- u

'j. _ Foward

current Ic

1

4 —

2 —

20 40 60 80 Foward current Ip (mA)

100

FIG. 2. Output power vs injection current for a typical laser. The sudden change in the slope of each curve marks the onset of laser action, and the current at that point is the threshold current for the laser. The different curves show how the temperature affects the laser output. ( Figure adapted from Ref. 4, with permission.

)

9 10 1.1 1.2 1.3 1.4 Wavelength (microns)

1.5 1.6 1.7

FIG. 3. cw diode laser output powers displayed as a function of wavelength.

The various cross hatched boxes are taken from manufacturers catalogs and

represent the distributions in wavelength and power that are advertised. In some cases it is possible to obtain lasers outside of these normal distributions. The range shown here is the distribution of lasers from the manufacturers and should not be confused with the tuning range of any specific laser which is much smaller. (The manufacturers shown in this table include; Hitachi, Mitsubishi, Nee, Oki, Sharp, and Spectra Diode and are listed only

as being representative, not as an endorsement; other sources should be

equally suitable. We have experience with some of these devices but we have

not verified all devices nor that the manufactures will deliver all of the devices as advertised.

)

flectance coating on the back surface and a reduced reflec- tance coating on the output facet. Higher power lasers that have special designs such as multistripes or very wide single

stripes are also available. These will likely be useful in the

future, but at the present time the difficulty and expense in obtaining these special designs at a desired wavelength is a formidable problem.

The output power ofa typical semiconductor diode laser as a function of the injection current and temperature is shown in Fig. 2. This shows the abrupt onset of laser action

at the threshold current and the increase in the threshold

with temperature. Alternatively, for fixed injection current, the laser's output increases rapidly as the temperature is lowered.

Figure 3 shows the power and wavelength characteristic ofcw diode lasers that are readily available from commercial

sources. These are divided into five main bands as driven by

commercial applications. The two bands in the infrared, at 1300 and 1500 nm, have been developed primarily for fiber optic systems and are based on quartenary InGaAsP semiconductors. The lasers in the 750-890 nm region are based on AlGaAs and have appUcations in consumer and commercial electronics as well as some fiber-optic applications. The

relatively new visible diode lasers near 670 nm are based on InGaAlP semiconductors and have many projected applications in commercial optoelectronic systems. In applying

these various lasers to spectroscopy we find that their spectral characteristics vary considerably. Those in the 750-870

nm region have the best overall characteristics.

A. Beam spatial characteristics Because the light i.*; emitted from a small rectangular

region (on the order of 0.1 fj.m by 0.3 //m) the output of a

Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-8
diode laser has a large divergence (see Fig. 1). A typical

output beam will have a divergence angle (full width at 50%

intensity) of 30° in the direction perpendicular to the junction, and 10° in the parallel direction. Normally the beam is collimated using a lens with a small /number. If the laser is operating in a single transverse mode, the collimated beam

will be elliptical, but it can be made nearly radially symmetric using anamorphic prisms. In addition to the different divergence angles, the output beam of most diode lasers is astigmatic. This astigmatism can also be compensated when

necessary.^ A typical diode laser wavefront collimated in

this fashion will often have a significant amount of structure. This is primarily a function of the quality of the first colli- mating lens and the amount it apertures the beam. However,

with relatively inexpensive lenses and spatial filtering, one

can obtain wavefronts with good Gaussian profiles. This can

be done with relatively little loss in power ( 10% ) , but sometimes the optical feedback from the filtering elements can be

a problem. If one is forced to work with a laser that is emitting light in a number of transverse modes, a highly struc- tured beam is unavoidable unless one sacrifices a substantial amount of power.

B. Amplitude spectrum

For most applications, the amplitude and spectral characteristics of the light are more important than the spatial characteristics. When compared to other tunable laser sources, the amplitude noise on diode lasers is relatively

small, but it can vary considerably depending on the actual

laser and its operating conditions. Figure 4 shows the amplitude noise spectrum of a typical single-mode diode laser tak- en with a fast photodiode and an rf spectrum analyzer. The

natural scale for the measurement of laser amplitude noise is the quantum-limited shot-noise level that is indicated on the

figure for this detected power. The general structure of the amplitude noise shows peaking at the lowest Fourier fre- quencies (/<500 kHz). At intermediate frequencies (500

Frequency (300 MHz/Div)

3 GHz

FIG. 4. Spectral distribution of amplitude noise on a typical commercial

diode laser operating near 780 nm. The logarithmic vertical scale shows the excess noise on the laser relative to quantum limited shot-noise level for the same detected power level of 4 mW. The laser is operating well above

threshold and the peak near 2.4 GHz is due to the lasers relaxation oscillation.

kHz </< 3 GHz ) there is a broad plateau that rises to a peak

at the laser's relaxation frequency (2-3 GHz), and then

drops to the shot-noise level for frequencies above the relaxation frequency. The fundamental noise level is a function of

both the injection current and the laser's temperature.'' The

amplitude noise decreases as the injection current is in- creased or the temperature decreased. Both of these changes move the relaxation oscillation to higher frequency. Special

laser systems have been built to bring the amplitude noise of

diode lasers down to, and even below,^ the shot-noise level but this performance cannot be expected from standard

commercial diode laser systems.

Most atomic physics experiments are done with detection bandwidths centered in the low or intermediate frequen- cy range. In this range, the amplitude noise for a good quality diode laser can be quite low relative to that of a dye laser, typically 10 to 20 dB above the quantum-limited shot-noise

level. This translates into power fluctuations for a typical

diode laser of one part in 10'' for a 10-kHz detection bandwidth. The situation can be much worse with some lasers, particularly when the laser runs multimode in only a few

modes; the resulting noise is called mode competition noise. External factors such as fluctuations in the injection current, the temperature, and the optical feedback can increase the amplitude noise substantially. Each of these influence the gam of the diode laser and hence its output power. The suppliers of diode lasers occasionally provide some

information about the lasers' intensity noise, but this infor- mation is usually specified in a way that is most useful for applications to consumer electronics. For example, the

specifications may give a signal-to-noise ratio {S /N) of 80

dB. This is a measure of the laser's amplitude noise taken in a

10 kHz bandwidth centered at 750 kHz. This information is useful but insufficient for many scientific applications.

The peak of the noise at the relaxation oscillation fre- quency is characteristic of many solid state laser systems**

and can be a problem for some applications. The fraction of

laser power that is contained in the relaxation oscillation peaks varies considerably from one type of laser to another

and even varies for a given laser depending on its operating

conditions. For example, the power in the relaxation side- bands can vary by as much as a factor of 100 with variations

in optical feedback. We find that good single mode AlGaAs

lasers operating near 850 nm will have relaxation sidebands

that are down from the carrier by a factor of ~ 1000. In contrast, some of the visible lasers (670 nm) we have tested show relaxation sidebands that are roughly 10% of the carrier. The relaxation oscillation sidebands are not always det- rimental. As discussed in Sec. V A, they can provide useful optical pumping.

C. FM spectrum

There are two natural scales to the oscillation spectrum

of diode lasers. The first scale is set by the spacing of the

cavity modes of the laser which is on the order of 160 GHz

( -0.35 nm). The second is the linewidth of a single cavity

mode. At the present time, it is quite routine to obtain "sin- gle-mode" lasers in the near infrared region (750 to 850 nm,

AlGaAs lasers) although the visible (670 nm, InGaAlP laRev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-9
1010

FIG. 5. Spectral density of laser frequency noise for an AlGaAs diode laser. The dots are experimental data which are compared to theory as represent- ed by the lines. The frequency noise peaks at low Fourier frequencies and

again at the relaxation oscillation frequency. The theory shows that current induced temperature fluctuations are responsible for the low frequency

peak, carrier induced index changes cause the high frequency resonance, and spontaneous emission contributes a flat background noise. (Figure

adapted from Ref. 1 1, with permission.)

sers) and infrared lasers (1300 and 1500 nm, InGaAsP la- sers) ordinarily will have their power distributed in many

modes. The distributed feedback (DFB) lasers in the in- frared will run in a single mode but have a limited tuning

range. We might mention a few caveats about nominally

single-mode lasers. First, they are not absolutely single mode

in that there are small but readily observable amounts of

power in numerous other modes that can occasionally be a problem. Second, a laser that has been sold as a single-mode

laser will often not run in a single mode for all injection currents. The lasers will always be multimode for very low

injection currents, but even at much higher currents there are often ranges of current and temperature where the laser

will continue to operate in several modes.

For the remainder of this section we will consider only

the linewidth of a single mode. For some applications, in818

20 30 40 Case temperature Tc(°C)

FIG. 6. Laser output wavelength vs the temperature of the laser case. The

short continuous segments indicate the tuning of the optical length of the cavity for a given longitudinal mode. When the peak of the gain medium has

shifted too far, the laser jumps to another mode. This is indicated by the breaks in the curve. (Figure reproduced from Ref. 4, with permission.)

eluding laser spectroscopy, coherent communications, and

precision measurements, the diode laser's linewidth can be a

serious problem. Many factors contribute to the linewidth of

diode lasers; the most fundamental of tnese is that the laser

cavities are so short that the Schawlow-Townes linewidth is significant (typically a few MHz).' The linewidths of com- mon single mode diode lasers are larger than the SchawlowTownes value because of fluctuations in the carriers, the temperature, and in the complex susceptibility of the laser"* (typically linewidths vary from about 10 to 500 MHz).

Linewidths of 20 to 50 MHz are typical for low power indexguided lasers. The spectrum of the frequency noise is similar (and coupled) to the spectrum of the amplitude noise. An

example of a frequency noise spectrum of a diode laser' ' is shown in Fig. 5. Unfortunately, we see that the frequency

noise is large and extends to very high frequencies. The high

frequency FM noise is a problem for two reasons: ( 1 ) it is difficult to make electronics that are fast enough to correct the frequency fluctuations and (2) even when the linewidth

is narrowed by some optical or electronic means there is usually residual high frequency phase noise that contaminates some types of measurements.

0. Tuning characteristics

A diode laser's wavelength is determined primarily by

the band gap of the semiconductor material and then by the

junction's temperature and current density.'^ The band gap

that determines the general range of the laser's wavelength is unfortunately not under the control of the laser user. The

range of wavelengths that are readily available is shown in Fig. 3, but a given commercial laser will only (and incompletely) tune over a wavelength interval of about 20 nm. Thus the user must buy a laser that is doped to operate within the tuning range of the wavelength of interest. The laser frequency tunes with temperature because

both the optical path length of the cavity and the wavelength

dependence of the gain curve depend on temperature. Unfortunately these temperature dependencies are quite different. For example, in the AlGaAs devices the optical length of the

cavity changes about -I- 0.06 nm/K, while the gain curve

shifts about + 0.25 nm/K. This results in a temperature

tuning curve which, in an ideal device, is a staircase with

sloping steps ( see Fig. 6 )

.

' ^ The slope of each step is just the tuning of that cavity mode, while the jump between steps

corresponds to hopping from one longitudinal mode to the next ( ::0.35 nm) due to the shifting of the gain curve. The

spectral "gaps" encountered in the laser tuning as it jumps

from one step to the next are the biggest drawback to using

diode lasers in atomic physics. We will discuss below some

empirical techniques that have been developed for dealing

with this behavior in an isolated laser, as well as techniques

for using external optical feedback to reduce or eliminate the problem. In practice, although the overall tuning follows the

staircase pattern described, often a laser may jump several cavity modes at once, and then perhaps jump back at a

slightly higher temperature as shown in Fig. 6. The choice of

which mode the laser will hop to next is often extremely

sensitive to optical feedback. "Room temperature" commercial diode lasers are typiRev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-10
cally rated to operate in a range of + 30 K about room

temperature. This provides a tuning range of about 2 1 nm for AlGaAs lasers. The elevated temperatures generally cause

noticeable degradation in the laser's lifetime. For example,

the data sheets indicate that a typical lifetime of about 10^ h

is reduced by a factor of 5 when the temperature is increased

by 10 K. Other performance characteristics may also be de- graded at higher temperatures. The temperature dependence of the laser characteristics varies substantially for dif- ferent models and types of lasers; however, detailed information is often provided by the manufacturer. Lasers can actually be cooled far more than 30 K ( experience shows

that at least some of the commercial lasers can be operated

down to liquid He temperatures); the lower temperatures

bring some additional complications such as the need to protect the laser from water condensation and mechanical stress due to large temperature changes. For very large temperature changes one must use the Varshni equation'^ to predict the wavelength, rather than the linear approximation given

above.

In addition to depending on the temperature, the laser wavelength also depends on the injection current. Changes

in the injection current affect both the diode temperature

and change the carrier density which also changes the index

of refraction, and these in turn affect the wavelength. For

time scales longer than about 1 jus the current tuning can

simply be thought of as a way to change the temperature

rapidly, because the carrier density contribution to the in- dex-of-refraction tuning is relatively small. The current af- fects the junction temperature because of Joule heating, and

the resulting tuning curve for wavelength versus current

looks much the same as that versus temperature. Only for times shorter than ~ 1 ^s is the temperature rise small

enough that the carrier density effect is not overwhelmed. '"* For typical AlGaAs diode lasers the variation in the lasers' frequency is ~ — 3 GHz/mA for frequencies below about 1 MHz, then it drops to ~ — 300 MHz/mA for frequencies

from 1 to 3000 MHz. It rises again to ~ - 1 GHz/mA at the frequency of the relaxation oscillation (typically ~3 GHz)

and then drops off rapidly above this frequency. The cross- over behavior between the different regions of FM response can cause considerable complication in high-speed modulation and frequency control systems for diode lasers. One of the important advantages of diode lasers over

other optical sources is that their amplitude and frequency can be modulated very easily and rapidly by changing the

injection current. Unfortunately, when the injection current

is modulated, one obtains both AM and FM, and these are not independent. The simplest useful picture of the modulation response of diode lasers is that the AM and FM are both

present but with different sensitivities. '^^ Also modulation

can be complicated by the fact that the relative phase

between the AM and the FM changes as a function of modulation frequency. To a good approximation, the AM and the FM are linear with the injection current but the FM modulation index can be more than ten times the AM index. This means that the amplitude change can be ignored in many

atomic physics applications. Thus the laser can be scanned

over spectroscopic features and/or jumped back and forth to

specific frequencies just by applying the appropriate modulation to the injection current. Applications of various modulation capabilities are discussed in Sec. V B.

E. Visible lasers

The new visible diode lasers'^ which operate near 670

nm are exciting for spectroscopic and other applications. Be- cause of the newness of these devices we have had only limit- ed experience with them. The primary problem with these

lasers is their broad spectral width. Most are gain-guided

rather than index-guided, which typically means that they

will have very poor spectral characteristics. We find that the

visible lasers usually run multimode, with limited regions of

single-mode operation. In addition, even in the regions of

single-mode operation (and with very limited data) the linewidths of unstabilized devices are 3{X) MHz or larger.

They also have a transverse mode structure that has a very

large and asymmetric divergence (7° and 40°). Without

compensation, this produces a laser beam with a linear shape

rather than a round spot. This structure could be corrected,

but it is still difficult to obtain optics designed specifically for these lasers. Finally, the output power of visible diode lasers has a very steep dependence on temperature and injection current which can lead one easily to a light intensity induced

laser failure!

III. PRACTICAL GUIDE TO USING DIODE LASERS

Having discussed the basic behavior of diode lasers, we

will now present some of the practical issues involved in set- ting up and using diode lasers for atomic physics. Although we do not discuss lasers with feedback in this section most of

the discussion applies to that case as well.

A. Purchasing diode lasers

Probably the single biggest frustration in using diode

lasers in atomic physics experiments has nothing to do with

scientific or technical issues. Instead it is the difficulty in purchasing diodes that have been doped to emit at the desired wavelength (or close enough to reach it with temperature tuning). Because of this unfortunate fact, it seems worthwhile to provide some discussion to prepare the potential user for some of the problems that must be handled.

These arise because the atomic physics market is an utterly

insignificant fraction of the total diode laser market, and

diode laser production is overwhelmingly Japanese. Therefore, unless you are fortunate enough to have some direct contact, you will probably be dealing with a distributor who

is unfamiliar with your special requirements and rather dis- tant from the supplier.

With this background we will now explain what is in- volved in getting the laser you desire. In the manufacturing

process there will normally be a target wavelength which the company is trying to produce, but there will be some scatter

in what is actually produced, and they will advertise this as the range over which lasers are available. Thus the first issue

is to get the company to screen the lasers and select the desired wavelength. Some manufacturers of lasers will do this and some will not. However, it is quite common for the local distributor for a company that does select to say that it is

Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-11
impossible to get wavelength selected lasers, or simply refuse

to handle them. Sometimes extended phone discussions with

the national headquarters and/or the distributor will solve

this problem. Once you have found a distributor willing to order selected lasers for you, there are still some additional

problems. First, if you want a wavelength that is well out on

the tail of the distribution of wavelengths produced, you

could have a substantial delay. Several years ago there were many anecdotes about 1.5-2 year waits for delivery, but our

impression is that in recent years this has happened less fre- quently, and the quoted delivery times (typically 2-3

months) have been fairly reliable. However, there is still the problem that after waiting several months for lasers, one may receive lasers that have been selected for a wavelength

that is not the requested wavelength. Based on our considerable direct and anecdotal experience concerning this phenomenon, the problem usually seems to be with the distribu- tors and their lack of familiarity with handling wavelength

selected lasers. There are two alternatives to going through the time

consuming and frustrating purchasing process just described. The first is to buy a wafer doped to your specifica- tions that will then produce a very large number of lasers. The second, and more common, approach is to find a sec- ondary supplier of diode lasers who will provide wavelength

selected lasers. There are a number of suppliers who buy

large numbers of lasers from various manufacturers and

then resell them, often with optional packages including

power supplies and/or optics. Frequently such companies

will wavelength select lasers from their stock. Of course this

is usually more expensive than obtaining them directly from

the manufacturer. Electronics distributors are also often

willing to select lasers from their stock. In concluding this discussion we strongly recommend

that if you are starting an experiment with diode lasers, buy

several lasers at once. Because of the difficulties and delays

in purchasing lasers, combined with the possibility that some

lasers may never reach the desired transition and others may

die abruptly, it is highly advisable to keep a number of spares on hand. Since the typical cost of AlGaAs lasers is $100-

$300, this is a worthwhile investment. However, with the

special high power and long wavelength lasers that are more

expensive, it may not be feasible to afford this luxury.

B. Mounting of diodes and related optical elements

Once the laser has arrived, it must be set up for use. Two

important initial considerations about mounting the laser, regardless of application, are optical feedback and temperature control. One needs to consider the best arrangement to minimize unwanted optical feedback and, if desired, provide

controlled optical feedback for frequency control. This

usually determines the overall physical layout. The details of

the mounting are then determined by considerations of how

to keep the temperature of the laser as stable as possible. This

is discussed below. Normally, the optimum design in terms

of temperature and mechanical stability, as with any laser system, is one that is as compact as possible and reasonably

rigid. However, because diode lasers and associated optics can be much smaller and lighter than other types of lasers.

Insulated

foil heater

Laser

Thermistor

Delrin standoffs

Metal

Plate

)///////// 7T77r

^y///////// /////y

FIG. 7. A simple mount for a diode laser. The heater and thermistor are for

stabilizing the temperature. The threaded mount for the collimating lens makes focusing simple.

the scale of the assembly is often quite different. In Fig. 7 we show a simple laser mount. The laser itself comes attached to a small heat sink. This is mounted with

good thermal contact to a small metal plate to which a heater

(or thermoelectric cooler) and sensing thermistor are bonded. This plate is then attached to a solid block through a connection that is mechanically rigid, but a poor thermal

conductor. The collimating lens is then mounted directly onto this block. A vast variety of types (and prices) of lens are available. Making a rather sweeping generalization, larg- er lenses that will be mounted farther away from the laser tend to cause less feedback, but it is more difficult to keep the feedback constant than with a small lens close to the laser. The transverse lens position is relatively unimportant; one

can simply translate it to the correct position by hand and

then tighten down the mounting screw. However, the focus- ing (longitudinal) adjustment is much more critical, so it is desirable to have some sort of fine screw adjustment on it. A specific warning to the beginning diode laser user about microscope objectives for collimating lenses: Standard

objectives may seem to be a desireable choice because they

are so readily available, but they are usually quite lossy for infrared wavelengths, and the optical feedback problems are

often quite severe. A superior, low cost alternative is one of

the many plastic aspheric lenses made specifically for diode

lasers. Another choice when beam quality is not important is the use of inexpensive gradient index (GRIN) lenses.

C. Temperature and current control

As a general rule, the day-to-day repeatability of the

laser system performance is determined primarily by the temperature stability. The most direct factor is the temperature dependence of the laser output frequency. However, we

have found that the benefits of good temperature stability

extend beyond the diode itself. If there is any external feed- back, the laser frequency is always somewhat sensitive to the

positions of the optical elements and these change with temperature. One almost unavoidable example is back scattering

Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-12
from the collimating lens that feeds back to the laser. If this is not too large and is fairly constant in phase, often it is not even noticeable. However, if variations in the temperature of

the apparatus start causing the distance and hence the phase

of the feedback light to vary, it can cause quite unwelcome

and, at the time, highly mysterious variations in the laser wavelength or linewidth. Thus, poor temperature control can affect the laser performance in a variety of ways. Although it is adequate for some purposes to use only a single

stage of temperature control on the laser, we have found that

in the long run it is usually worth the small extra effort to add

a second stage of temperature control on the base of the mount or on the box enclosing the laser assembly.

A detailed discussion of temperature control servoloops

has been given by Williams'^ and we will not dwell on them

here. The basic idea is to use a thermistor as one leg in a balanced bridge circuit, and any voltage across the bridge is amplified and used to drive a heater or cooler. As discussed

in Ref 17, one must carefully consider the thermal time delays and the time constants in the electronics to achieve optimum performance. However, we have found that if effort is made to reduce the thermal mass and the thermal delays by

mounting the sensing thermistor and the laser in close proximity to the heater, a relatively simple circuit will achieve

stabilities on the order of 1 mK. A circuit diagram for such a simple controller is shown in Fig. 8. To achieve this kind of

performance, the reference voltage and the bridge resistors must have low temperature coefficients. In addition because

of thermal radiation and air currents, it is advisable to enclose the laser mount in some sort of metal container. This

has the added benefits of keeping dust out of the system and

isolating the laser system from acoustic vibrations. The last important element in setting up a diode laser is the current control circuit. It is difficult to recommend a

generally useful circuit because the requirements of various

experiments can be so different. In every case one needs to

start with a low-noise current source and some protection

against unwanted transients that can destroy the laser. Such

a setup can range from a battery and a potentiometer plus a few diodes and capacitors, to quite elaborate circuits. Often

the primary consideration in selecting a circuit is its current modulation capabilities. In Fig. 9 we show two sample cir- cuits. See also Bradley and co-workers.'^ As discussed in Sec. Ill G, it is important to mount the protective diode right on the laser mount.

D. Tuning to an atomic transition

The main difficulty in using diode lasers in most atomic

physics experiments is the problem of tuning them to the desired wavelength, usually that of some atomic transition. We have developed some empirical procedures for addressing this problem. To find a transition we set the laser current

at the value we would like to operate, and then tune the temperature of the laser to near the correct value by observing the laser's wavelength on a spectrometer. (A note of

warning—if one follows the usual procedure of sending a collimated beam into the spectrometer, which no doubt has

metal slits, the backscattered light from the slits will often cause the laser wavelength to shift and make the measure-

"^r LM399

V^ iV|^|<30V

0K| tr^

?20

lOT^ ^>-^ "''^ •/ 910

FIG. 8. This simple temperature controller uses a variable combination of proportional and integral feedback and can work as a diode laser controller. The

circuit acts to match the resistance of the thermistor with the value of the reference resistor in the bridge. The controller only requires two IC chips { 2 - Quad

op amps) and a few readily available components. The load R, can be either resistive or a Peltier element for heating or cooling. R 1 and C 1 determine the integration time constant and are chosen for a given application based on the appropriate system response time. The current is limited to a maximum of 2,4 y/R.. The LEDs and associated circuitry are optional but useful to indicate whether the temperature is above or below the set point. (This circuit adapted from that of J. Magyar, NIST, Boulder.)

Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-13
ment meaningless. ) Once the laser is near the correct temperature, the current is then rapidly ramped back and forth over a large range, while the mount temperature is adjusted

by small increments. The fluorescence or absorption from an

atomic absorption cell is used to determine when the desired

transition wavelength is reached. Because of the tuning gaps, there may be no combination of current and temperature

that produces the desired wavelength. However, there may

also be several and one must choose which is most desirable.

If maximum laser power is needed, a temperature should be

chosen where the laser is on the transition at a high current. On the other hand, if only a small amount of power is needed

it is better to pick a low current point so that the diode life- time will be maximized (although the linewidth and amplitude noise will be somewhat larger). We repeat our previous

warning: Never buy a single laser and expect to do an experi1.SK 2K

-15 <J V^ifA • ^vvv

5K 10 Turn

LN399

LASER DIODE CURRENT CONTROLER

OP - 5

301mt S.74Kmf —WW

33K

Current

Control

=|V|mf

Voltag*

Increases Current

500

• Use .lut Bypass Caps

on All Opamp.

IN914

500

+ 15 I"

IN4001 —+«—

his Volts

LM317

J.I.,

7805

IN4001

240n ''^ T-^'*' J

2k 10 Turn

n., Ad|. 500

2N2219

33Hf + _ Tant -r

T.33

V Mono

-TT,

-> +5 Voltl _, . _-^lMt For Digital

I 1(i( I I Panal Meter

Slow

Start Up

€) 2N2219

S.IIKmt OP27

25 n. at Least 1/2W. \\w

10K

-v^fv/' 9 ( m ] Mon Out.

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_:75K

10 Turn , _ . IK .1 Scale i \>. Control

20K

10 Turn

Offset Control

<7 f««« , ff Modu100 ^ 5000pf ^-^^|atlon ln| Input

' Current Will Change Slightly when Imput Sees a Low

Impedance.

•2.3K

> To Input of

Digital Panal

Meter

75

FIG. 9. Two examples of diode laser current sources. ( a ) A simple diode laser current source that is adapted with permission from the Sharp Corp. ( Ref. 4 )

.

This circuit has automatic feedback control from a photodiode to maintain constant laser output power. ( b ) A low-noise diode laser current source that has

high speed modulation capabilities. (This circuit with permission from S. Swartz and J. L. Hall.)

Rev. Scj. Instrum., Vol. 62, No. 1, January 1991 Diode lasers TN-14
ment with it. There is always a significant probabihty that a

given laser will have a tuning gap just at the output wavelength of interest. We have found that, if no external feed- back is used, this probability varies between about 30% and

60% for different batches of lasers operating near 852 nm. As discussed below, additional optical feedback to tune

the laser can almost always force it to oscillate at the desired

wavelengths, but of course this results in a more complicated

device and procedure.

E. Avoiding unwanted optical feedback

We have mentioned several times that the laser perfor- mance is affected by optical feedback. One of the unique

features of diode lasers relative to most other lasers is their astonishing sensitivity to such feedback. This can be both a

blessing and a curse. In Sec. IV we will discuss the blessing

aspect; here we will consider the curse. As discussed in several references,'** the sensitivity of

diode lasers to optical feedback arises from a combination of

factors. First, the gain curve is very flat as a function of

wavelength; second, the cavity finesse is quite low; and third, the cavity is very short. As a result, the overall gain of the system has an extremely weak dependence on wavelength

and there are relatively few photons in the cavity, so that the

lasing frequency is very easily perturbed. In addition, when

light is returned to the laser it acts as a photodetector, generating more carriers in the junction and affecting the net laser gain. Detailed quantitative discussions are given in the refer- ences, but it is probably more useful here to give some general rules for laboratory work using a free-running laser with

uncoated output facets. We have already mentioned the problem with scattering from spectrometer slits. In general, we can say that if the laser beam is collimated and hits a surface which scatters strongly, such as burnished metal or a white lab wall, there will be a significant effect on the laser wavelength (frequency shifts on the order of 10 MHz or

greater, and easily observable variations in the laser amplitude as the distance changes), but if the surface has a dull black appearance there will probably be little effect. If the beam is going through a focus a larger fraction of the scat- tered light will be focused back into the laser thus increasing

feedback sensitivity. We have found that, as a general rule, one cannot put anything, even good optical glass, at a focus

without causing a large perturbation on the laser. These

rules must be considered only as very crude guides since there are significant differences in sensitivity among the var- ious types of lasers. How much feedback can be tolerated generally depends on how the laser is being used and the

stability of the feedback. If the amplitude and phase of the feedback are constant, it can often be ignored unless one

needs to scan the laser's wavelength. Lasers with an output

facet coated for reduced reflectance are more sensitive to optical feedback than uncoated lasers. On the other hand,

lasers set up to have strong optical feedback to control the wavelength are correspondingly less sensitive to stray feed- back.When using a laser in an experiment where simple positioning of the optical elements does not avoid feedback, one

9 Rev. Sci. Instrum., Vol. 62, No. 1 , January 1 991

must use some form of optical isolator. The simplest and

least expensive isolator is an attenuator in the beam, but this of course is useful only when one can afford to waste most of

the laser power. An alternative is a circular polarizer that does not waste light, but only works if the incident and feed- back light have the same polarization. This is still fairly inex- pensive. When the polarization of the return light is different from the incident light, which happens if there are any bire- fringent elements in the beam, it is necessary to use a Fara- day isolator.^ Unfortunately these usually cost several times

as much as the laser itself.

F. Aging beliavior

A key consideration for any experimenter is the reliability of the laser. With diode lasers this has two different aspects. The first is euphemistically referred to as cata- strophic failure, which usually means the experimenter did

something to destroy the laser. The second is a gradual

change in the behavior of the laser, referred to as "aging."

Normally one must gain considerable experience with diode

lasers before aging becomes relevant compared to cata- strophic failure. We will discuss aging first. Although we

have not done careful statistical studies of aging behavior we

can provide some observations based on our experiences

with on the order of 100 lasers. First, while operation at high

temperatures and/or high currents can contribute to aging, the original manufacturing process seems to be the dominant

factor. We have had some lasers that we used extensively for two or three years before they showed any aging while others

changed markedly in just a few weeks. Usually all the lasers

in a given manufacturing run will age in a similar fashion. There are a variety of ways that the characteristics will change with age. One that is hardly noticeable because it is usually slow is that the tuning steps will gradually move.

This means that one will occasionally have to adjust the current and/or temperature to keep the laser on the atomic reso- nance. This becomes serious if eventually the shift causes one

to lose the transition entirely, but the opposite can also happen: namely, a laser which formerly could not be tuned to the resonance may age until it can. Aging drift rates can be as large as + 30 MHz/h and may be due in part to increases in the thermal conductivity of the laser to the heat sink''*'''' and changes in the laser due to nonradiative recombination.

There are two other symptoms of aging that are more immediately detrimental. The first of these is an increasing ten- dency for the laser to emit in more than one longitudinal

mode, which often means that higher and higher currents must be used to obtain single mode output. The second characteristic is that the spectral width of the single mode output can gradually increase from its initial 20-30 MHz up to several hundred megahertz.

G. Catastrophic failure modes, or 1001 ways to kill a

laser

In a lab where diode lasers are applied to a variety of

problems and there is a constant flux of students and guest

workers, it is a highly unusual laser that can age gracefully

and die of the "natural causes" listed above. It is far more common for the lasers to be abruptly destroyed. We have

Diode lasers 9

TN-15
discovered many ways this can be accomplished, and we Hst these here in the hope it may save others from repeating our

experiences. A major weakness of diode lasers is that a very

brief transient, which causes too much current to flow or produces too large a back voltage across the junction, can be

fatal. A common way this can happen is switching transients when turning the laser on or off. Although one obviously

must put in protective circuitry to deal with transients when

the laser power supply is switched on and off intentionally, it

is also necessary to be concerned with the potential effects of

accidental disconnection of the power supply, or intermittent connections in power cables or the ac power line. Other

sources of transients are discharges of static electricity and

high voltage arcs in other parts of the lab. These last two are minimized by good grounding and shielding procedures.

Also the protection diode normally used to prevent excessive

back voltage should be as close to the laser as possible. If there is even a fraction of a meter of moderately shielded

cable between the laser and the protective diode, a high vol- tage spark nearby will often destroy the laser. We should

point out that a laser which has been electrocuted will often continue to emit laser Hght, but the wavelength, threshold,

and output spectrum will be quite different. Although electrocution is by far the most common form

of death for diode lasers, the lasers that are not mounted in a

protective can are also quite delicate and one must be careful not to touch the laser itself, or the tiny current leads, while

mounting the laser or associated optics.

Considering all of the possible failure modes for the di- ode lasers, we find that, on the average, the lasers need to be

replaced approximately every six months. This average in- cludes lasers dying for whatever reason or becoming impossible to tune to the appropriate wavelength. Presumably the replacement rate would be much less if the lasers were left alone and not always being tampered with in evolving ex- periments. This average rate is for moderately experienced

users and failure is much more frequent with inexperienced

users.

IV. TECHNIQUES FOR CONTROLLING AND

NARROWING LASER OUTPUT SPECTRA

Several techniques, both optical and electronic, have

been devised to narrow the linewidth and control the center frequency of diode lasers. As mentioned earlier, the effects of

optical feedback on semiconductor diode lasers are both pro- found and complicated, but they have been studied in detail."* In particular, the effects of optical feedback on the

spectral properties of these lasers can be found in Ref. 20. However, the essence of the optical feedback methods is the simple idea that by increasing the quality factor (Q) of the

laser's resonator, the linewidth will be reduced. The simplest

implementation of the optical method for spectral narrowing is just to reflect back to the laser a small fraction of its output power. The basic electronic method uses feedback to the laser's injection current to control the laser's frequency.

Both the simple optical and simple electronic methods have

severe limitations in terms of general applicability.

More elaborate frequency control systems are usually necessary to deal with the variety of diode lasers that are

commercially available. No one method has been found to narrow the linewidth and control the frequency of all types

of diode lasers. Here we will briefly review some of the more

successful methods.

We should mention that there are many errors that one

will find in the literature relative to measurements of diode

laser linewidths and frequency stability. The most common

mistake is that the experimenters will measure the residual noise on an error signal inside a servo loop and use this infor- mation to infer a frequency stability. Such measurements do

not guarantee that the error signal actually represents laser frequency fluctuations, and they are fraught with systematic

errors. Picque and co-workers'^' and Pevtschin and Ezekiel"^ have made more realistic measurements and pointed out some of the possible pitfalls.

A. Simple feedback

Some limited success in narrowing the linewidth of a diode laser has been achieved by using simple optical ele- ments to feed back to the laser some of its output power.

Among the optical elements that have been used for feed- back are simple mirrors,'^ etalons,^* gratings,^' fiber cavities,^^ and phase conjugate mirrors.^^ The resulting sys- tems must be described as lasers with complex resonators where the diodes' facets and the external optical elements all play a role in creating the net resonator structure as seen by

the semiconductor gain medium. By providing optical feed- back from a small mirror or glass plate placed close to one of

the laser facets, sometimes one can force a multimode laser to oscillate on a single mode, or induce a single-mode laser to tune across the forbidden "gaps."^** The limitations to this method are that it does not work with all lasers, and still requires some sort of frequency reference to stabilize the la- ser's frequency. Also, as with any complex resonator, it can

be difficult to achieve long-term stable performance with

such systems.

B. External cavity lasers

The method of the "external cavity laser" uses antireflection (AR) coatings on the diode laser chip, and some

external optics to provide the laser resonator. The external

optics may contain frequency selective elements such as a

grating^"^ and/or etalons,'° with the grating being the least expensive and most common. A variety of geometries are

possible and one example of an external cavity laser is shown

in Fig. 10. For the nonspecialist these systems can be a chal- lenge because they require having the laser diode facets AR

coated, which is usually an expensive and nontrivial procedure. In addition one may need access to both output facets, which is often difficult given the packaging of commercial

devices. In principle, this method should work with all types

of diode lasers, although only a limited number of systems

have been built, and they are not commercially available. A number of variations on the basic external cavity idea have been demonstrated. These include the use of prisms,

birefringent filters, and various other clever optical schemes

(of particular interest is the paper by Belenov et al.^^ ). An

example is putting AR coatings on one facet of the laser chip

and building pseudo-external cavity lasers as discussed in

10 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 10 TN-16
ANTIREFLECTION

COATED

DIODE LASER

OUTPUT

GRATING OUTPUT

MIRROR

ANTIREFLECTION

COATED

LENSES

FIG. 10. External-cavity diode laser. This schematic shows an AR coated diode laser chip used in an external cavity with a grating for wavelength

selectivity. ( Figure from Fleming and Mooradian, Ref 29, reproduced with

permission.

)

the next section. This technique has been useful in control- Hng the spectral properties of 670-nm diode lasers."

C. Pseudo-external cavity lasers

Various laboratories have shown that if only one of the

facets of a diode laser is AR coated, the laser's linewidth can

be narrowed and its oscillation frequency controlled by pro- viding external frequency selective optical feedback. Fortunately, many of the high power ( > 15 mW) commercial la- sers already have reduced reflectance coatings on the output

facet and high reflectors on the back facet. Gibble and

Swann and collaborators have demonstrated that without

modification these commercial lasers with coatings can be

spectrally narrowed and tuned effectively with grating feedback.'*'' An example of such a system is shown in Fig. 11. This method is a combination of the two listed above in that

it is not really an external cavity laser, since the laser oscil- lates without the extra feedback, but the system can operate

so that external feedback dominates that from the low reflec- tance facet. These devices have fundamental linewidths on

the order of 100 kHz or less, but the true linewidth is usually

dominated by the mechanical and thermal instabilities in the length of the grating-laser cavity. This linewidth can be several hundred kilohertz or larger if the cavity length is not

electronically stabilized. We and others have found such la- sers to be quite well suited for a variety of applications. Their

virtues are that they use standard commercial lasers and in- expensive components, and the grating allows tuning over a range larger than could be easily covered by temperature

tuning. Also the tuning can be continuous over much larger

spectral ranges, and it is quite easy to set and keep the laser frequency on particular atomic transitions. Minor difficulties in the design are that the grating alignment is moderately

sensitive, and to achieve the necessary degree of collimation

of the laser light, the distance between the laser and the colli- mating lens must be adjusted to within a few micrometers or

less. In practice it is adequate to have the lens position ad- justed with a fine-pitch screw, with the position set so that the beam appears the same diameter to the eye over a path of

several meters. There are tradeoff's one can make in the detailed design

between greater feedback, and hence more frequency conDiode

Piezo

FIG. 1 1. A pseudo-external cavity laser using a standard commercial laser and a diffraction grating for feedback. The flex pivot is used to obtain the

precise focusing of the collimating lens which is necessary. The peizoelectric transducer under the grating is used for fine frequency tuning by changing

the length of the cavity. Other tuning options are to have the piezo-electric transducer on the other side of the mount so that it rotates as well as translates the grating, or to do the tuning using an uncoated piece of glass which

is mounted on a galvanometer near Brewster's angle and is precisely rotated. Not shown is the temperature control elements (sensors and heaters or

coolers) that must be used on the diode and may be used on the baseplate.

trol, versus coupling out more power. The exact perfor- mance will depend strongly on the reflectance of the output

facet of the laser. For illustrative purposes, we will describe

the behavior of such a laser system using a Sharp LTD 15

laser (mention of this product does not represent a recom- mendation and we expect other lasers to behave similarly),

with ~70% feedback to the laser. As the grating is rotated, the laser will tune continuously over a region of about 80

GHz spanning the peak of the semiconductor laser cavity resonance. To obtain continuous tuning, the grating is mounted so that, as it rotates, the change in the cavity reso- nant frequency due to the change in the cavity length

matches the angle tuning of the grating.'*'* A small (2 cm)

piezoelectric speaker disk placed between the grating tilt screw and the block on which the grating is mounted is a convenient and inexpensive way to rotate the grating

smoothly. There will then be a gap in the tuning of 70-80

GHz until one reaches the next mode of the small semiconductor cavity. This pattern repeats itself as the laser is tuned

farther from its gain peak, with the range of continuous tuning gradually decreasing. The maximum range the laser wavelength can be pulled from its gain peak is about + 10 nm, at which point the tuning range per diode mode is about

10 GHz. With the feedback reduced to 25% to increase the output coupling, the maximum range ofcontinuous tuning is about + 6 GHz, and the farthest the frequency can be pulled

is about 6 nm. Gaps in the tuning are easily filled by adjusting the laser current or temperature to shift the frequency of

the laser diode modes. The output power is about 10 mW

with this output coupling.

11 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 11 TN-17
ModD.C.

Diode

Laser V

Isolator

. PZTC

Optical Locking

V

I Aperture

:j: •> Det. 1

Monitor

Cavity

Det.

FIG. 12. Schematic diagram of an optical feedback locking system for laser diodes. In the geometry shown optical feedback (type II) occurs when the

lasers frequency matches the resonance frequency of the optical locking

cavity. This type of feedback locks the laser's frequency to the cavity reso- nance frequency and narrows the laser's linewidth. The monitor cavity is used as a diagnostic and does not affect the laser's frequency because of the

optical isolator. (Figure from Ref. 59, reproduced with permission.)

D. Feedback from high-C7 optical cavities

Another optical feedback locking system that we have

used quite successfully is diagrammed in Fig. 12. In this sys- tem we use weak optical coupling of the laser's output to a high-^ optical resonator.'^ The geometry is such that the

laser sees optical feedback from the Fabry-Perot cavity only

when the laser's frequency matches a resonance of this cavity. The result is that the coupled (laser plus cavity) system

has lower losses at a cavity resonance and the laser's frequen- cy automatically locks up to the cavity resonance. In this way the laser's linewidth can be reduced to a few kilohertz

and the laser's center frequency is stabilized to the cavity.

One of the limitations of this system is that it requires some

additional slow electronics to keep the laser locked to the same cavity mode for long times and to keep the laser syn- chronized with the cavity for long scans (greater than about

1 GHz). Without the additional electronics, the laser will stay locked to the same cavity mode for times that vary from

less than 1 to as much as 30 min, depending on the stability of

the cavity and the temperature and current controls for the

laser. By reducing the distance between laser and cavity to a few centimeters and mounting the cavity and laser in a pres- sure-tight temperature-controlled enclosure, we have been

able to extend this to several hours without electronic control. We and others use this system with good results with

unmodified commercial lasers operating in the diode laser wavelength bands at 780, 850, and 1300 nm. With rather

limited experience, we have been disappointed in the results of this method for unaltered gain-guided lasers operating at 670 nm. However, the method appears to work with the new

index-guided versions that have some AR coating.^* The

major advantages of this system of frequency control are that the linewidth is very narrow and the stability is determined

by the external cavity, which can be made very rigid and

insensitive to changes in temperature and atmospheric pressure. Also, the laser retains some high speed modulation capabilities. The disadvantages are the sensitivity to cavity la- ser separation mentioned above, and the fact that laser tuning range ( and gaps ) is still essentially the same as that of

the basic unstabilized laser. There are a number of optical configurations that can produce resonant optical feedback from a high Q resonator,

but in practice the V configuration shown in Fig. 12 is a very convenient one. The alignment procedure is straightforward

and after a little practice can be done fairly quickly when one

recognizes the proper signal shapes. During the alignment

and afterwards it is best to sweep the laser's frequency over

several orders of the Fabry-Perot and to monitor the power

transmitted through the cavity. The effects of feedback from

the cavity to the laser will be obvious in the shape of the transmitted fringe. By sweeping many cavity modes the ef- fects of the feedback can be observed. The system requires

only a small amount of the laser's output power ( ~ 1 % ) for locking but for alignment it is easier to start with higher

powers ( ~ 1 0% ) so that it is easy to see the beams. After one becomes familiar with aligning the optical feedback lock, the feedback power can be reduced. This 10% of the output is split off and sent through an attenuator and a lens that ap- proximately mode-matches the beam into the high-^ FabryPerot cavity. An easy way to determine that the mode

matching is correct is to ensure that the return beam reflect- ed from the Fabry-Perot cavity is about the same size as the beam that is incident on the cavity. Next, one looks to see

that the input beam is centered on the Fabry-Perot's input

mirror and that the reflected beam is at a small angle relative to the input beam. The divergence angle can be quite small

but it is necessary that the return beam is a few spot diameters away from the input beam by the time it returns to the

laser. One should also observe that there are two output

beams transmitted through the cavity on resonance (see Fig.

12). By setting the attenuator for very low powers one will see the usual Fabry-Perot peak structure in the transmitted

light; then as the feedback is increased the laser will begin to lock to the cavity resonance and the Fabry-Perot shape will broaden and become squarish. The fringe will typically

broaden to a few hundred megahertz, corresponding to the range over which the cavity controls the laser's frequency.

The feedback power can be increased to enhance the locking range and to reduce further the laser's linewidth. When the feedback becomes too strong the system will become unsta- ble."The phase of optical feedback (distance from the laser to the cavity) is optimum when the power transmitted

through the cavity is maximum. One can force the lock to the optimum condition by modulating the path length from the

laser to the cavity (with a PZT) and detecting the transmitted power. This signal is then demodulated with a lock-in amplifier and fed back electronically to control the position

of the PZT. Variations in the optical feedback phase can be

minimized by good mechanical stability and by making the distance from the laser to the cavity small. In fact we often operate these optically locked systems without active elec- tronic control. Although commercial cavities are often adequate it is useful to be able to make simple inexpensive tunable Fabry12 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 12 TN-18
Perot cavities. The simplest method is to glue laser quality

mirrors onto a cylindrical Invar or quartz tube, with a PZT

disk under one of the mirrors so that the cavity can be

scanned. If one of the mirrors can slide inside a tubular

mount, the cavity can be aligned and set to the confocal condition by aligning it with a laser before the last mirror is glued in place. For the best stability it is useful to have a

hermetically sealed cavity. In these simple cavities this can

be accomplished with a glue that does not unnecessarily

stress the mirrors ( such as Tracon 2 1 43D epoxy, mention of

this product does not represent a recommendation). An al- ternative design uses a fine thread on the Invar spacer to set the cavity to the proper length. For most of our diode laser spectroscopy we use reference cavities with finesses of about

100 and free-spectral ranges of 0.25-8 GHz.

E. Other optical feedback techniques

Other monolithic or semimonolithic extended cavity di- ode lasers with good spectral qualities have been reported in the literature, *** but they are usually laboratory test devices

that are not commercially available and usually not tunable. There are indications that some of these systems will become

commercially available in the near future, but it is not likely there will be broad spectral coverage anytime soon.

F. Electronic feedback

The other competing method for laser frequency stabili- zation is electronic feedback. It is straightforward to use

electronic feedback to lock the center frequency of diode

lasers to cavities or atomic absorption lines using standard

laser stabilization methods. ^'^ On the other hand, narrowing

the laser's linewidth with electronic servos is a much more

difficult task. The problem is that the frequency noise spec- trum extends to such high frequencies that most servosys- tems are not able to act fast enough to correct the laser's frequency fluctuations. A few groups*"'"*^ have been successful in developing very fast (few ns delay time) electronic servosystems that can be used to narrow the linewidth of

diode lasers if the laser's intrinsic linewidth is not too broad

to start with. Linewidths on the order of 100 kHz have been

achieved with these techniques. Electronic systems have the advantage over most of the optical methods in that they do

not degrade the modulation characteristics of the lasers. However, a disadvantage is that they do not extend the la- ser's tuning range. Unfortunately, considerable expertise in electronics is required to design and build the necessary cir- cuits.

G. Hybrid systems

Hybrid designs are of two basic types. In the first case, electronic feedback is simply used to tune a cavity that controls the laser frequency by optical feedback. In the designs

described in Sees. IV B, IV C, and IV D, for example, this would entail moving the end mirror or graving using a pie- zoelectric transducer. Typically this is done to achieve long- term frequency stability by locking the cavity frequency

( and thereby the laser ) to an atomic or molecular transition. Promising results have also been obtained with a second

type of hybrid system which uses electronic feedback in addition to optical feedback to reduce the laser's linewidth."*^ In this hybrid optical-electronic system the optical feedback

is used to initially narrow the laser to the point that less sophisticated electronics (than that mentioned in Sec. IV F)

can further narrow the linewidth and stabilize the laser's frequency. With such systems it should be possible to achieve frequency stabilities that are limited only by one's

ability to provide an adequate frequency discriminator. Using this type of servosystem, phase locks between diode la- sers have been demonstrated."^

H. Injection locking

It is also possible to stabilize the frequency of diode la- sers by optical injection locking.'*'* The frequency of an unstabilized diode laser can be locked to a spectrally narrow, master laser oscillator by coupling a small amount of power

from the master laser into the slave diode laser. This tech- nique may be useful for some applications (e.g., generating

higher power) but obviously does not meet many spectroscopic needs, because if a good master laser were available the diode laser would not be needed. The notable exception is that injection locking allows one to use the high powers

available from arrays or wide channel lasers and still maintain the precise frequency control which can be obtained

with a feedback-stabilized diode.**^

I. Summary

For some spectroscopic applications the spectral characteristics of commercial diode lasers are good enough as they stand, but for many others that is not the case. Also,

unstabihzed lasers can be quite difficult to tune in a controlled manner. Unfortunately, none of the existing frequen- cy stabilization methods (perhaps with the exception of the

external cavity system ) are able to narrow the linewidth and

control the frequency of all of the types of semiconductor

lasers that are potentially useful for atomic physics. We do

not mean to discourage the potential user of high resolution

lasers, because at many wavelengths the existing solutions

work very well and provide tunable narrow linewidth lasers from commercially available diodes. Such devices have the advantages of very narrow linewidths and excellent amplitude stability, and they are much simpler and more reliable to tune to a particular frequency than are unstabihzed lasers.

V. APPLICATIONS

Having discussed how to build and use diode lasers, we

will now discuss some of their applications in atomic physics. Ofthe numerous possibilities, we have chosen to describe

a few novel applications that demonstrate some of the new

capabilities of diode lasers that have not previously been appreciated. Many of the examples are related to our own

work. We do not wish to imply that this is the only work in

this field; rather these are simply a number of representative

samples that are most familiar to us.

A. Optical pumping

One of the earliest applications of a diode laser to atomic

physics was as the light source for optical pumping and prob13 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 13 TN-19
ing of a polarized medium. Many applications of this type

are reviewed by Camparo. ' Here we want to mention briefly some interesting new optical-pumping applications using

traditional laser approaches.

Diode lasers have been used extensively in frequency

standards and atomic clocks. In these applications they optically pump the atoms of interest, and then detect the atoms

that have undergone the microwave frequency clock transitions. Fortuitously, the atoms used in some of our best fre- quency standards (rubidium and cesium) have resonanceline wavelengths that are easily produced by semiconductor

lasers. The work in this area started in earnest in the midTO's**" and continues with promising results today. ''^** Significant research and development efforts to incorporate di- ode lasers into rubidium, cesium, and other atomic

frequency standards are under way around the world. These

eflForts are driven by vast improvements in signal-to-noise

ratios, ultimate accuracy, and the relative simplicity obtained by using diode lasers. Figure 13 is a schematic dia- gram of a diode-laser-pumped cesium atomic clock. The la- sers are first used to prepare the atomic beam by putting all the atoms into the appropriate hyperfine level using optical

pumping. Then, after the atoms have passed through the microwave region, a laser excites the initially depleted level. Thus the microwave transitions are detected by the increase

in the downstream fluorescence. In an optical-pumping experiment of a different sort, Streater, Mooibroek, and Woerdman'*'^ used the light from a diode laser to drive very successfully a rubidium "optical

piston." The optical piston is an atomically selective drift that is driven by laser light. We list this under optical pumping because a key element in the experiment was the novel

scheme of using the relaxation oscillation sidebands of the diode laser to assist in optical pumping of Rb atoms. In this particular case the 3-GHz ground state hyperfine splitting of

''^Rb matches the relaxation oscillation frequency of the 780-

nm lasers. Thus a single laser allowed them to excite atoms in both hyperfine ground states, which greatly enhanced the operation of the "piston."

B. Applications using fast frequency modulation

One of the unique aspects of semiconductor diode lasers

is the ease with which their amplitude and frequency can be

modulated. The amount of modulation can be both large and

very fast. For common diode lasers the modulation response extends out to a few gigahertz, with a few special lasers capable of modulation rates of more than 10 GHz. This modulation capability has applications in spectroscopy as well as other fields. As mentioned earlier, modulation of the diode

laser's injection current produces both AM and FM, but in many cases of atomic transitions the frequency modulation

is the dominant effect and we will focus attention on it here. The frequency modulation is dominant simply because the atomic linewidth corresponds to such a small fractional change in frequency.

We can picture the frequency modulation of the laser either in the time domain or in the frequency domain, de- pending on the particular application. If we first think in the frequency domain, modulation of the injection current at high frequency produces a laser spectrum with modulation

sidebands. The application of modulation sidebands to all types of lasers has proven very useful for spectroscopy and

other applications.'" The principal advantage of these optical heterodyne methods is that they increase the signal-tonoise ratio in detecting absorption and dispersion signals.

These techniques have been extended to diode lasers by

Bjorklund," Lenth," and others." The diode laser case is complicated somewhat by the additional AM that accompanies the desired FM. Lenth in particular has sorted out the

effects of having both AM and FM modulation simultaneously."

We have used optical heterodyne methods with frequen- cy modulated diode lasers to detect alkali atoms and optical

cavity resonances with high sensitivity. External frequency

modulators have been also used with InGaAsP lasers to detect NH, using FM spectroscopy.''* Ohtsu" and collaborators have achieved excellent results with optically pumped

Rb clocks by using frequency-modulated laser diodes for

Microwave

Electronic ( F— 4 State F=3

I

I Cs - Oven I

I

I

rF=4 (

C avit y

F =3

Photodetector

C- Field

T //^* Fluorescent Light

>C

"i 1 Laser 2

Laser 1

14 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991

Cs-Beam

Laser 3

Diode lasers

FIG. 13. Diagram of an optically pumped cesium atomic frequency stan- dard. The cesium atomic beam travels in a vacuum through the first laser interaction region where the atoms are optically pumped, it then traverses the microwave

cavity region and then on to the second

laser interaction region where the atoms

are detected. The population in the ground state hyperfine levels is indicated along the path by the Fand w, values. The microwave clock transition is between the f=4, m,=0, and the F= i,m, =0 states. As shown here the system uses two lasers with different fre- quencies for optical pumping and a third

laser for detection. ( Figure from Ref. 2, reproduced with [jermission.

)

14 TN-20
Optical Spectrum, 367 MHz Modulation

FIG. 14. Modulation response of an optically locked diode laser. The spec- trum shown here is taken with the detector ( Det. ) and monitor cavity sys- tem shown in Fig. 1 2. The laser's injection current is modulated at 367 MHz

through the modulation port (Mod.). The modulation frequency is rationally related (

,' times) to the free spectral range of the locking cavity. In this case the optical lock is stable and provides an array of narrow linewidth

laser side bands each spaced by the modulation frequency. Lasers without

optical locking have similar modulation response but with broad

linewidths. (Figure from Ref 57, reproduced with permission.)

optical pumping and high sensitivity detection. Other apphcations of frequency-modulated diode lasers include communication systems, length measurements, range finding,

and laser radar. A great deal of spectroscopic work with diode lasers and

frequency modulation has been done with the lead salt diode

lasers operating in the infrared. Methods have been devel- oped using modulation at two frequencies ("two-tone"

modulation) to detect molecular species with high sensitivity.'*' The techniques employed with these lasers are also generally applicable to the GaAs lasers. If we increase the strength of the modulation of the in- jection current, it is possible to spread out the diode laser's spectrum into many discrete sidebands. These sidebands can

cover spectral windows of many gigahertz. Figure 14 shows

a spectrum of a diode laser whose injection current (97 mA

dc) is modulated at 367 MHz with an amplitude of 4 mA.

This modulation produces eight discrete sidebands spaced

by the modulation frequency, in addition to the original carrier, and does not otherwise broaden the spectrally narrow

laser (~10-kHz linewidth). Potential applications of this high modulation index case include laser frequency control,

fixed local oscillators for coherent communication systems,

and atomic and molecular physics experiments where nu- merous frequencies are required.

Some applications of diode laser frequency modulation

are best viewed in the time domain. For example, rapid

chirping or jumping of the output frequency has been used

successfully in several experiments. Watts and Wieman'"^

demonstrated that the output frequency of a laser can be

changed by 1 GHz and become stable to within a few megahertz in a time of 2 //s. This was accomplished by simply

changing the injection current through the laser using an

appropriately tailored pulse. With this high speed switching

it was possible to optically pump all the atoms in a cesium

beam into a specific magnetic sublevel {F, Mp ) using a single

laser. Normally this would be impossible because cesium has

two ground state hyperfine levels that are separated by 9.2 GHz. However, in a fraction of the time it took the atomic

beam to pass through the laser beam, the laser frequency was

switched to excite both levels. Robinson"^'' has also used this frequency jump technique to polarize a rubidium cell with a

single laser. This capability to rapidly sweep the laser fre- quency over a large range in a controlled manner is unique.

In these experiments it was used to reduce the number of

lasers needed for optical pumping, but it may find greater

utility in studies of various types of transient phenomena.'

A recent application of the frequency chirping capability of diode lasers is the stopping of atomic beams. Ertmer et

al.^^ showed that by frequency chirping the light from a dye

laser it was possible to slow and stop a beam of sodium

atoms. To achieve the necessary frequency scan a sophisticated broadband electro-optic modulator was developed. A

corresponding frequency chirp is very easy to produce with a diode laser by merely adding a small sawtooth ramp to the

injection current. Watts and Wieman used this technique to stop a beam of cesium atoms'"' with a surprisingly simple

and inexpensive apparatus. Salomon et al.'^^ have carried out

a similar experiment to study the optimization of the cooling. They showed that by adding 1 10-MHz sidebands to the

laser, they could enhance the number of stopped atoms by

50%. Recently Sheehy et al.^^ have used frequency chirped

diode lasers to stop rubidium atoms. These various experiments demonstrated that, in addition to slowing atoms, the frequency modulation capability of diode lasers is also well

suited to probing atomic velocity distributions rapidly

enough to avoid distortion. The resulting 15-m/s velocity spread of the nearly

stopped atoms reported in Ref 61 was limited by the 30- MHz linewidth of the diode laser. To improve on this, Sesko,

Fan, and Wieman*''* stopped atoms in a similar manner using

a cavity-stabilized laser of the type discussed in Sec. IV D. In

this case, the frequency was ramped by changing both the

laser current and the length of the stabilization cavity ( using

a piezoelectric transducer). The speed of the cavity response was less than that of the laser, but was still adequate for atom

stopping. With a cavity-stabilized stopping laser, the number of stopped atoms was found to improve dramatically and

the final velocity spread was substantially smaller. We have

obtained similar results by stopping atoms with the light

from grating cavity lasers of the type discussed in Sec. IV C.

C. High resolution spectroscopy

We mentioned briefly the improvements that cavity

locked lasers have made for atom stopping. This is only one

of a large number of experiments made possible by optical

feedback stabilization. This technique provides a very nar- row bandwidth source which is valuable for high resolution

spectroscopy and other experiments where narrow

linewidth is important. Although often neglected in the English literature, a great deal of forefront work on diode laser stabilization and applications to high resolution spectroscopy has been done by Velichanski and co-workers. ''' Other

examples of high resolution and high sensitivity spectrosco15 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 15 TN-21
o

(/) <

0.46

0.48

0.50

200 400

Frequency (MHz)

FIG. 15. A saturated absorption spectrum of the 65 to 6P,/2 transition in cesium obtained using a stabilized diode laser. This spectrum was a single oscilloscope trace with no signal processing except the subtraction of the Doppler broadened absorption line. This demonstrates the signal-to-noise

ratios that can be obtained with diode lasers. The diode linewidth gave a

negligible contribution to the resolution ( 10 MHz for the narrowest- line).

py are described in Refs. 66-69. Figure 15 illustrates the

capabilities of cavity stabilized lasers for high resolution

spectroscopy. This figure shows a fluorescence spectrum of

the 65-6/'v2 transition in cesium observed in a single 100-ms

oscilloscope trace. The spectral linewidths were limited entirely by the 6-MHz natural linewidth of the transition, and

had no contribution from the laser linewidth. Figure 15 also

illustrates how the amplitude stability of the laser leads to very good signal-to-noise ratios. This laser was used to make

precise measurements of the Stark shifts and the hyperfine

structure of the SP^yj state of cesium. These measurements

had an uncertainty of only 20 kHz.

Good examples of applications that use the unique modulation capabilities ofdiode lasers for precision spectroscopy

10 MHz

Laser Frequency

FIG. 16. Fluorescence measurements of the 6S F= 4 to 6/*,,. F= 5 reso- nance line in a cesium atomic beam. The laser's frequency noise causes excess amplitude noise on the cesium fluorescence signal. This noise is surpris- ingly irregular as can be seen by comparing it to the noise observed on the Fabry-Perot cavity transmission signal that was taken simultaneously. We

see the frequency noise shows up on the sides of the cavity transmission

fringe whereas it is enhanced on the peak and one side of the fluorescence

signal. This noise disappears when the lasers linewidth is narrowed.

are the work ofMartin and co-workers.^* They have demonstrated time-resolved spectroscopy of BaCl and velocitymodulation spectroscopy of N^

.

Avila et al.^'' have used diode lasers to make a high precision measurement of the absolute energy of the dPi/j state

in cesium. The laser frequency was locked to the cesium

resonance line by observing fluorescence from a collimated

cesium beam. A wavemeter was then used to measure the absolute frequency to 12 MHz (3 parts in 10*). In the work of Gibble and Gallagher,*^ a pseudo-external cavity laser with grating feedback was used to study velocity changing colhsions in rubidium. Using a saturated ab- sorption technique and this continuously tunable

narrowband laser, they were able to measure collisional dis- tortions ofthe saturated absorption line shapes which were a

small fraction of the 10-MHz natural linewidth. Feedback-stabilized diode lasers are uniquely simple

and inexpensive sources of very narrowband tunable light.

For this reason, they will undoubtedly be widely used for high resolution spectroscopy in the future.

0. High sensitivity spectroscopy

Another developing area of application of diode lasers is to high sensitivity spectroscopy. This includes the application to optical pumping, optical heterodyne or FM spectroscopy,^'"" uhrasensitive detection,TM optogalvanic spectroscopy,^' and other areas.^* Also, significant work in sensitive spectroscopy has been done using the lead salt diode lasers^^ which we have not addressed in detail in this article. Often

these applications are just extensions (to diode lasers) of

well-established techniques of spectroscopy. On the other

hand, there are a few applications that utilize the unique

capabilities of the diode lasers. Diode lasers stabilized by optical feedback have been

found to be much better than unstabilized lasers for high

precision measurements of fluorescence or absorption where

the signal-to-noise ratio is important. In some cases the feed- back not only reduces amplitude noise on the laser, but also reduces some previously unexpected noise on atomic spectra

associated with the laser FM spectrum. In using diode lasers for precision spectroscopy some workers have reported that the measured signal-to-noise ratios are much lower than ex- pected.'^ For example, we observe large amounts of excess

noise in diode laser-induced fluorescence and direct absorption measurements of the F= 4 to F= 5 resonance line in cesium ( see Fig. 16). This noise results from the frequency

fluctuations in the diode laser and is eliminated when the diode laser's linewidth is reduced by using the high-^ cavity

feedback lock. Two surprising features are observed in this excess noise relative to what one would expect from simple

rate equation analysis of the laser induced transition: first, it

is much too large; and second, the noise can also be asymmetric with respect to laser detuning from the resonance. By

properly treating coherence and atomic saturation with a noisy laser source, Zoller and co-workers'* have provided an explanation of these observations.

Two significant instances in which the elimination of

this noise has been a major concern are the new optically

pumped cesium clocks being constructed at NIST and other

16 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 16 TN-22
national standards labs*** and the precise measurement of

parity nonconservation in cesium using an optically pumped

beam.^^ In these experiments the use of feedback-stabilized

lasers has been essential because of the reduced noise in the atomic fluorescence.

E. Self-locking power buildup cavities

Another application of feedback from high-ig cavities is the self-locking power-buildup cavity, which can provide

large enhancements in laser power. One obvious shortcoming of diode lasers is the small output power, but buildup

cavities allow one to overcome this limitation in some experiments where there is little optical absorption. The basic idea

of such a cavity is the same as discussed in Sec. IV D, but the

optics are arranged so that a large fraction of the laser power

is coupled into the locking cavity. This results in the intracavity power becoming much higher than the output power of

the laser. Buildup cavities have been used with lasers for many years; however these always required some electronic feedback system to keep the cavity and laser frequencies the same. With a diode laser, the need for electronic feedback can be eliminated because the optical feedback locks the la- ser to the cavity resonance. Enhancements as high as 1 500 in the one-way power buildup^^ have been obtained with such

"self-locking buildup cavities." These have provided a circulating power of 45 W.

Tanner, Masterson, and Wieman^*" used a self-locking

buildup cavity to study how a strong blue-detuned standing wave can collimate a cesium atomic beam. Using this tech- nique they were able to reduce the divergence of the beam

from 15 to 4 mrad using only a 10-mW laser source. In another application, over 1 mW of tunable light at 432 nm was produced by placing a potassium niobate crystal inside such a self-locking buildup cavity to produce the sec- ond harmonic of the diode laser light. ^^ With the proper

lasers and crystals, it may be possible to use this approach to achieve several milliwatts of narrowband tunable light over much of the blue region of the spectrum. When this technol- ogy is combined with injection-locked diode arrays or arrays

that are themselves optically locked to buildup cavities,^** many tens of milliwatts will be available. On the other hand,

for applications not requiring a large amount of second-harmonic light, Ohtsu^" has shown that it is possible to do spec- troscopy with the small amount of second-harmonic light that is emitted from ordinary diode lasers.

F. Trapping and cooling atoms using diode lasers

Another area in which stabilized diode lasers have been

used very successfully is in cooling and trapping neutral atoms. Such experiments often require several different laser frequencies with linewidths of less than 1 MHz, and thus

they are quite expensive to set up using dye lasers. This ex- pense precludes the use of dye laser-cooled and/or trapped

atoms in a wide range of atomic physics experiments for which they would otherwise be well suited. The use of cavityand grating-stabilized diode lasers overcomes this problem.

Sesko and co-workers'"* have recently cooled cesium atoms

using a three-dimensional standing wave tuned to the red

side of the cesium resonance line (so called "optical molasses"). This has produced atomic samples containing 5 X 10' atoms with a temperature of 100 //K. In a related experiment

he and co-workers then observed the cesium "clock" transi- tion between the two ground hyperfine states in this cold

sample.**" The low temperature allowed an interaction time

of 20 ms and hence a linewidth of only 44 Hz, in an interaction volume of less than 1 cm\

In other experiments Sesko et al.^^ have succeeded in trapping atoms using a Zeeman shift spontaneous force trap

created with diode lasers. Using four stabilized lasers, samples of up to 4 X 10** atoms were trapped, and trapping times

of greater than 100 s were obtained.**' A variety of interac- tions between the trapped atoms were studied. In both the

optical molasses experiments and these trapped atom experiments, features of the diode lasers other than their cost have

been important. There were a number of probe studies where

very low amplitude noise and ease of rapid frequency

changes were invaluable. Inexpensive diode lasers are proving to be valuable tools for atomic spectroscopy. They offer continuously tunable

sources of radiation with linewidths under 100 kHz and

powers of 30 mW or more. They can cover much of the near

infrared region of the spectrum and are moving into the visible. These devices can (though they may not) be simple and

highly reliable. Their low cost and ease of use make multilaser experiments quite feasible, and more importantly, di- ode lasers allow laboratories with limited resources to still be

involved in "state-of-the-art" laser-atomic physics experi- ments. These include the areas of laser cooling and trapping,

nonlinear optics, and high precision spectroscopy.

ACKKOWLEDGMENTS

The authors acknowledge valuable discussions with,

and contributions made by J. Camparo, J. L. Hall, G. Tino,

V. L. Velichanski, M. Ohtsu, H. Robinson, R. Drullinger, R.

Hulet, K. Gibble, W. Swann, C. Tanner, B. Masterson, D.

Sesko, and R. Watts. Readers can obtain a copy of the refer- ences including the titles of the articles by contacting the JILA Publications Office. C. Wieman is pleased to acknowledge support in this work from the Office of Naval Research

and the National Science Foundation through the University of Colorado.

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(Springer, Berlin, 1989); J. Dalibard, C. Salomon, A. Aspect, E. Ari- mondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Pro- ceedings ofthe 1 1th International Conference on A tomic Physics, edited by

S. Haroche, G. Grynberg, and J. C. Gay (World Scientific, Singapore,

1989).

"'B. Sheehy, S-Q. Shang, R. Watts, S. Hatamian, and H. Metcalf, J. Opt.

Soc. Am. B 6, 2165 (1989). "D. Sesko, C. G. Fan, and C. E. Wieman, J. Opt. Soc. Am. B 5, 1225

(1988).

"' Yu. A. Bykovskii, V. L. Velichanskii. I. G. Goncharov, and V. A. Maslov,

Sov. Phys. Semicond. 4, 580 ( 1970); V. L. Velichanskii, A. S. Zibrov, V.

S. Kargopol'tsev, O. R. Kachurin, V. V. Nikitin, V. A. Sautenkov, G. G.

Kharisov, and D. A. Tyurikov, Sov. J. Quantum Electron. 10, 1244

(1980); V. A. Sautenkov, V. L. Velichanskii, A. S. Zibrov, V. N. Luk'yanov, V. V. Nikitin, and D. A. Tyurikov, Sov. J. Quantum Electron.

11, 1131 (1981); Y. A. Bykovskii, V. L. Velichanskii, I. G. Goncharov,

A. P. Grachev, A. S. Zibrov, S. I. Koval. and G. T. Pak, Sov. J. Quantum

Electron. 19,730 (1989).

'*C. E. Tanner and C. E. Wieman, Phys. Rev. A 38, 162 (1988); C. E. Tanner and C. E. Wieman, Phys. Rev. A 38, 1616 ( 1988); G. M. Tino, L. Hollberg, A. Sasso, M. Inguscio, and M. Barsanti (to be published).

'~'K. E. Gibbleand A. C. Gallagher, in XVI ICPEAC (in press). ""T. Gustavsson and H. Martin, Phys. Scripta34, 207 ( 1986); B. Lindgren,

H. Martin, and U. Sassenberg, in Laser Spectroscopy VIII, edited by W.

Persson and S. Svanberg (Springer, Berlin, 1987), p. 402; G. Gustafsson, H. Martin, and P. Weijnitz, Opt. Commun. 67, 112 (1988).

"

" G. Avila, P. Gain, E. de Clercq, and P. Cerez, Metrologia 22, 1 1 1 ( 1986 )

"'J. Reid, M. El-Sherbiny, B. K. Garside, and E. A. Ballik, Appl. Opt. 19, 3349 (1980); W. Lenth and M. Gehrtz, Appl. Phys. Lett. 47, 1263

( 1985); L. G. Wang, H. Riris, C. B. Carlisle, and T. F. Gallagher, Appl.

Opt. 27, 207d (1988); C. Clinton and D. Cooper, Opt. Lett. 14, 1306

( 1989); L.-G. Wang, D. A. Tate, H. Riris, and T. F. Gallagher, J. Opt.

Soc. Am. B6, 871 (1989). " S. Yamaguchi and M. Suzuki, Appl. Phys. Lett. 41, 597 ( 1982); S. Yamaguchi and M. Suzuki, IEEE J. Quantum Electron. QE-19, 1514 ( 1983).

'- D. T. Cassidy and J. Reid, Appl. Phys. B 29, 279 (1982); M. Gehrtz, G.

C. Bjorklund, and E. A. Whittaker, J. Opt. Soc. Am. B 2, 1510 ( 1985); J.

S. Wells, A. Hinz, and A. G. Maki, J. Mol. Spectrosc. 114, 351 ( 1985); D. E.Cooper and J. P. Watjen. Opt. Lett. 11,606 (1986);D. E. Cooper and

R. E. Warren, J. Opt. Soc. Am. B 4, 470 ( 1987 ); D. E. Cooper and R. E. Warren, Appl. Opt. 26, 3726 (1987); A. Hinz, J. S. Wells, and A. G.

Maki, Z. Phys. D5, 351 (1987); D. E. Cooper and C. B. Carlisle, Opt.

Lett. 13, 7 19 ( 1988 ); C. B. Carlisle and D. E. Cooper, Appl. Opt. 28, 2567

( 1989); C. Clinton and D. Cooper, Opt. Lett. 14, 1306 ( 1989).

'

' V. Giordano. A. Hamel. G. Theobald, P. Cerez, and C. Audoin, Metrologia 25, 17 (1988); L. Hollberg, Applied Laser Spectroscopy. NATO ASI

series, edited by M. Inguscio and W. Demtroder (Plenum, New York)

(in press). "Th. Haslwanter, H. Tirsch, J. Cooper, and P. Zoller, Phys. Rev. A 38,

19 Rev. Sci. Instrum., Vol. 62, No. 1, January 1991 Diode lasers 19 TN-25
5652 ( 1988); H. Ritsch. P. Zoller, and J. Cooper, Phys. Rev. A 41, 2653 "G. J. Dixon, C. E. Tanner, and C. E. Wieman, Opt. Lett. 14. 731 ( 1989). (1990). '"M. K. Chun, L. Goldberg, and J. F. Weller, Appl. Phys. Lett. 53, 1170

S. L Gilbert and C. E. Wieman, Phys. Rev. A 34, 792 ( 1986); M. C. ( 1988). Noecker, B. P. Masterson, and C. E. Wieman, Phys. Rev. Lett. 61, 310 '"M. Ohtsu, Electron. Lett. 25, 22 ( 1989). (1988). ""D. W.Sesko and C.E. Wieman, Opt. Lett. 14,269 (1989).

'C. E Tanner, B. P. Masterson, and C. E. Wieman, Opt. Lett. 13, 357 "' D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, Phys. (1988). In subsequent work we have achieved higher buildup (1500) and Rev. Lett. 63,961 (1989);T. Walker, D. Sesko, and C. Wieman, Phys.

higher circulating power (45 W). Rev. Lett. 64, 408 ( 1990).

20 Rev. Sci.lnstrum., Vol. 62, No. I.January 1991 Diode lasers 20 TN-26
»

High-Sensitivity Spectroscopy with Diode Lasers

R. W. Fox, H. G. Robinson^ A. S. Zibrov*, N. Mackie, J. Marquardt,

J. Magyar, L. W. Hollberg

National Institute of Standards and Technology

325 Broadway, Boulder, CO 80303

ABSTRACT

Linewidth reduction of an extended cavity diode laser at 657 nm was accomplished by negative

feedback to an intra-cavity ADP crystal. High resolution (170 kHz wide) saturated absorption signals were recorded of the calcium intercombination line which is of interest for a frequency standard. The

spectrum of the red 6^f2-9\p^ cesium line in a magneto-optical cell trap was also investigated.

1. INTRODUCTION

The advance of diode lasers into the visible offers opportunities in the area of frequency standards and frequency

metrology. Diode lasers stabilized to known spectral features have the potential to be low-cost, high precision frequency

markers and length standards. The calcium intercombination line at 657 nm is one such feature that has generated much

interest '•^.

An optical frequency reference may in general be realized by first reducing the short term laser frequency fluctuations by locking to a Fabry-Perot cavity, then locking the cavity to an atomic or molecular line. This approach allows enough

signal-to-noise in the short term (< 1 s) for tiie performance to be limited by systematics associated with measuring the

spectral feature, such as field shifts or time of flight broadening. A caveat to this is that the lock to the optical cavity must

be relatively immune from offset drifts. Offsets may occur, for instance, when the injection current of a diode system is modulated to produce sidebands for a rf heterodyne lock. Some fraction of the inherent amplitude modulation (am) is detected along with the desired signal, leading to an intensity dependent dc term at the output of the phase sensitive detector. Strategies to deal with this include demodulating at 3f and/or sampling the laser intensity prior to the reference cavity in order

to subtract any fluctuations out of the cavity transmission or reflection. However there are both fundamental limits (with

regard to the power that must be expended in the sampling channel), and practical limits such as the inhomogeneity of the am across the beam that will induce drift at some level. Thus it is of interest to start with as low residual am from the modulation as possible.

Employing a phase modulator external to the laser cavity to apply sidebands and to reduce the frequency^hase

fluctuations is a method that has met with much success.^ We have positioned the phase modulator inside the extended cavity,

where it serves as a frequency modulator. In comparison an external modulator has much lower gain as a frequency

transducer. Although external multiple pass configurations have been used, the poor quality of the diode laser beam makes

this approach increasingly difficult. A disadvantage of placing the crystal in the laser cavity is the coupling of Uie output

power to the frequency modulation (fm), albeit at a much lower level than direct injection current modulation. However the

injection current channel is now available to be part of a closed loop for intensity control, with a servo bandwidth independent

of the frequency control loop. If the intensity control loop bandwidth is extended to cover the fm sideband frequency, the

residual am and subsequent dc lock drift will be further decreased. Similar approaches using negative feedback to externally

placed modulating crystals to eliminate residual am have worked well.

*

2. LASER FREOUENCY NOISE AND LINEWIDTH REDUCTION

The extended cavity laser consisted of an anti-reflection coated' red diode laser operating near 660 nm, a f/1 collimating

lens, a 29 mm long Brewster-cut ADP modulator crystal, and a high diffraction efficiency holographic grating.® The laser was built on an invar baseplate and enclosed in an aluminum box to reduce acoustics. The grating was mounted on an invar

Contribution ofNIST, not subject to copyright

Proc. SPIE Conference on Frequency Lasers & their Applications, 1837 (edited by Y.C. Chung) pp. 360-365 (1992).

TN-27
10^ p

10*

10^ ^

10^ s

,10^ I

«10^

10^ ^

support with a simple hinge and a piezo-electric

crystal, allowing about 12 Ghz of tuning without

mode hops. The zero-order beam from the grating was reflected from a mirror mounted perpendicular

to the grating, and served as the output. This

configuration reduces the output beam's angular

sweep with tuning. The output power was 1 mW

to 1.5 mW, depending on the lasing wavelength.

The spectral linewidth of the unlocked (and

locked) laser may be examined by a heterodyne

measurement using a similar or more stable laser as the local oscillator. In lieu of building two

complete systems, the linewidth may also be

studied by observing the laser's frequency noise

spectrum. This provides information on the

spectral distribution and magnitude of the frequency fluctuations that generate the linewidth. The noise spectrum can be measured by using an

independent optical cavity as a discriminator. Locking the laser and discriminator cavity together

with a low bandwidth (-1 Hz) side-lock

conveniently cancels drift and permits faster differential frequency fluctuations between the

laser and cavity to be accurately converted to intensity fluctuations. The 12 cm extended cavity length resulted in a measured frequency noise level of approximately 8000 Hz^/Hz (see fig.

1). Below about 50 kHz the fluctuations increase in a typical 1/f fashion, obliging the noise density to rise as 1/f^. A numb^

of distinct acoustic peaks are evident in figure 1; these result from structural resonances of the grating mount The frequency

noise data was taken with a Av=8 MHz hnewidth discriminator cavity in transmission. The data shows the cavity roll-off (-40 dB/decade) at 8 MHz, indicating that the laser's frequency noise spectrum is flat out to at least 30 MHz. At about 30

MHz the measurement noise floor causes a deviation from -40 dB/decade. The fast frequency noise level ^parent between

50 kHz and 30 MHz indicates an inherent Lorentzian laser linewidth of about 25 kHz (Av= 7C-8000 Hz ^/Hz). This is additionally broadened by the low frequency noise.

iQi y

10,0

; :;;;;;; k

j

i i^^

i'If n1

: : : :::::

: IB

k«

: : : :

= "Tl

= \^itLiJ til H" • .••• \

jfy ntfiifi(Wmi\

I \\]§K^^

1 V

I 1LJuLLLui 1uuLiiiii 1 i i iiiii —i i i iiiii i—uJ

10^ 10* 10^ 10^ 10^

Frequency (Hz)

Fig. 1 The unlocked extended cavity laser frequency noise spectrum. The line indicates the discriminator cavity roll-off slope.

JO EXPERFENT

T

POLARIZER

0>-^®-K>-^

"JT

EXTEM3ED

CAVITY

LASER

NTEGRATOR ^

HV

TOGRATNG

TO CRYSTAL

Figure 2. The extended cavity laser was locked to a 2.5 MHz linewidth optical cavity by the rf heterodyne technique. The rotator- polarizer pairs provide 35 dB of isolation each.

TN-28
The frequency fluctuations at rates above 100 i

' ""i ' '

' ' ""I '

i

'

i niii kHz comprise relatively little of the laser linewidth. This is a consequence of the fast frequency noise level, H^, and the corresponding

integrated phase noise. For a white fin noise

spectrum, the phase noise integrated^ beyond a

given arbitrary frequency f, i.e. integrated from f

to infinity, is Hyf. Note that significant

contributions to the laser linewidth appear only

when the integrated phase noise density approaches

1 rad^.^^ The measured noise level indicates the integrated phase fluctuations above 100 kHz are on

the order of Hyf-O.l. Therefore we expect a

sharp reduction of the linewidth when the noise

below 100 kHz is reduced, in contrast to the

situation of a solitary diode laser where the frequency noise in the MHz range is important.

The non-confocal cavity used for the lock had

a linewidth of 2.5 MHz, a free spectral range of 1 GHz and a piezo-electric transducer (pzt) for tuning. A conventional rf heterodyne set-up

provided the error signal as shown in figure 2. Two negative feedback loops were implemented to reduce the frequency noise. An integrating loop

(^ dB -300 Hz) to the grating pzt primarily served to limit the necessary dynamic range of the faster loop. This rather low

bandwidth was dictated by mechanical resonances of the grating structure, the fundamental resonance being at 3 kHz. The

faster (ADP) loop had approximately 80 dB of gain below 100 Hz, which was then rolled-off with double-pole and single-pole

sections to a unity gain frequency of -1 MHz. Compensation was made for the lock-cavity phase shift and much of the

crystal high-voltage driver's phase shift The bandwidth and consequently the attainable low-frequency gain were limited by

the residual uncompensated phase shift of the high-voltage driver. Higher frequency fluctuations could be corrected by using a low-voltage higher-bandwidth feedback path to the other side of the crystal.

10* 105

Frequency (Hz)

Fig. 3 The unlocked and locked eiror signal out of the mixer. The noise

density values agree well with an independent measurement, fig. 4

Most of the laser power was reserved for the

saturation spectroscopy, leaving 30 pW incident on

the detector used for the lock channel. This

incident power was just sufficient to allow

intensity noise limited operation. The 1 MHz

bandwidth allowed enough low frequency gain to impart this limiting noise floor onto the laser at frequencies below 10 kHz.

The ADP crystal transfer function was -0.78

MHz/volL The crystal was bonded on one side to a ceramic mount and acoustically damped to reduce piezo-electric resonances in the 90 kHz

range. The modulation frequency was chosen to be well above the cavity bandwidth to produce a broad lock acquisition range. Modulation

frequencies of 12 MHz and 26 MHz were used. However the modulation index was limited by the

available synthesizer power, so the crystal was

driven as a series resonant LC circuit at the modulation frequency. Q's of about 10 yielded

I I I 1

I I 1 1

GOa

O

*o

10

2*

-40 dB/decade

Intensity Noise

Level

_l_l_U ' I ' I I 1 1

10^ 10* 10^

Frequency (Hz)

10^

Fig. 4 The locked extended cavity laser frequency noise spectrum. The data was obtained with a 50 KHz linewidth discriminator cavity.

TN-29
adequate sideband amplitudes.

Reduction of the frequency noise and attendant linewidth were observed with an independent high quality reference cavity

used as a discriminator. The reference cavity is constructed from a ULE glass cylinder with optically contacted mirrors. It has a 50 kHz linewidth, a 3 GHz free spectral range, and is mounted inside a vacuum housing (-10^ Pa) to reduce index drifts and acoustic noise. Frequency noise measurements were obtained by side-locking to this high finesse reference cavity with

slow feedback (f odB~l Hz) to the Av=2.5 MHz "lock" cavity pzt. The resultant fm to am conversion is indicative of the

laser's frequency flucmations only to the extent that the two cavities do not exhibit common mode vibrations. The

heraietically sealed lock cavity was hard-mounted to the optical table and the reference cavity was supported in a "cradle" fashion by 2 fine wires that allowed pendulum modes but strongly damped high frequency oscillations. We believe that the frequency region of "common mode" vibrations was « 100 Hz.

The locked laser exhibits frequency fluctuations (see fig. 4) at the 200 Hz^/Hz level out to several hundred kHz. At

approximately 400 kHz the increasing laser noise (due to the falling servo gain) and measurement noise floor (due to detector^ntensity noise) combine to deviate the slope from -40 dB/decade. The laser noise increases to the meet the open-loop

level of 8000 Hz^/Hz as the servo gain drops to unity at about 1 MHz. Inadequate servo-loop phase margin causes an increase

at this point over the open-loop noise, but in terms of fluctuations that contribute to the linewidth this is not significant since the integral of the phase noise contribution from this frequency region is negligible compared that of the lower frequency

region. This noise spectrum indicates'" a linewidth reduced to less than 1 kHz, sufficient for high resolution saturated spectroscopy of Calcium in an oven.

Modulating the laser frequency with the ADP crystal was accompanied by measurable residual amplitude modulation.

The level of am depended slightly upon the particular mode and wavelength. This can be understood by noting that the

residual am will be a function of the slope of the composite gain curve G(v) of the extended cavity laser at the lasing

wavelength. The grating reflection and the residual etalon of the AR coated chip are the two primary contributors to dG(v)/dv. A modulation index of p=1.0 at 12 MHz was accompanied by 0.015% amplitude modulation. Modulation via the

injection current at the same modulation index (as determined by the average of the induced sideband amplitudes) resulted

in 1.7% amplitude modulation.

The above mentioned residual am could be reduced by a simple feedback loop to the injection current. However, this may

in general cause a change in P and the phase of the modulation, which is a cause for concern if it effects the lock

discriminator. Although to first order the lock discriminator is insensitive to small changes in the signal phase," for highquality locks this may be a noise term.

3. CALCIUM SATURATION SPECTROSCOPY

The calcium intercombination line at 657 nm

exhibits a number of desirable properties of a

spectral reference line. Among other attributes it has a 400 Hz natural linewidth and a simple

ground state configuration ('Sq) that should allow

nearly all of the atoms present to take part in the absorption process. A laser cooled calcium beam

or neutral atom trap approach may well be

required to take advantage of it's full potential.

However calcium saturated absorption in an oven

provides excellent frequency stability in a simple

system.

A high density calcium beam about 6 cm long was created in an oven with uncoated bk-7 glass

windows. The background gas pressure was kept

at less than 1.3-10 -^ Pa (10'^ Torr) to avoid

pressure broadening. The windows were partially

E<

Wavelength

Fig. 5 435 kHz wide absorption of the calcium intercombination line at 657 nm. The linewidth is limited by time-of-flight broadening. The sidebands are spaced by 2.3 MHz.

TN-30
protected from calcium deposition by the oven design.

A pair of coils provided a transverse magnetic field that was

aligned with the laser polarizatioa This allows only AMpO

transitions, which have only a very small quadratic Zeeman

sensitivity (~l(f Hz/T^. The saturating beam power was

approximately 400 pW, and was reflected by a flat mirror to serve as the probe beam. The Doppler absorption at the operating

temperature was 10% and 1.4 GHz wide. The Doppler curve was

narrowed somewhat due to a directional calcium flux in the oven. The saturation feature (see fig. 5) was about 5% of the Doppler

absorption. The hot calcium and a 2 mm diameter lasCT beam size resulted in a short interaction time (~1 ps), limiting the observed

linewidth to 435 kHz. The laser's spatial profile was sh^ed by a

pair of anamorphic prisms and a telescope to provide a 7 mm beam,

with which 170 kHz linewidths were obtained. Further reductions

will require a better spatial mode. Lock-in detection at 40 kHz

resulted in signal-to-noise ratios of -10^ (1 Hz bandwidth) at modulation levels that produced no modulation broadening.

Fig. 6 Cesium energy level diagram. Wavelengths are in nm, and the hyperfine splitting of the 9s state is shown.'^

10 MHz -

V—

4. CESIUM TRAP SPECTROSCOPY

Cesium magneto-optic cell traps may well serve as the basis for the next generation of atomic frequency and time standards. There

is a cesium transition (6p j^ to 9s,/2) at 658.8 nm which is close to calcium in wavelength and within the tuning range of the laser. We

note that the essentially Doppler-free absorption from the 6p3^ levels

is a potentially useful indication of trap characteristics. The 852 nm

cooling laser in this trap is typically locked several linewidths to the red of the ground state F=4 to F=5 transition (see fig. 6), and a second laser tuned 9 Ghz away re-pumps atoms in the lower ground

state level back into the cycling transition. The red absorption from the upper trapping level was measured

with a weak probe beam (-10 pW, 0.05 mW/cm^) approximately

the same diameter as the cluster of trapped atoms. An optical fiber was used as a spatial filter and conveniently transmitted

the red probe light from the locked laser to the trap. Etalon fringes with a period of 4 MHz and spurious low frequency

amplitude noise resulting from polarization changes also caused by the fiber were reduced by a double beam subtraction

configuration. FM modulation at 50 kHz and lock-in detection with a 1 ms time constant were employed, yielding signal-tonoise ratios of -2(X). The absorption detection limit extrapolated to 1 s was 3- 10^^, limited by mismatching of the double

beam configuration that allowed laser and fiber noise to be detected. The 1% absorption (see fig. 7) of the 6P3/2 F=5 -> 9s

F=4 transition indicates a trap population of -2-10 'atoms, which agrees well with 852 nm fluorescence measurements.

Fig. 7 Cs derivative spectroscopy at 658.8 nm. The larger

peak is 1% absoiption. The cooling laser is tuned to the red of the 852.1 nm transition.

1/2

We observe a double peak absorption spectrum which is preliminarily attributed to Auder-Townes splitting (AC Stark

effect) caused by the 852 nm cooling laser fields. A frequency separation that varies as the square root of the intensity and

an asymmetry that depends on detuning from line center is expected," and is consistent with our observations.

5. SUMMARY

A 12 cm long extended cavity laser at 657 nm stabilized to a precision reference cavity by electronic feedback to an intra- cavity ADP crystal has been described. The residual am that accompanies fin is approximately 100 times less when the laser

is modulated with the crystal rather than the injection current. This laser was used to measure linear doppler-free absorption

from the cesium 6^3^ state in a magneto-optical trap. In addition we used the laser for non-linear absoiption experiments

of the calcium intercombination line. Linewidths of 170 kHz were observed, limited by laser spatial mode size and quality.

TN-31
6. Acknowledgements

We acknowledge useful discussions with C. Weimer, J. Berquist, J. L. Hall, J. Helmcke, F. Riehle, and V. Velichansky.

This work was supported in part by NASA and the AFOSR.

^Present address: DepL Physics, Duke University, Durham, N. C.

* Permanent address: P. N. Lebedev Physics Institute, Leninsky Prospect, 53, 1 17924, Moscow, Russia

6. REFERENCES

1. R, L. Barger, J, C. Berquist, and D. J. Glaze, "High-Resolution Saturated Absorption of the 'So-^Pj Calcium Transition in an Atomic Beam," J. Opt Soc. Am., Vol. 68, No. 11, p. 1634, 1978.

2. J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, "Optical Frequency Standards," IEEE Trans. InsL Meas., Vol. 38,

No. 2, p. 524, 1989.

3. Ch. Salomon, D. Hils, and J. L. Hall, "Laser stabilization at the millihertz level," J. Opt Soc. Am. B, Vol. 5, No. 8, p. 1576, 1988

4. N. C. Wong and J. L. Hall, "Servo control of amplitude modulation in frequency-modulation spectroscopy: demonstration

of shot-noise-limited detection," J. Opt Soc. Am. B, Vol. 2, No. 9, p. 1527, 1985

5. The coating was AI2O3 and hafnium oxide, which nearly doubled the solitary laser's threshold current

6. M. S. Soskin and V. B. Taranenko, "Hologr^hic total-intemal-reflection selector for tunable lasers," Sov. J. Quan. Elect,

Vol 7, No. 3, 1977.

7. This follows immediately from the fact that the phase noise density in rad^/Hz is equal to the frequency noise density in Hz^/Hz divided by f I

8. E. Bava, A. DeMarchi, and A. Godone, "Spectral analysis of synthesized signals in the mm wavelength region," IEEE

Trans. Inst and Meas., Vol IM-26, No. 2, 1977

9. R. W. P. Drever, et. al, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, p. 97, 1983.

10. D. S. Elliot, Rajarshi Roy, and S. J. Smith, "Extracavity laser band-shape and bandwidth modification," Phys. Rev. A,

Vol. 26, No. 1, p. 12, 1982

1 1. J. L. Hall, H. G. Robinson, T. Baer, and L. Hollberg, "The lineshapes of subdoppler resonances observable with fin side- band (optical heterodyne) laser techniques," Proc. Nato Advanced Study Institute on General Relativity and Quantum

Electronics, 1981

12. E. Arimondo, M. Inguscio, and P. Violino, "Experimental determinations of the hyperfine structure in the alkali atoms," Rev. Mod. Phys., Vol. 49, No. 1, p. 31, 1977.

13. R. M. Whidey and C. R. Stroud, Jr.,"Double optical resonance," Phys. Rev. A, Vol. 14, No. 4, p. 1498, 1976.

TN-32
Spearochimica Acta Rev Vol 15. No 5. pp 291-299. 1993 Pnnted in Great Bniaui All nghts reserved 0958-319X.'93 S24.00

1 1993 Pergamon Press Ud

The diode laser as a spectroscopic tool

R. W. Fox,* C. S. Weimer,* L. Hollberg* and G. C. TuRKt

•National Institute of Standards and Technology, Boulder, CO, 80303, U.S.A.

tNational Institute of Standards and Technology, Gaithersburg, MD 20899, U.S.A.

Abstract—The properties of diode lasers that make them attractive as spectroscopic sources are discussed, along with the use of extended cavities to enhance their tuning range and reduce their linewidths. Semiconductors can now provide efficient, tunable, narrow linewidth laser light over much of the red and

near-i.r. region of the spectrum. The progress in using nonlinear optics to extend the useful wavelength

range of diodes lasers is also considered. Our recent analytical work with diode laser spectroscopy provides

examples of their application.

1. Introduction and Basic Properties

Inherent low noise, low cost, tunability, and simplicity make diode lasers unique

spectroscopic sources, and their use in this respect has been reviewed several times

[1-5]. Here we will focus briefly on general characteristics and then explore some of

the new technologies and appUcations, with particular interest in spectroscopy and

ultrasensitive detection.

There are two main types of laser diodes available. The type we will deal with here

are the visible and near-infrared lasers fabricated from the group III-V semiconductor

compounds (for example: AlGalnP, AlGaAs, InGaAs and InGaAsP). The approximate

distribution of wavelength and power for commercial lasers of this type are shown in Fig. 1. The other basic type of diode lasers are commonly known as lead-salt lasers which operate at wavelengths between 3 and 30 p-m. These lasers are distinct in that they are only operated at cryogenic temperatures, and are not considered here [6]. Although red cw diodes with nominal wavelengths as short as 635 nm are commercially

available, there have been diode lasers developed at shorter wavelengths [7, 8]. However, coincidences between strong atomic or molecular lines and wavelength

ranges of available diodes remain the exception rather than the rule. The visible and

near-i.r. diodes can be tuned roughly 3-4 nm from the nominal wavelength with a 20°C temperature change. The tuning is in a step-wise fashion; for instance, smooth

0.6 0.7 0.1 0.9 1.0 1.1 1.2 1.3 1.4 Wavelength ()im)

Fig. 1. Commercially available cw laser diodes in the 600-1600 nm wavelength range. The

data bars represent families of laser products as advertised by a number of different manufacturers.

291

TN-33
292 R. W Fox et al^

tuning for typically one fourth of a nanometer, followed by a transition (mode-hop)

in wavelength to another mode. Tuning with injection current (-0,01 nmymA) e.xhibits similar behavior, and hysteresis is often observed at the mode hops in either case. Thus it is difficult to ensure that a given diode will reliably reach all wavelengths near

the nominal. This problem is usually overcome by either having a sample of several diodes to choose from or by using optical feedback to control the lasing frequency.

A common example of the latter method is the use of a diffraction grating in an extended cavity laser, as discussed in the next section. A second example is the use of a small mirror placed close to one of the laser facets, effectively forming an etalon

which forces the laser to operate in a specific longitudinal mode [9], The mode may

then be wavelength tuned with current or temperature; success in achieving complete

wavelength coverage near the nominal has been reported [10.11] with this technique.

These comments on tuning apply mainly to single-mode Fabry-Perot type diodes as opposed to distnbuted-feedback (DFB) lasers. DFB lasers have superior tuning

characteristics (but restricted wavelength range), typically tuning -10-12 nm with

temperature before encountering a mode-hop. Unfortunately, they are as yet widely

available only in the 1.3 and 1.55 |xm telecommunications band wavelengths and are

relatively expensive.

Many of the diode lasers available now are designed to operate in a single

longitudinal mode. This is of course preferable for absorption measurements, since power in side modes (off the absorption feature) does not contribute to the signal but

does add shot noise and mode competition noise to the detected photocurrent. A

laser running with significant power in more than one mode may exhibit greatly

increased amphtude noise (AM) due to mode competition [12]. Lasers with a few

modes running usually have the highest level of mode-partition-noise whereas those

with either a large number of modes or one mode have low AM noise. In fact the detected photo-current of a typical near-i.r., single-mode laser driven with a good low

noise current source will show amplitude fluctuations that are within a factor of 10 of

the shot noise limit in the frequency range above 100 kHz. These low intrinsic noise

levels are just one of the reasons that diode lasers are attractive as spectroscopic

sources. Many groups have reported impressive sensitivities in detecting atoms and molecules

by exploiting modulation techniques to take advantage of the low amplitude noise

exhibited in the higher frequency range [13-15]. Several studies have compared

detection sensitivities obtained at different modulation frequencies [16-18]. A separate

approach is to work closer to the base-band frequency range but use negative electronic

feedback to suppress the amphtude fluctuations inherent at the lower frequencies [19,

20]. With these methods it is possible to approach the shot noise limit and greatly

enhance the signal-to-noise ratio in absorption detection. It is important to realize that the low intrinsic noise does not, however, mean that diode lasers are free from

systematic amplitude changes as their frequency is swept or modulated. The linear power vs. current curve exhibited by diodes leads to a sloping baseline if direct detection is used. A more serious problem that limits detection sensitivities is the

residual AM that accompanies frequency modulation.

The spectral linewidth of even a typical solitary diode laser is quite narrow with

respect to Doppler or atmospheric pressure-broadened lines. AlGaAs, near-i.r. lasers operating well above threshold have linewidths in the 10-40 MHz range. Some highpower long-cavity solitary lasers have reported linewidths of a few megahertz. The

visible AlGalnP lasers exhibit broader linewidths. typically 150 MHz. For high

resolution work a number of methods have been developed to achieve greatly reduced

linewidths. The most common method is to employ an extended cavity (see Section

2), but resonant optical feedback from a confocal cavity has also been successfully

used in a number of experiments [21, 22]. Techniques to achieve substantially narrower

linewidths than the hundreds of kilohertz afforded by standard extended cavities are discussed in a number of articles [23-25].

TN-34
The diode laser as a spectroscopic tool 293

Peltier Cooler/Heater

Grating

0.6 NA Objective

Output

Fig. 2. Basic form of an extended cavity diode laser system. In this example an optical grating

in a Littrow configuration is used as a wavelength selective tuning element. A piezoelectric element (not shown) on the grating assembly provides for fine wavelength sweeping. Angular sweep of the output beam with tuning is eliminated with a mirror attached at 90° to the grating as shown.

2. Methods for Broad Tuning

At NIST most of our work with diode lasers has concentrated on high resolution

spectroscopy of narrow atomic resonances, but there is a much wider spectrum of

applications that will require broadly tunable sources without stringent linewidth

requirements. For most of these applications it is also necessary to reach a specific

wavelength of interest. This may require some form of wavelength-selective optical

feedback in order to extend and even fill in a laser's tuning range [26]. The most

common method is to use an optical grating for selective feedback in an extendedcavity-diode-laser (ECDL) configuration. An example ECDL system is shown in Fig. 2. Extended cavity lasers are relatively simple, and up to now many groups have

been building these systems for their own use. The number of users and applications can be expected to increase as more advanced commercial diode laser sources become

available. Many variations on the basic ECDL scheme are possible, and a variety of different tuning elements have been used, although gratings seem to be the most common.

Grating tuning of ± 20 nm from the nominal diode wavelength is possible with neari.r. AlGaAs lasers without changing the diode temperature. However, this represents

rather optimum results, dependent upon the device and laser anti-reflection (AR)

coating. A tuning range of ± 10 nm is more common.

Other important characteristics of a diode used in an extended cavity include a moderate loss of power and a much narrower Hnewidth as compared to the solitary

diode. The usable single-frequency, tunable output power can be as low as 30% of

the rated single-mode diode power. This is due in part to a change in the output

couphng, but is also often due to lower injection currents required to stay in a stable operating regime. The observed linewidth will depend upon the cavity length as well

as the lasers' environment. Although the fundamental Hnewidth decreases as the square of the cavity length, low frequency (^ 100 kHz) environmental and 1// noise soon become the dominant frequency noise contributions. This leads to observed

linewidths that range from tens to hundreds of kilohertz depending mostly on

construction and external perturbations. We also note, that with this sort of frequency

fluctuations, the "linewidth" that one measures depends on the observation time of

the measurement, and is thus somewhat ill-defined [25]. With simple grating feedback and average anti-reflection coatings an ECDL will not

usually tune single-frequency with no mode hops over the laser's entire gain bandwidth.

This is due to a number of factors, paramount of which is the residual output facet reflectance of the laser chip (as discussed below). For single-frequency scanning

without mode-hops it is necessary to synchronously scan the extended cavity length

with the pass-band of the wavelength selective element(s) (such as a grating and/or

etalon). Several techniques that accurately change the cavity length together with the

TN-35
294 R, w. Fox et al.

grating angle have accomplished single-mode tunmg over 1000 GHz [27, 28]. Again

these are exceptional results rather than typical, which might show scanning from 10

to 100 GHz depending on a number of factors. Special regimes of ECDL operation called "autostabilization" also exist [29] where

single-mode tuning ranges of more than 20 GHz are possible with just cavity length

changes and no change of the grating angle. This broad tuning is the result of

semiconductor device non-linearities that help to maintain single-mode operation. We

note that this is typical for -5-20 cm long ECDLs, and is in fact single mode scanning

of about ten free spectral ranges of the extended cavity with no mode hops.

ECDLs generally operate in a straight-forward, single-mode manner but it is also easy to reach unacceptable operating conditions (multimode or chaotic) that depend

on parameters both internal and external to the laser. Spectroscopic applications are

particularly sensitive to outside factors that affect the laser's frequency, such as stray

optical feedback, temperature and current fluctuations, and even vibrations for ECDLs.

A more fundamental cause of instabilities in ECDLs is the fact that the laser is a coupled-cavity system with potentially incommensurate boundary conditions [30-32].

In applying these lasers we have to find ways to avoid regions of instabihty. Three

techniques are useful to increase the stable operating regions of grating tuned lasers: (1) operate at slightly lower powers, (2) use short extended cavities [33,34] and

(3) improve the AR coatings on the output facet so that the system is dominated by

the grating feedback. All of these techniques are helpful in achieving broad tuning

and stable operation even though they have the inherent disadvantages of low output

power, broader linewidths, and complications of additional processing respectively. A

compelling reason to strive for very low output facet reflectance (R < 10"^), is that with such AR coatings it is possible to obtain complete spectral coverage over the

laser's gain profile without having to change the laser's temperature [35]. Fortunately, many of the higher power lasers that are commercially available already

have some AR coating on their output facet. These lasers will work as supplied in ECDL systems, but they can also be improved. For our extended-cavity systems we

generally add additional coatings to the output facet in order to reduce the reflectance. After some experience we routinely achieve facet reflectances of I0~^ on ordinary

commercial lasers. Lower reflectance is possible but is difficult to achieve because of a number of factors; not the least of which is the fact that we lack detailed knowledge

of the structures and materials of specific commercial lasers. In addition, most of the

lasers come from the manufacturers with coatings already on the facets. We typically find single layer \J4 coatings with reflectance of -5% for high power lasers and \J2

with 30% reflectance for low power devices. These coatings are for passivation as well

as tailored reflectance and generally make it more difficult to reach very low reflectance with additional coatings. Quite a lot of information on coating lasers is available in the literature [36-39], particularly with regard to making optical amplifiers. Our

coatings at NIST achieve good reliable results with common optical coating materials

(Hf02, AI2O3 and SiO) and techniques (thermal, e-beam and RF-sputtering) [40].

3. Higher Power .\nd Access to Other Spectral Regions

The main problem in using diode lasers for spectroscopic applications is the limited

number of wavelengths that are accessible. Using only semiconductors based on various

derivatives of GaAs and InP, the wavelength coverage could be nearly complete over

the spectral region from 630 nm to 1.7 \i.m. In practice this is not the case (see Fig. 1) because the manufacturers concentrate production at certain wavelengths. Other

wavelength regions may be accessible with different semiconductor materials; for example blue-green diode lasers based on ZnSe have been reported recently [7]. Also some research laboratories have produced i.r. lasers in the 2.0-2.3 |xm region based on GalnAsSb [41, 42]. These spectral regions will see important spectroscopic

applications if development is successful and if there is sufficient commercial demand

to support production.

TN-36
The diode laser as a spectroscopic tool 295 An alternative to direct semiconductor sources for other spectral regions is to use diode lasers in conjunction with nonhnear optical techniques to generate new

wavelengths. This requires high intensity beams and materials with large nonlinear

coefficients. Until recently we have been limited to a few tens of milliwatts of singlemode power from diode lasers in the best cases. Consequently, resonant cavities are

useful to increase the intensity and thus generate nonlinear products more efficiently.

The future promises to make this much easier with new higher power lasers and better nonlinear materials.

Two basic techniques have demonstrated high-power single-mode single-frequency

operation of semiconductor diode lasers. These are (1) injection-locking of high-power

broad-area lasers with a single-mode laser [43-45] and (2) single-mode masteroscillator-power-amplifier systems (MOPAs) [46]. The distinction between these two

methods is just whether the power device operates above or below threshold without

the master laser's input. Injection locking can be done with low power single-mode master lasers to lock the frequency of the higher power (hundreds of milliwatts)

semiconductor laser sources. MOPA systems have been reported with pulsed outputs

of 27 W and cw outputs of up to 2 W. At present many of these high power systems

are relatively expensive which we expect to change with time. The question remains

of how broad a wavelength coverage will be available with these very high power

systems.

There are already a few nonlinear optical techniques that work particularly well with diode lasers. One of these is the fortuitous match of the wavelength of the highpower AlGaAs lasers and 90° phase-matching in potassium niobate (KNbOs). High

efficiency second-harmonic generation (SHG) at fundamental wavelengths from about

840 to 930 nm can be achieved in this material with temperature tuning of the crystal

from about -40 to 180°C [47]. As much as 40 mW of blue light has been generated

with a diode laser and KNb03 [48]. Using less infrared power, others [49, 50] have

reported conversion efficiencies from diode power to blue hght in the range of 1-10%.

These results are consistent with our experience in using a ring buildup cavity that generates 30 mW of blue light at 423 nm for 150 mW of diode laser power. The main

Umitation in our system is the spatial mode of the diode laser that limits the coupling

efficiency of the laser into the ring. Improvements in the mode matching and laser power should increase the overall conversion efficiency since KNbOs is capable of

producing much higher blue light powers [51]. A promising technique that has demonstrated excellent results for SHG and sumfrequency mixing is the fabrication of periodic domains in the crystal structure [52-54].

This involves reversing properties of the crystal on a periodic basis, which allows the fundamental and harmonic waves to retain a constructive phase relationship over much

longer distances than would otherwise be the case. Yet another approach to tunable

blue light from semiconductor sources is to phase-match for sum-frequency mixing of

a diode laser output with the second harmonic of a diode pumped Nd-Yag laser. Output powers of 4 mW at 459 nm have been demonstrated [55] in this manner, using

a monolithic KTP resonator and approximately 30 mW of input power from each

laser. Nonlinear mixing to longer wavelengths has also been recently demonstrated using

diode lasers. Using difference frequency mixing Simon [56] and collaborators have

generated tunable mid-i.r. light from diode lasers. The i.r. output powers are low at present (~3 nW), but the principle of difference frequency generation from diode

laser sources has been proven. In this case the non-linear materials that seem the most appropriate are AgGaS2 and AgGaSe2, which can potentially cover the wavelength

range from 4 to 18 jxm.

TN-37
296 R. W Fox et al.

10 ppb Cs

20 30 40 Time (s)

so 60

Fig. 3. Diode laser-enhanced ionization (LEI) signal obtained with 10 ppb of Cs in water. The

laser was tuned to the strong peak of the Cs D^ hne. The limiting background noise was

contamination by easily ionized elements in the burner equipment, which led to an increased flame background current.

4. Applications

4.1. Atomic spectroscopy

The use of diode lasers as spectroscopic sources in the setting of analytical chemistry

for trace detection of atoms has been reported by several groups. Absorption,

fluorescence and ionization-based methods have all been demonstrated, using a variety

of atom sources including flames [57], a graphite furnace [58, 59], a thermionic diode

[60], a glow discharge [61], and a thermal filament [62]. Along these lines we have used diode lasers for the detection of trace levels of Rb

and Cs in solutions using laser-enhanced ionization spectroscopy (LEI) in a flame. Our very elementary set-up consisted of a water-cooled cathode in a premixed

air-hydrogen flame with a pneumatic nebulizer for liquid sample introduction [63, 64]. The cathode was held at a potential of about -100 V with respect to the burner, and

the laser beam chopped and directed through the flame. Resonant absorption on the

Si/2 to P3/2 transition in the alkahs changes the charge density in the flame since there

is a differential ionization potential between the S and P states. This causes a change

in the current flowing between the burner and the cathode, which is phase sensitively

detected at the laser chopping frequency.

Figure 3 shows the signal obtained with a water solution of Cs at a concentration

of 10 ppb (an atomic density of approximately 10* cm~^ in the flame). The baseHne

is obtained by aspirating deionized water into the flame. An extended-cavity grating

tuned laser was used, which produce 1.9 mW of output power with a 2 mm diameter

beam that was passed through the flame twice. In this example the use of a relatively narrow linewidth (-100 kHz) extended-cavity laser as opposed to a solitary diode

laser is not significant (other than for ease of tuning) since the absorption is homogeneously broadened by atmospheric pressure. The laser beam was positioned

for maximum signal, approximately one beam diameter below the flame electrode. Limits of detection for Cs and Rb were calculated by extrapolating the signals

obtained for 10 ppb solutions down to the concentration that would give a signal equal

to three times the r.m.s. noise level of the deionized water baseline. A 1 s time

constant on the lock-in amplifier was used for these measurements. For Cs at 852 nm

a limit of detection of 0.25 ppb was achieved. For Rb at 780 nm the limit of detection

TN-38
The diode laser as a spectroscopic tool 297 was 0.3 ppb. The limiting source of noise at the detection limit was contamination by

easily ionized elements in the burner equipment, which led to an increased flame

background current. For both Cs and Rb, the sensitivity was diminished by the high

fraction of normal flame ionization of these low ionization potential elements, which

reduces the atomic fraction available for LEI. In the case of Cs, approximately 90%

of the population is thermally ionized before laser excitation. Our limit of detection for Rb compares well with that reported by Havrilla [65],

using LEI in the air-hydrogen flame with a dye laser pumped by a cw krypton ion

laser. They reported a limit of detection of 0.09 ppb, with a laser power approximately

two orders of magnitude higher. The laser system used in that work was considerably more complex and expensive, requiring 30 kW of power and cooling water at 50 1 min~^ No comparable LEI measurement of Cs has been reponed. Future development of LEI using diode lasers depends on expansion of wavelength availability.

Several attempts were made to make LEI measurements of other elements using

transitions beginning from excited states with near-i.r. wavelengths where diode lasers were available. The very low Boltzmann population of the lower levels of these

transitions in the flame prevented our observation of LEI.

4.2. Molecular spectroscopy

The detection of molecular species instead of constituent atom concentrations is often of interest. Although in general the molecular absorption bands in the near-i.r. are weak compared to the vibrational bands at longer wavelengths, the room

temperature operation of the near-i.r. lasers makes them very attractive nevertheless. Many groups have apphed the L3 and L5 p.m lasers to probing various molecular

resonances, including CH4 [66, 67], C2H2 [68], CO2 and CO [69], NH3 and H2O [70],

HCN [71], HDO [72] and HCl [73]. Particularly important due to its role in atmospheric

pollution is NO2, which has been investigated by several groups [14, 15, 74, 75]. In some on going work at NIST in collaboration with NOAA [76], red diode lasers are being used to detect NO3 radicals. This molecule plays an important role in atmospheric photochemistry. In the stratosphere its photochemistry affects ozone

depletion, and it acts as a strong oxidizer in the troposphere. NO3 has a strong

electronic absorption band at 662 nm that can be reached with commercial red diode

lasers. In these experiments a soUtary diode laser is used to detect the time-dependent

concentration of NO3 in an excimer-laser photodissociation experiment. Good detection

sensitivities are achieved with simple direct absorption measurements (noise-limited

absorption sensitivity —10"* at DC with a 200 kHz detection bandwidth). This

corresponds to about 5 x 10^° NO3 molecules/cm-' and aim single-pass absorption

path length. The detection sensitivity could be improved with: subtraction of residual

low-frequency AM noise, or high frequency modulation, or multi-passing the absorption

cell. This experiment illustrates the potential for using very simple diode laser systems

to detect reactive molecular species that play an important role both in the laboratory

and in the earth's atmosphere.

5. Summary and Projections

The rapid growth in the field of diode laser spectroscopy is the direct result of the

simplicity and good performance that can be achieved with inexpensive commercial

semiconductor lasers. These lasers are becoming more readily available, and in addition we now have a better understanding of how to control them and apply them to a variety of scientific and technical problems. With some acknowledged limitations we

can now have low cost, portable, tunable, low noise, narrow linewidth laser sources

at a number of wavelengths. Very high power devices are becoming available which

will extend the opportunities with diode lasers in part by accessing other wavelength

regions. Important spectroscopic and analytic roles are recognized for both simple

soUtary laser systems as well as broadly tunable extended cavity laser systems. Areas

of precision optical physics such as atomic clocks, frequency and length standards.

TN-39
298 R. W. Fox et al. and laser cooling of atoms are also being strongly affected by diode lasers. The

capabilities of these systems continues to increase as does the number of applications.

The time is not far in the future that we will consider diode laser systems as standard

research tools.

Acknowledgements—We acknowledge the important contributions to this work by N. Mackie. T. Zibrova, A. S. Zibrov, J. H. Marquardt, J. S. Wells and the NOAA group [76], Our thanks to U. Simon for information about difference frequency generation. This work has been supported in pan by the NASA

upper atmospheric research program, and the Air Force office of scientific research.

(1(2

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[7

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[9

[10

[11 [12

[13 [14

[15 [16

[17

[18

[19 [20

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[23 [24

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[26

[27

[28

[29

[30

[31 [32

[33 [34

[35 [36

[37 [38

[39 [40

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[72] T. Ohshima and H. Sasada, J. Mole. Spec. 136, 250 (1989).

[73] A. C. Stanton and J. A. SUver. Appl. Opt. 27, 5009 (1988).

[74] M. Gehrtz. G. C. Bjorklund and E. A. Whittaker, / Opt. Soc. Am. 82, 1510 (1985).

[75] J. Reid, M. El-Sherbiny, B. K. Garside and E. A. Ballik, Appl. Opt. 19, 3349 (1980).

[76] R. J. Yokelson, J. B. Burkholder, A. R. Ravishankara anc C J. Howard, National Oceanic and Atmospheric Administration Aeronomy Laboratory, Boulder, Colorado.

TN-41
A CPW PHASE-LOCKED LOOP FOR DIODE-LASER STABILIZATION'

L. D'Evelyn*, L. Hollberg% Z.B. Popovic''

^ National Institute of Standards and Technology

Boulder, Colorado 80303

^ Department of Electrical and Computer Engineering

University of Colorado

Boulder, Colorado 80309-0425

ABSTRACT

A low-cost, phase-lock circuit for slaving an extended-cavity

diode laser to a stabilized reference laser has been developed.

Grounded coplanar waveguide and surface mount technology

have been used. An internal mixing stage allows continuous

tuning of the laser difference frequency between 5 MHz and

1 .5 GHz. Absolute phase locks exceeding 8 hours have been

demonstrated.

INTRODUCTION

Precise control of the frequency and/or phase of diode lasers opens up a wide variety of scientific and commercial

applications. Consequently, several research laboratories have

recently demonstrated phase-stabilized diode-laser systems

[1-4] similar to the one presented in this paper. The diodelaser phase-lock circuit described below has been developed

to address a number of scientific applications at the National

Institute for Standards and Technology. These applications

require both extreme stability and frequency control of extended cavity lasers and include: high resolution spectroscopy, optical frequency synthesis, and laser cooling

and trapping. In combination with new, commercially

available extended-cavity lasers [5], our phase-lock servo could also be integrated into numerous commercial

applications, such as laser ranging and distance measurements

and coherent communications systems. In the future, this circuit may serve as a fundamental building block for a tunable optical synthesizer. A precision optical synthesizer

would allow optical heterodyne and RP conversion techniques

to be applied to the optical regime.

OPTICAL PHASE-LOCKED LOOP

The phase-lock circuit serves to slave an extended-cavity

diode-laser to a highly stable reference laser. Grounded

coplanar waveguide (CPW) on a FR4/G10 circuit board and

* Contribution of NIST, not subject to copyright

surface mount technology have been employed for all microwave and RP sections to maximize performance while minimizing cost. Only low-cost, commercial-grade parts have

been used in the design. Figure 1 shows a photograph of the 11.7 X 14.2 cm (4.6 x 5.6 in) circuit.

The basic operation can be understood as follows (Figure 2). The beat note between the two lasers is detected with a fast photodiode, then input to the microwave mixer. An external synthesized LO source allows continuous tuning of the difference frequency between the two lasers between 5 MHz

and 1.5 GHz. The filtered IF signal is first converted to an ECL signal and then detected by a low phase-error ECL

phase/frequency detector [6-7]. High speed op-amps perform

active loop filtering on the low pass filtered error signal and

load compensation for the combined FM response of the current source and extended-cavity laser. The final error signal is fed back to the slave laser via two ports: a wide

bandwidth channel (DC to = 1 MHz) to the laser's injection

Figure 1: Phase-lock loop for diode-laser stabilization. CPW lines and surface mount technology

allow input frequencies to 1.5 GHz.

Proc. of 1994 IEEE MTT-S International Microwave Symp., San Diego, CA (1994).

TN-42
current controls fast frequency jitter, while a high dynamic

range channel (DC to = 2 kHz) to a piezo-electric transducer (PZT) adjusts the laser's cavity length to compensate for drift.

The design requirements were determined, in part, by our

desire to have a simple system that allows offset frequency sweeps from near DC to at least 1.5 GHz with a resolution of < 1 Hz. The_J^. GHz. specification was dictated by our requirement of complete spectral coverage and the 3 GHz free specUaJ-xangcofJiie Fabry-Perot reference cavity that we use tsJQCJfthe master laser. The maximum tuning range is jiot

fundamentally limited, but is rather naturally set by the

availability and cost of microwave synthesizers capable of < 1 Hz resolution. The grounded CPW lines on the low-cost FR4/G10 printed circuit board perform adequately to the required 1.5 GHz. Extension of the sweep range beyond 1.5 GHz, however, would require more accurate transmission-line design equations and/or improved circuit board fabrication. Alternatively, external microwave mixing stages can be used

to extend the maximum offset frequency. Special Schottky

diodes can be used as harmonic mixers, for example, to detect beat notes between near-IR diode lasers to frequencies higher

than 600 GHz [8].

LOB r n

BEAT A

NOTE ^ {>-h8>

ECL 60 MHz LPF COMPARATOR J

ECL

PHASE/FREO DETECTOR

TTL XTAL OSCLLATOR Ml^CL°N55mz

GAM i LOAD

COMPENSATION

LASER ^

CURRENT

j—w-p..^ PAD f^^

PIEZO <

LOOP FLTER

PEZOELECTRIC SERVO L J

Figure 2: Block diagram for phase-locking extendedcavity diode lasers. The 55 MHz IF signal is detected by an ECL phase/frequency detector. High-speed op-amps provide loop filtering and

compensation.

30 MHz to about 50 kHz and allows tuning of the laser's wavelength/frequency. The narrowed spectral characteristics of the extended-cavity greatly facilitate locking and control of

the slave laser.

Figure 3: Extended-cavity laser. The rear facet of the laser-diode and the holographic diffraction grating form an "extended cavity." The

narrowed spectral characteristics greatly

facilitate locking the slave laser.

No additional auto-locking features have been added to the

electronics. The PZT provides a 20 GHz continuous tuning range and can easily be used to tune a laser within the -20 to +100 MHz capture range of the electronic circuit. Broader stepwise tuning can be accomplished by mechanical

rotation of the grating. Laser mode-hopping remains the greatest impediment to initially locking the long (50 cm)

cavity lasers (free spectral range = 300 MHz). An etalon in the extended laser cavity or a clamp on the maximum

correction current [3] should solve this complication.

Figure 3 shows the extended-cavity laser [9-10] controlled by

the phase-servo circuit. A commercially available diode-laser (with the output facet AR coated) is used together with a high-efficiency holographic diffraction grating [11] in a Littrow geometry. The rear facet of the diode and the grating

form an "extended cavity." Cavity lengths ranging from 6 to 50 cm have been used in our experiments. The PZTadjustable mirror provides a precise adjustment of the optical

length of the cavity. Optical feedback of the first-order beam

from the grating narrows the linewidth from greater than

APPLICATIONS

The laser phase-lock circuit is now used in two experiments

with different laser setups. In both cases, the servo-loop

bandwidth of about 1 MHz results in robust phase-locks.

Locking times exceeding 8 hours have been demonstrated.

Unfortunately, the sensitive nature of the experimental laser systems preclude longer tests. Both laser systems will be

described to illustrate the flexibility of the phase-lock circuit. Plans to include this circuit in a laser cooling and trapping

experiment will also be outlined.

TN-43
The first experiment uses two phase-locked AlGalnP lasers at 657 nm for high resolution spectroscopy of calcium

(Figure 4). Phasejocking allowsthe stability of_a nontunable reference laser to be transferred to the offsex^-tuaable slave

laser. Extremely narrow laser linewidths are required to observe and lock the laser to narrow saturated-absorption

signals. The "master" extended-cavity laser, electronically locked to a stable Fabry-Perot cavity, has a fast linewidth of only 500 Hz and a residual frequency jitter of 5 kHz [12]. Figure 5 shows a spectral plot of the locked beat note between the two lasers. In future experiments the master laser will be referenced to a very high Q (= 10'°), stable FabryPerot cavity. Such a laser system locked to the calcium

resonance could serve as a high accuracy transfer standard of

optical wavelength/frequency.

CONCLUSION

The CPW phase-lock circuit described in this paper has

consistently demonstrated robust locks of several hours

duration between diode-lasers. Measured results in two

different laser systems illustrate the circuit's potential for advancing many scientific experiements, especially those involving high-resolution spectroscopy and laser cooling and

trapping. This low-cost, highly reproducible circuit could also be used in many additional applications. For example, the PLL could be utilized to reduce the number of oscillators required in an optical frequency synthesis system [15-16]. In short, the laser phase-lock circuit promises future viability of coherent optical applications of diode lasers.

In the second example, the phase-locked loop (PLL) locks an AlGaAs extended-cavity laser (792 nm) to an Ar* laser pumped Ti: AI2O3 laser. Here, the offset frequency of 47 GHz

is established using an external harmonic mixing stage. This

system is being used by J.C. Bergquist of NIST for experiments on laser-cooled

Hg"^ [13]. Because of the ground-state hyperfine structure

splitting, laser cooling of Hg'^^ requires two lasers (at 194 nm) separated by 47 GHz. The 194 nm is generated by

summing the 792 nm light with the second harmonic of an Ar* laser line (514 nm).

ACKNOWLEDGEMENTS

We thank J.L. Hall, J.C. Bergquist, and R.W. Fox for important contributions to the development of this technology.

This work was supported in part by the Air Force Office of

Scientific Research.

Future plans include incorporating the phase-lock circuit into a laser system for high resolution spectroscopy of laser- cooled, trapped cesium atoms. As demonstrated by Kasevich

et al [14], this can lower the effective temperature of the cooled cesium atoms from about 500 \iK to less than 1 |iK.

TO EXPERTCNT

LASER CURRENT SOURCE

T LO—

I

EXTEM3ED

CAVITY LASER

TO PEZO

NTEGRATOR ^

TO ELECTRO-OPTC CRYSTAL

Figure 4: Laser setup for high resolution calcium spectroscopy. Multi-hour pha,se- locks between two AlGalnP diode-lasers have routinely been demonstrated.

TN-44
RL 0.00 dBm nKR si^FRQ 9E7 kH: RTTEN 10 dB 10.00 dB/OIU

-33.05 d3

nflRKER ^

PCS P^

927 kHz -33.05 dO

CENTER E1B.000 MHz RB 10.0 kHz "UB 3.00 kHz SPAN 5.000 HHz

ST 500.0 msec

Figure 5: Beat-note between locked diode-lasers. The

circuit's loop bandwidth of about 1 MHz

results in robust phase-lock

REFERENCES

[1] H.R. Telle, H. Li, "Phase-Locking of Laser Diodes",

Electronic Letters, vol. 26, pp. 858-859, 1990.

[2] M. Ohtsu, K. Nakagawa, M. Kourogi, and W. Wang,

"Frequency Control of Semiconductor Lasers", J. Appl. Phys., vol. 73, no. 12, pp. R1-R17, June 1993.

[3] G. Santarelli, A. Clairon, S.N. Lea, and G.M. Tino,

"Heterodyne Optical Phase-Locking of ExtendedCavity Semiconductor Lasers at 9 GHz", Optics

Communications, vol. 104, pp. 339-344, January 1994.

[4] S. Schwartz, J.L. Hall, K. Gibble, D. Weiss, "Robust

Phase-Locking of Diode Lasers", submitted to JOSA B 1993.

[5] "NIST, SDL Develop High-Power Laser", Optics &

Photonics News, pp. 50, January 1994.

[6] Analog Devices AD9901 Product Data Sheet,

Norwood, MA.

[7] W. Egan and E. Clark, "Test Your Charge-Pump

Phase Detectors", Electronic Design, vol. 12, pp. 134-137, June 1978.

[8] S. Waltman, A. Romanovsky, J. Wells, R.W. Fox, and

L. Hollberg, "Precise Optical Frequency References and Difference Frequency Measurements with Diode

Lasers, Proc. Soc. Photo.-Opt. Instrum. Engrs., vol. 1837, pp. 386, 1992. (Note: range now extended to at least 620 GHz)

[9]

[10]

[11]

[12]

[13]

C. Wieman, L. Hollberg. "Using La.ser Diodes

Atomic Physics", Rev. Sci. Instrum., vol. 62.

pp. 1-20, January' 1991.

for

[14]

[15]

[16]

M. Ohtsu, Highly Coherent Semiconductor Lasers. Artech House, Norwood MA. 1992.

M.S. Soskin and V.B. Taranenko, "Holographic TotalInternal Reflection Selector for Tunable Lasers", Soviet Journal of Quant. Elect., vol. 7. no. 2, pp. 298-304, 1977.

A.S. Zibrov, R.W. Fox, R. Ellingsen. C.S. Weimer.

V.L. Velichansky, G.M. Tino, and L. Hollberg. "High

Resolution Diode Laser Spectroscopy of Calcium",

submitted to Appl. Phys. B 1993.

J.C. Bergquist, W.M. Itano, D.J. Wineland, "Laser

Stabilization to a Single Ion", Proceedings of the International School of Physics «Enrico Fermi»,

edited by T. Hansch and M. Inguscio, North Holland,

Amsterdam, July 1992.

M. Kasevich and S. Chu, "Laser Cooling Below a Photon Recoil with Three-Level Atoms", Physics

Review Letters, vol. 69, pp. 1741-1744. 1992.

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle,

"Optical Frequency Standards", IEEE Trans, on

Instrumentation and Measurement, vol. 83, no. 2, pp. 524-532. April 1989.

K. Nakagawa, M. Kourogi, and M. Ohtsu. "Proposal of a Frequency-Synthesis Chain Between the Microwave and Optical Frequencies of the Ca

Intercombination Line at 657 nm Using Diode Lasers", Appl. Phys. B, vol. 57, pp. 435-430, 1993.

TN-45
Amplitude Modulation on Frequency Locked Extended Cavity Diode Lasers

R. W. Fox, L. D'Evelyn, H. G. Robinson, C. S. Weimer, and L. Hollberg

National Institute for Standards and Technology, 325 Broadway, Boulder, CO, 80303

Abstract The increase in low frequency ampUtude noise on several extended cavity diode lasers was measured when frequency or phase lock servos were applied using the injection current as the feedback channel. The AM noise increase inside the FM servo bandwidth is approximately

that expected from the suppression of frequency noise uncorrelated with the inherent amplitude

noise of the laser.

I. Introduction

The noise characteristics* of semiconductor diode lasers are relevant to a number of applications,

including communications and spectroscopy. The noise can be quite complex due to optical feedback and

the well known AM to FM coupling, and is an area of active research.^ Diode lasers are often used with

extended cavities to provide wavelength tunability and to narrow the linewidth. It is now common practice

to use active (electronic) control systems to suppress portions of either the AM or FM noise. The coupling

between AM and FM in the semiconductor laser complicates the noise characteristics in these active

feedback control systems. For example, in many systems the feedback path is via the laser's injection

current, which simultaneously alters both the amplitude and frequency of the laser. In previous experiments we studied some of the limitations of using active electronic control of the

injection current to suppress AM noise on the output of an extended cavity diode laser (ECDL).^ The

fundamental shot-noise-limit may be approached (fig. 1), but only by using most of the laser output for the

feedback control channel. The photo-current signal-to-noise (s/n) of the useful experimental beam reaches

a maximum in between the extremes of using most of the light for the experiment (in which case the

technical AM is not suppressed) or for the servo

control (in which case the shot s/n level is relatively

high). In some applications both the AM and FM

laser characteristics are important. For instance in

very high-resolution spectroscopy, it is desirable to have a narrow linewidth laser with low AM noise, zero frequency drift, and precise tunability. Towards

this goal we have phase-locked (with a tunable offset

frequency) an ECDL to a stable low-drift reference

ECDL, by using feedback to the slave injection

current. However the injection current feedback path

cannot also be used for AM control, and furthermore

the FM control adversely affects the laser's AM. In

this paper we report measurements of the power

fluctuations when frequency control is employed.

In the case of a frequency servo acting

through the injection current, the output power is affected primarily by the injection current

c

c

oo

Q.X

14

12

10

o ^

(/)<u 2 >on

<

m

o 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Transmission to Feedback Channel

1.0

Fig. 1 The performance of an AM feedback loop to the

injection current of an ECDL. The residual AM noise of the experimental beam photo-current is plotted versus the beamsplitter transmission to the servo detector.

Proc. SPIE Conference, vol. 2378, pp. 58-62 (1995).

TN-46
fluctuations. More generally, for any method of feedback the changes induced in the FM noise by the servo

will also be mapped to amplitude noise by any element in the extended cavity that has a frequency

dependent gain or loss. The amount of FM to AM conversion is dependent on the dispersion of the

longitudinal mode selector (usually a diffraction grating), and the lasing wavelength with respect to the mode

selector, as well as the chip facet reflectance and alignment effects.

When diode lasers are built into extended cavities of moderate lengths (=10 cm), the inherent

frequency noise is reduced so that a relatively low bandwidth (=1 MHz) electronic feedback loop is sufficient

to frequency lock the laser.'* At low Fourier frequencies piezo-electric elements may be used to adjust the

cavity length, while higher bandwidths require feedback either to the laser injection current, or to intra-cavity

tuning elements.^ Most often the slow piezo feedback loop is necessary to keep the higher bandwidth loop

in the center of it's dynamic range.

We can make an estimate of the AM induced by a frequency control servo that uses the injection

current by assuming no correlation between the inherent FM and AM fluctuations of the ECDL. In this case

the induced AM wiU add in a root mean square fashion to the inherent amplitude noise. We can estimate

the induced power fluctuation AP(/) (in mW/VHz) from the frequency noise density S- (f) that is suppressed when the loop is closed. The dependence of the output power with current Ap/Ai, and the

dependence of the laser frequency with injection current Av/Ai are used to estimate the induced AM. The

ratio Ap/Ai is assumed flat with frequency, which is justified by noting that we are only interested in the

effects within the servo bandwidth (relatively low frequencies). We write

AP(J)= =- (1)

as an estimate for the maximum increase in the output power noise spectrum within the servo bandwidth.

The increase of the relative intensity noise (RIN) is then [AP(/) /PJ^.

n. Experiment

The increase in the AM noise due to frequency control loops using current feedback was measured

in two separate experiments. A Littrow type extended cavity laser at 657 nm was frequency locked to an

optical cavity by electronic feedback to the injection current and the changes induced in the AM spectrum were measured. Secondly, two grazing incidence ECDL's were slaved to reference lasers with a phase-lock

by feeding back to the slave injection current ports.^ The changes induced in the AM spectrum of the slaves were measured.

The Littrow laser was built using an anti-reflection coated 3 mW laser, and frequency locked to the

optical cavity with a Pound-Drever-Hall RF lock scheme.^ The RF modulation was applied with an external

modulator resonant at 20 MHz. In the case of injection-current locking the feedback bandwidth was

approximately 500 kHz. The power versus injection current had a slope of 0.09 mW/mA, as shown in figure

2. Also shown in figure 2 is the dc change in frequency with injection current Av/Ai, measured at different

bias current levels by sweeping the reference cavity and monitoring the correction signal to the injection

current. The laser would lock for a frequency interval which could easily be determined with the help of

the modulation sidebands, and during this interval the change of the injection current correction signal was

measured. The laser cavity length was 12 cm, and the power output at the normal operating point of 1/1,=

1.16 was about 1.0 mW.

TN-47
<

E\NI2

<

120

100

80

60

40

20

5

E

At this bias-current level the complex

frequency dependence of Av/Ai was measured out to 4 MHz with a network analyzer. The response was

flat out to several hundred kHz, decreasing 10 db in

magnitude by 1.5 MHz. The phase of the response

was nearly constant to 100 kHz, but lagged by

approximately 90° at 1.5 MHz.

An alternative method for frequency

stabilization of this laser was also used for

comparison. An electro-optic modulator (a 1 cm

aperture ADP crystal) was used in the extended laser

cavity^ to provide a feedback path to the cavity

length that is independent of the injection current

(and hence to first order the power). For this path

the feedback bandwidth was approximately 1 MHz.

The AM noise with the laser unlocked and

locked with the two feedback paths is shown in

figure 3. The laser was operating with a dc injection current of 1/1,= 1.16, and Av/Ai = 40 MHz/mA when

the locked data was recorded. No change in AM is observed with feedback to the intra-cavity EO crystal.

1.3

1.2

1.1

1.0

0.9

0.8

0.7

1.08 1.22

0.6

1 .10 1.12 1 .14 1.16 1.18 1 .20 Injection current l/lth Rg.2 The ou^t power of the Littrow AlGalnP extended

cavity laser above threshold and the dc change in frequency

with injection current, Av/Ai. The frequency response was

also measured (see text).

-40

locked

10 10 10

Frequency (Hz)

10

Fig. 3 The low frequency amplitude noise spectrum of the Littrow AlGalnP ECDL. The upper-most trace is the

laser locked to an optical cavity by feedback to the injection current The lower trace is the amplitude noise of the unlocked laser, which on this scale does not change when the laser is locked to the cavity with the intra-cavity

electro-optic crystal. The detector noise level is indicated, and the dc photo-current is ^210 \jA.

In the second experiment, a slave ECDL was constructed with an anti-reflection coated 5 mW red

diode laser. A diffraction grating with 1800 1/mm was used at a grazing incidence angle of about 85

degrees, and the cavity length was approximately 8.8 cm, resulting in a free spectral range of 1.7 GHz.

The output power at the normal operating point was about 2 mW. This laser was phase-locked to the

Littrow laser discussed above, and the beat note is shown in figure 4. A significant AM noise increase in

TN-48
the frequency region near the phase-lock

servo's unity gain point was observed, i.e. where the noise shoulders appear in the beat

note. An example of this induced AM is shown in figure 5. The other AM measurement of a phase-locked slave was also with a grazing

incidence type ECDL, except the laser was a 100 mW AlGaAs laser operating at 792 nm.

This ECDL was slaved to a Ti: Sapphire laser

with a feedback bandwidth of approximately

800 kHz. The phase-lock on the AlGaAs

laser was implemented with a similar degree

of phase margin, and a similar increase in the

slave's AM noise spectrum was observed.

-45

Fig. 4 A beat note between the 657 nm Littrow laser and the phase-locked slave. The offset frequency is approximately 200

MHz. The trace is over a 10 MHz band, and the noise peaks are

at 1.5 MHz. The noise close to the carrier peak is -60 dBc.

65

85

i

9 -105

-125

-

1 1 ^^1

-

-^— detector noise level unlocked

H4*^(jN.^^

-

1 1

Io=360nA

1

-

10^ 10

Frequency (Hz)

10

Fig. 5 The AM noise of the phase-locked slave laser (upper trace). The broad noise peak at 1.5 MHz corresponds to the increase in phase noise at the FM servo's unity gain frequency. The peak in the phase noise at this point, combined

with the decreasing sensitivity of the laser frequency to injection current, acts to increase the AM noise.

m. Discussion

The frequency locked ECDL noise data (fig. 3) clearly shows a broad-band increase in the AM noise

level, and further increases at distinct frequencies. The FM noise spectrum typically exhibited by an ECDL

operating in the single-mode regime has a 1/f fi-equency dependence, reaching a spectrally-white noise-floor

at approximately 100 kHz. Structural resonances will cause narrow-band frequency noise, and the FM servo response to this narrow-band noise shows up as AM peaks in the locked spectrum. A noise floor of

approximately 10"* Hz^/Hz in the frequency noise density was measured in the 12 cm long ECDL.' The

network analyzer measurement indicates that the current to frequency transfer function value at dc (Av/Ai=

40 MHz/mA) is valid at 100 kHz. The induced AM noise can then be estimated at 100 kHz.

TN-49
Approximately 50% of the laser output was incident on the AM noise detector, and the detector

responsivity at 657 nm was measured to be 0.43 mA/mW. Using equation (1), at 100 kHz the estimated

maximum photo-current noise level for the induced AM is -86.3 dB|iA/VHz.

The data of fig.3 shows good agreement with this level, even though we have used a very simplistic

model. The current servo-loop bandwidth used was about 500 kHz, and the data shows the locked AM noise

approaching the unlocked case at about this frequency.

The AM noise of the phase-locked slave laser (figure 5) displays a large increase in the frequency

region near 1.5 MHz. The phase margin of the f^ loop at the unity gain frequency was such that the beat

note between the two lasers had broad noise sidebands centered at approximately 1 .5 MHz from the carrier

peak. Only the dc value of the transfer function Av/Ai(f) of the slave was measured, which was 40 MHz/mA

at the operating current level.

However as the laser chip is of the same type^ and the extended cavity is a similar length as the

Littrow laser, we assume that the transfer function Av/Ai(f) of the slave is similar to that of the Littrow laser. If so, the 10 dB decrease of Av/Ai(/) together with a 20 dB increase in the phase noise near the FM servo's unity gain point would account for the increase in the AM noise observed in figure 5.

rv. Summary

An increase in the AM noise when an extended cavity diode laser is frequency or phase locked by

feedback to the injection current was measured. The increased AM was consistent with a simple model that

relates FM noise to AM through the sensitivity of the laser frequency, and power to injection current. The

most prominent increases in the AM noise were from low frequency mechanical vibrations that the I^ servo

suppressed, and from the servo gain peaking near the bandwidth limit, which is accentuated in this frequency

region by a decrease in Av/Ai, the dependence of frequency on the injection current.

References

1 . Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Ed. Y.

Yamamoto, Wiley & Sons (1991), and references therein.

2. J. Kitching, R. Boyd, A. Yariv, and Y. Shevy, "Amplitude noise reduction in

semiconductor lasers using weak optical feedback with dispersive loss," Opt. Lett. 19, 1331

(1994).

3. L. Hollberg, R. Fox, N. Mackie, A. S. Zibrov, V. L. Vehchansky, R. Ellingsen, and H. G.

Robinson, "Diode lasers and spectroscopic applications," in Tenth International Conference on

Laser Spectroscopy, Eds. M. Ducloy, E. Giacobino, and G. Gamy, World Scientific, 347

(1992).

4. H. R. Telle and H. Li, "Phase-locking of laser diodes," Elect. Lett. 26, 858 (1990).

5. R. W. Fox, H. G. Robinson, A. S. Zibrov, N. Mackie, J. Marquardt, J. Magyar, L. W.

Hollberg, "High sensitivity spectroscopy with diode lasers," SPIE Vol. 1837, 360 (1992).

6. L. D'Evelyn, L. Hollberg, and Z. Popovic, "A CPW phase-locked loop for diode laser

stabilization," IEEE MTT-S Int. Microwave Symp. Digest, San Diego, 65 (1994).

7. R. W. P. Drever, J. L. HaU, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H.

Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31,

97 (1983).

8. The lasers used were Toshiba TOLD9421 and TOLD9321. This is mentioned only to allow repeatability of experimental results, and does not imply endorsement of these products.

Contribution ofNIST, not subject to copyright

TN-50
CHAPTER THREE

High-Accuracy Spectroscopy

with Semiconductor Lasers:

Application to Laserfrequency Stabilization

LEO HOLLBERG, V. L. VELICHANSKY,* C S. WEIMER/

and R. W. FOX

United States Department of Comnrtefce, National Institute of Standards and

Technology, Boulder, Colorado

3.1 INTRODUCTION

In this chapter, we focus on the performance of diode lasers used for

high-precision spectroscopy, with an eye toward optical frequency

and wavelength references in the visible and near-infrared spectral

region. A brief summary is given of the existing optical references and

the major physical processes that limit the performance of optical

•Currently, Lebedev Institute of Physics, Moscow, Russia. tCurrently, Ophir Corp., Littleton, Colorado.

Frequency Control of Semiconductor Lasers, Edited by Motoichi Ohtsu. ISBN 0-471^13412 © 1996 John WUey & Sons, Inc. 73

TN-51
74 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

frequency-wavelength standards. Present state-of-the-art high-stability diode laser systems and laser technology are outhned. Particular

attention is given to our present results in high-resolution diode-lascr

spectroscopy of calcium and the prospects for the future. For many years there has been the promise of future optical

frequency standards that could augment or even replace the now

traditional microwave frequency standards. In terms of reproducibility, the best proven standard is still the microwave frequency stan- dard based on the cesium ground state hyperfine structure. The

present performance of the best cesium standards is a frequency

uncertainty of (^v)/v % 1 x 10"'*. None of the proposed optical

standards in the visible region have been tested at a level that is comparable to this. Nevertheless, projected performance is quite

impressive, and significant progress has been made in the past few

years by using cold trapped ions and neutral atoms.

Prior to the present era of laser cooling and trapping, the highest

resolution that had been achieved in the visible was the work of

Barger and Bergquist, who in the late 1970s demonstrated optical

Ramsey-fringe widths of approximately 2 kHz on the 657-nm calcium

transition [1,2]. Now with laser cooling, Bergquist and collaborators

have demonstrated an approximately 50-Hz-wide optical transition

at 563 nm in a single, trapped mercury ion [3]; Hansch's group has

demonstrated approximately 7-kHz-wide lines at 486 nm on the very

important hydrogen IS to 2S transition [4]; Ertmer's group has

detected approximately 2-kHz-wide lines on the 457 nm transition in magnesium in a magnetooptical trap [5]; and Riehle and collaborators have also shown approximately 2-kHz-wide resonances on the

657 nm line in calcium in a magnetooptical trap [6]. In the visible, the most common wavelength-frequency reference is the Ij-stabilized helium-neon laser at 633 nm. This system provides

very good performance, has been carefully studied, and is well understood at the approximately 3-kHz level of precision. Achieving

much higher performance with the 633 nm helium-neon seems improbable, given the width of the transition (^5 MHz), the cell- dependent systematic shifts, and the amount of time that has gone

into optimizing the system. However, it is an excellent stabilized laser and its widespread use is not only because of its high accuracy, but

TN-52
INTRODUCTION 75

also because of practical considerations: it is compact, relatively low

cost, easy to use, and it lases in the visible. The excellent performance

is due in a large part to the many years of developmental work that

have been invested throughout the world.

Relative newcomers to the field of high-performance optical refer- ences are diode lasers stabilized to the rubidium 2-photon transition

at 778 nm [7], and the I^-stabilized frequency-doubled Nd:YAG-laser

at 532 nm [8]. Both of these systems look very promising and are already competitive with existing standards, but neither has been

developed, nor tested to the degree that pnor systems have, so the

ultimate performance is yet to be determined.

In the infrared spectral region there are two other well-estabhshed

standards for quality frequency references, the CH^-stabiUzed helium-neon laser at 3.39 /mi, and the OsO^-stabilized COj lasers at 10 /im. In the best cases, frequency stabihties have been reported at the level of a few hertz. In terms of fractional frequency uncertainty,

the CH4 system is now known by optical frequency measurements to

((5v)/v % 3 X 10"^^, and the OSO4 system is known to 50 Hz, ((5v)/ v%2xl0-'2[9].

For a new optical reference to be useful, it needs to provide

something that cannot be achieved with existing standards. For

example, it could feature better stability, higher accuracy, access to

different spectral regions, lower cost, portability, or better reliability, or it might be more easily realized in the lab or transferred to other

locations. For a combination of these reasons, diode lasers are beginning to play an important role in high-precision spectroscopy.

They are obviously lower cost and more compact than other tunable

laser sources, but importantly they give us access to different spectral

regions. Until recently, the best stabilized lasers have either been dye

lasers or gas lasers. Because of their transportability the gas lasers have served the role of wavelength and frequency- transfer standards.

But stabilized gas lasers have only limited tunability. so we have had

to rely on a few fortuitous overlaps of narrow molecular hnes with

common gas-laser wavelengths. With some limitations, tunable diode

lasers now give us the opportunity to choose the best atomic or molecular transitions and, at the same time, have the option of a

transportable instrument. Some of the interesting possibilities that

TN-53
76 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

are now being pursued with diode lasers are the alkaline earth atoms

(calcium, strontium, and barium) and ions (Ca* and Sr"^).

3.2 LIMITS TO SPECTROSCOPIC ACCURACY

In evaluating the merits of various optical references, it is easy to focus on the linewidth and signal-to-noise ratio that can be obtained

with a given transition. These are cleady important parameters, but

they do not necessarily guarantee high accuracy. More often than

not, the accuracy, and even the stability, are limited by systematic

effects, rather than the signal size, the fundamental noise processes, or the linewidth. The effects that limit the precision and accuracy in optical frequency references are discussed in many places [9]. An

early article by Hall [10] provides a clear insight into the physical

processes that limit the performance of high-resolution saturatedabsorption spectroscopy. Precise theoretical treatments of many of

the important effects were done by Borde and collaborators [11-14].

In the highest performance neutral-atom systems, we are almost

always limited by velocity-dependent shifts and broadening due to limited observation times. Even with the thermal velocity reduced by

laser coohng and trapping, gravitational acceleration limits the

practical observation times. Trapped ion systems in contrast have

essentially unlimited observation times but are limited in signal size by a relatively small number of ions. With neutrals we can use large

numbers of atoms and hence have large signals, but we do not have

unperturbed atoms that can be observed for times much longer than

approximately 1 s. Some of the important physical effects that limit the resolution and

accuracy in optical spectroscopy are listed in Table 3.1. For any

specific system, one effect or another may be the dominant one. But

because of optical phase uncertainties and second-order Doppler

effects, it is clearly difficult to push beyond 10~ '^ fractional frequency

uncertainly using fast atoms. Surprisingly, even at low pressures,

collision with other atoms actually limit the accuracy that can be

achieved in many frequency standards. For example, at the highest

levels of accuracy, collision effects are significant even in cesium

TN-54
DIODE LASER TECHNOLOGY 17

atomic clocks, some microwave trapped-ion systems, and Ij-stabilized lasers.

3.3 DIODE LASER TECHNOLOGY

3.3.1 Extended Cavity Diode Lasers The sensitivity of diode lasers to optical feedback, can be an advantage for stabilizing the laser frequency. When used judiciously, optical

feedback can easily narrow the linewidth of a solitary laser from tens of megahertz to tens of kilohertz (extended cavity diode lasers,

ECDLs, are a good example of this). In the case of ECDLs (as with optically locked lasers), the natural

wavelength of the solitary laser chip is independent of the extended

cavity; it is a function of temperature, injection current, and semiconductor properties. For stable ECDL operation at a specific

wavelength we have to suppress the modes of the solitary chip with

good antireflectance coatings, or we must rely on stable current and

temperature control to keep the natural frequency of the laser chip

within the control range of the grating. This control range depends

critically on the dispersion, the feedback level, and the reflectance of

the output facet. For a typical ECDL with a facet reflectance of a few

percent, the control range of the grating might be approximately

10 GHz, whereas the solitary mode spacing might be approximately

120GHz. Thus we are faced with the fact that the ECDL laser can

still jump modes if the environment is not stable or as the laser ages.

If, on the other hand, the facet reflectance is reduced with a broadband coating to a power reflectance of 10"*, the grating can

control the wavelength over the entire gam curve (-^40nm for AlGaAs lasers), and broad single-mode scans are possible.

3.3.2 Amplitude Noise

Even though the amplitude-modulated (AM) noise level on diode

lasers is very low, it does increase at low Fourier frequencies. Because we are greedy for a low signal-to-noise ratio in our experiments, we

TN-55
TABLE 3.1 Typical Uncertainties in Optical Frequency-Wavelength References

Dependence,

or Frequency

Effect Uncertainty 5(jj/ioq Hot Atoms" Cold Atoms* Comments

Uncertainty in (Ny)-"' Amplitude uncertainty improves

size of signal with number of atoms N, and

linewidth y Natural linewidth y/<^o 10" to 10'* 10" to 10'* Frequency uncertainty improves

with (Dq and l/y First -order k'\/(Oo 10* 10-10 Need Doppler-free method!

Doppler • 10'^ * 10" Uncertainty is method dependent

Second-order v'/c' 10'^ 10" Requires knowledge of velocity

Doppler * 10" * lO'" distributions or cold atoms

Ramsey method A</>k • y/iOQ 10" 10" Optical geometry dependent and

interaction * 10" • 10" relative Ramsey-phase A4> dependent

Wavefront v/{WoOJo) 10" 10" Geometry dependent. Need flat curvature 10" to 10" 10" to 10 "

wavefronts and low velocities Power (y/coo)N/(i + ///.) Need low intensity / relative to broadening saturation intensity /, Light shift. (tx„EyTio^hHio-(o^ lO'to 10'* <0 10" to 10'* Significant for atoms with

(a.c.-Stark shift) hyperfine structure and for

Gas lens L/(kwl)

d.c. E&B field shifts Stark (lif^Ey/hcjo

Zeeman |i, B/hoj^

Collisional Broadening {Na^vmVtOo)

Shift {Na.v)/{yto„)

Transit (dAWoOIo)

broadening

Adjacent yJ{u)o-o)JoT

transition yl/(<oo-oiy

line pulling Recoil shift hwjmc^

Gravity acceleration.g

Broadening 9"'<"W

Frequency shift ( wjgy^k • g/(t»o

10" 'Mo 10

lO'^to 10-'^ 10-*/T

10" '/T^

10" '"/Pa 10" "/Pa

10- '»

10" '"to <io-'*

lO"

10""

10'"

10" 'Mo 10"

?

?

10""

10- '"to <10"

10"

10'^

10"

'«toio-''

two-photon transitions. Need

low power and isolated lines

Significant in cells. Depends on

geometry, absorption path length

L, wavelength 1/lc, and mode

size tVo State dependent

Lower lying states and S states better Use Arti = 0, or first-order field-independent transition

State and collision partner

dependent; cross section a, magnitude often unknown

Requires large beam waits Wg

or low velocities v Perturbation by nearby lines with transition rates y„. Need well-isolated lines Depends on atomic mass m

Horizontal laser beam. Need

large mode w^ or fountain

SOURCE: Parts of this table have been adapted from a similar table presented by J. L. Hall [10], and some of the data comes from

Sergslock et al [S] and Kistcrs et al. [6]. 'Listed here arc the general dependencies of the varioui physical effects, and some typical values found in neutral-atom spectroscopy.

Trapped-ion systems have similar effects, but typical values can be quite different. *The magnitudes of the fractional frequency shifts and broadening coefficients are indicated by 0. and the uncertainties designated

with a •. These values are not for a specific system, but are given for order-of-magnitude comparisons.

TN-56
80 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR UKSERS

frequently try to reduce the noise even further. One approach is to sample the laser's amplitude noise with a beam splitter and photodetector, then to feedback to the injection current with an electronic servo to reduce the amplitude noise. This has the appearance of

simplicity and does work, but the results depend on the degree to which the sampled beam represents the experiment beam. In the limit where the sampled beam is simply some fraction of the experiment

beam, the fluctuations of the experiment beam, expressed in decibels

above the shot-noise limit, may be reduced to -10 log 5. S is the

fraction of the power sampled (e.g., with a 50% beam splitter, a servo can put the expteriment beam noise within 3dB of the shot-noise

limit) [15]. To reliably attain this level of noise reduction, care must

be taken to ensure that the sampled beam accurately represents the

experiment beam. Many lasers are packaged with an internal photodiode, which is used to detect the beam out of the laser's rear facet. Caution should be exercised in using this signal for the sampHng

channel, because it is not an accurate representation of the intensity

fluctuations on the front facet beam.

3.3.3 Frequency Stabilization

Because diode laser cavities are small and facet reflectances are low,

the residence time for a photon in the cavity is short ( :$ 1 ns), which

results in a substantial amount of frequency noise and hence broad

spectral linewidths. Linewidths of solitary diode lasers can range

from approximately 10 MHz for the near-infrared AJGaAs lasers, up

to 200 MHz for the visible AlGalnP lasers. Good discussions of the

various contributions to diode laser noise are given in Yamamoto et

al. [16-19] .Of particular interest is the paper by Telle [19], which

gives a clear and concise overview of diode laser frequency noise and

stabilization. Also Zhu and Hall [20] give a good detailed description

of how laser frequency noise contnbutes to a laser's spectral line shape.

Quite a lot of useful information about the spectral quality of

diode lasers can be inferred from the measurements of the fre- quency-noise spectral density, an example of which is shown in Figure 3.1. The frequency noise on solitary lasers is largest at low

frequencies and decreases monotonically toward higher frequencies.

TN-57
DIODE LASER TECHNOLOGY 81

N

s

ea

«

(A *Sz

Frequency (Hz)

FIGURE 3.1 Frequency-noise spectral density of diode lasers. The fre- quency noise of an ECDL was measured by using the transmission fringe of a Fabry- Perot cavity as a frequency discriminator. The bandwidth of the

cavity fringe is responsible for the roll-off in the measured noise near 8 MHz.

The data was taken with an InGaAlP laser (657 nm) and was adapted from

Fox et al. [21]. For comparison, the approximate noise level of a solitary

diode laser is indicated as a sohd line.

reaching a plateau that extends from approximately 1 MHz out to many gigahertz. For typical AlGaAs lasers the level of this plateau in the frequency noise is on the order of lO^Hz^/Hz. In the case of

extended cavity lasers the spectral characteristics depend on the

cavity length, optical feedback ratio, and mechanical stability of the

cavity [16-19, 21]. The frequency-noise density is reduced by a large

factor (typically in the range of 100 to 1,000) from the noise level of a solitary laser. However, we still find that the laser's frequency

fluctuations are largest at low frequencies, and then they level off to a plateau at intermediate frequencies (a typical spectral density is approximately 10*HzVHz between 50kHz and 100 MHz). For ext- ended cavities approximately 10 cm long, the fast linewidth will be near 50 kHz. Low-frequency fluctuations of the cavity length that will modulate the inherent fast linewidth, effectively broadening it The

low-frequency vibrations show up as resonant peaks in the frequency

TN-58
82 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

noise as can be easily seen in Figure 3.1. As with any oscillator that

exhibits increasing noise at lower frequencies, the actual hnewidth

will depend on the averaging time that is used to measure it, making

linewidth statements very ambiguous.

It is very clear from the Figure 3.1 curves that the frequency noise on solitary diode lasers is large in magnitude and broadband. The

ECDLs have a much lower level of frequency noise, but it still extends to fairly high Fourier frequencies. As is usually the case, the

magnitude of the frequency noise diverges toward low frequencies.

Fluctuations in carrier density, localized temperature fluctuations,

and mode competition noise are believed to be the main contributions to the frequency noise at low frequencies; whereas spontaneous

emission [enhanced by a factor of (1 -l-a^), with 2 < a < 12] contnbutes throughout.

In the literature we often find simple theoretical models (such as the phase diffusion model) of diode laser frequency noise, which are then used to declare that diode lasers have Lorentzian line-shapes.

This is not our experience in the laboratory. Actual diode laser line shapes are complicated by fundamental interactions that introduce

excess frequency noise (some mentioned above) as well as other less interesting, but important, technical details (like even small amount

of optical feedback) that dramatically alter the spectral character of

diode laser light. The lasing frequency of ECDLs is also perturbed by

thermal and vibrational changes in the cavity length, which lead to peaks in the frequency noise as can be seen in Figure 3.1. Only in hypothetical cases where the frequency-noise spectral density depends in a simple way on Fourier frequency can the line shape be

described by simple analytical functions. In most practical diode laser systems, the frequency noise does not satisfy these conditions and the

resulting line-shape is complicated.

As mentioned above, we are usually faced with the situation that even the laser's line width depends on how long an observation time we use to measure it. Nonetheless, it is still useful to have some

simple, qualitative, one- or two-parameter measure of the spectral

width of a laser. Because the actual linewidth depends on the

observation time, one approach is to define a fast linewidth and then

lump fluctuations that occur at lower frequencies into frequency jitter

TN-59
DIODE LASER TECHNOLOGY 83

and drift (which are often conveniently neglected). Although imprecise, one prescription for determining the fast linewidth comes from

using the spectrally flat portion of the frequency-noise spectral

density (e.g., the region between approximately 50 kHz and 5 MHz in Figure 3.1). It turns out that, if the frequency noise is spectrally flat, then the line shape is really Lorentzian and the Unewidth is given by

Av = nSfif). So applying this definition to the ECDL data in Figure

3.1 gives a fast linewidth of approximately 30 kHz, and a fast linewidth of approximately 15 MHz for the solitary laser. Alternative

methods to measure the hne shape are to make a beat note with a narrow Hnewidth laser, or, in the case of spectrally broad lasers, an

optical delay Hne can be used for a self-heterodyne measurement.

These techniques can also be used in the time domain by measunng

the amount of time it takes for the optical phase to become

ambiguous by n radians; this serves as another indicator of laser linewidth.

The usual models of semiconductor laser gain predict that the

plateau of frequency noise at high frequencies extends out to the

laser's relaxation frequency (typically a few GHz) and then drops

rapidly toward higher frequencies [16]. Although we have not

carefully measured the frequency (phase) noise out to very high

Fourier frequencies, we have inferred from noise measurements in atomic absorption experiments that the frequency noise density can

be almost flat to frequencies as large 9 GHz away from the laser

carrier. This admittedly indirect measurement implies that these

lasers AlGaAs Fabry-Perot lasers operating at 7//,^ * 3.0) have

frequency noise that is almost spectrally flat (for frequencies between

1 and 9 GHz) with a spectral density that is approximately — 40dBj

in a 1 MHz bandwidth. Although it has not been proven, we could

speculate that this level is dominated by the background spontaneous

emission in the spatial mode of the coherent field of the laser. To have a spectrally narrow laser that is also precisely tunable

relative to a stable reference frequency, we follow the general approach developed some time ago by J. L. Hall and others. With this method, a nontunable Fabry-Perot cavity is used to stabilize the

frequency of a reference laser; a second laser is then phase-locked to the reference laser but with a frequency offset. The frequency offset is

TN-60
84 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

Beatnote Frequency (1 MHz/Div)

FIGURE 3.2 Beat-octe between phase-locked diode lasers operating at 657 nm. Curve shows the log of the power spectral density of the beat note between the reference laser and the frequency offset laser when the system

is phase locked. Noise close into the carrier is down -60dB, from the peak.

The resolution bandwidth is 1 kHz and the horizontal axis has a full span

of 10 MHz. The frequency offset of the phase-locked laser, relative to the

reference laser, is continuously tunable between 10 MHz and 2 GHz with

sub-Hertz precision.

provided by a RF-microwave synthesizer, which thus allows precise

tunability of the laser frequency. Figure 3.2 shows the beat note

between the reference laser and the tunable phase-locked ECDL

under locked conditions.

To achieve the highest accuracy in the lock of the reference laser to the Fabry-Perot cavity we use the Pound-Drever-Hail optical-heterodyne technique. Frequency-modulated sidebands at approximately 20 MHz are generated with an external, resonant, phase

modulator. Two feedback loops are used to frequency stabilize the

reference ECDL, a low-frequency path to a piezo-crystal (PZT) that

controls the ECDL length, and a high-frequency path to an AD*P

phase modulator within the laser cavity. Servo-loop bandwidths of

TN-61
DIODE LASER TECHNOLOGY 85

approximately 1 MHz result in a fast linewidth of approximately

500 Hz for the stabilized reference laser. More details on the stabil- ized reference laser can be found in Fox et al. [21]. In the laser phase locked to the reference laser, there are also two

feedback channels, a slow one to a PZT, and a faster feedback

channel to the laser's injection current [22, 23]. In this ECDL, the

injection current tunes the frequency of the laser with a coefficient of

approximately 40MHz/mA. Unfortunately, changes in the laser's injection current also change the laser's output power, with a

coefficient of approximately 0.09 mW/mA. It was not clear a priori

whether the injection-current loop for frequency stabilization would

reduce the ampHtude noise or increase it. In studying a few of these

ECDL systems, we have found that using the injection current to

stabilize the laser's frequency always degrades the laser's amplitude

noise. This can be understood from the tuning coefficients and the

relative magnitudes of the frequency- and amplitude-modulated noise on ECDLs. The diode laser's amplitude noise is very small, but the

frequency noise is significant. Thus, the injection current that re- moves the frequency noise causes an increase in the amplitude noise.

The dependence of the relative phase between the amplitude and the

frequency modulation for ECDLs (also a function of Fourier fre- quency) is an interesting question, but it is almost irrelevant(becausc

of the difference in magnitude) in the usual regime of frequency

stabilization by using the injection current. An example of this effect

is the degradation of the amplitude noise of the red diode laser when

it is phase locked to the reference laser. Figure 3.3 shows the

amplitude noise of the laser with, and without, the phase lock. This

amplitude-modulation data corresponds to the same lasers and

conditions as the beat note curve in Figure 3.2. In an analogous manner to locking to a Fabry- Perot cavity, an ECDL can also be stabilized to an atomic or molecular resonance

such as absorption, fluorescence, saturated absorption, or an optogalvanic signal. The easiest way to lock to the peak of a resonance

is to use a modulation lock [24]. In this case, the laser's frequency is modulated by dithenng either the PZT that controls the cavity length or the injection current. The optical power transmitted through the resonance is detected, demodulated with a locking amplifier, and fed

TN-62
86 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

-3U 1 I 1 tU^ phase-locked

-70

1 wv/V^^VW*^ \i - N

X

-90

-J^*^^^'^^ ••^^rv^Wv^^ittL,it ^i \ .

QQ

"O -110

detector noise level unlocked

IWx^

-130

1 1

1

-

10^ 10 10

Frequency (Hz)

FIGURE 3.3 Amplitude-noise of the phase-locked laser for the lock conditions shown in Figure 3.2. The phase-lock servo to the injection current of

the ECDL removes the frequency noise, but it simultaneously degrades the

laser's amplitude noise. The upper curve shows the amplitude noise on the phase-locked laser when the system is phase locked, and the lower trace shows the intrinsic amplitude noise on the laser when the system is not

locked. The equivalent shot-noise for the detected photo current of 360 /iA

is approximately — lOOdBj^A/^/Hz. Adapted from Fox et al. [23].

back to the PZT to control the laser frequency. These lockin systems

that require modulation of the laser's frequency are often con- taminated by unwanted amplitude modulation that comes along with

the frequency modulation. In many cases, this is not significant, but

the problem has to be addressed for high-accuracy frequency control.

For some applications that require a spectrally clean output beam

the frequency modulation can itself be a problem. In these cases, it is possible to lock to the side of a resonance without using modulation,

or it is sometimes possible to derive an error signal by modulating

the atomic resonance rather than the laser's frequency. A good

example of this is the use of an a.c. magnetic field to Zeeman

modulate atomic resonances.

TN-63
CALCIUM SPECTROSCOPY WITH DIODE LASERS 87

3.4 CALCIUM SPECTROSCOPY WITH DIODE LASERS

The calcium intercombination line at 657 nm has been thoroughly

studied using dye lasers with atomic beams for use as a wavelengthfrequency reference [2, 6, 25]. The availability of red diode lasers at

this wavelength, and also high-power diode lasers at 846 nm has

stimulated renewed interest in calcium as a wavelength-frequency

reference [26]. The whole system can be greatly simplified by use of

diode lasers; with reduced size and power requirements a compact,

transportable, transfer standard seems feasible. The 846 nm lasers can

be frequency-doubled efiBciently to produce the 423 nm light that is required for laser cooling and trapping. Similar research efforts and

results in high-resolution spectroscopy of calcium with diode lasers have also been reported from the PTB group in Germany [27], and

by Kurosu et al. at NRLM in Japan [28].

We have been working to improve diode laser technology to the

performance level required for very-high-precision spectroscopy of

calcium. This includes precise tuning, amplitude noise reduction, and

frequency stabihzation. The laser that probes the 657 nm hne needs

to be narrower than the width of the transition, and so requires

precision in the frequency control that is approximately :$ 1/lOth of

the 400 H2 natural width, i.e., approximately 40 Hz. Our present

system does not achieve this required level of performance, but rather

has a fast linewidth of 500 Hz, and residual frequency jitter that causes laser frequency excursions of approximately 5 kHz at acoustical frequencies. In addition, the system is presently plagued by

frequency drifts in the reference cavity that amount to approximately

1 kHz/s at the optical frequency. The jitter and the drift are solely due

to instabilities in the reference cavity. The laser frequency is locked

tightly to the cavity resonance and so follows the fluctuations

inherent in the cavity resonance frequency. With a better cavity and

using the vibration isolation and stabilization techniques that have

already been demonstrated with dye lasers [3], we can expect to reach the required diode laser frequency stability.

At 657 nm, the diode lasers are a little challenging (large initial Hnewidths and relatively low powers) but most of the difficult problems have now been solved. In terms of ultrahigh-resolution

TN-64
88 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

spectroscopy, we have not done quite as well with the diode lasers as

the previous results with dye lasers, but the diodes are fairly new and

improving rapidly. The semiconductor lasers themselves do not seem

to present a fundamental limit, and we expect equal performance will be achieved with diodes or dye lasers. The one remaining challenge

is that we would like to have more optical power than is readily

available from single-frequency tunable ECDLs. This is particularly

relevant for time-domain Ramsey spectroscopy of cold-trapped

atoms. In this case, the optimum power at 657 nm will be approximately 50 mW deHvered to the atoms in a repetitive pulse sequence.

The power Umitation of diode lasers should not be a serious

long-term problem, because there are at least two possible solutions:

(a) higher power single-mode lasers in the red appear to be on the near term horizon, and (b) we can use injection locking of broadband

lasers to increase the usable single-mode power.

We have constructed two very different vacuum systems to do the

saturated absorption in calcium. In earUer work [26], we developed

a high-flux atomic beam-cell that allowed detection of the saturated

absorption signal by optical heterodyne saturation spectroscopy.

That system is relatively compact and achieves good spectral resol- ution with an exceptionally good signal-to-noisc ratio. The detected

saturated-absorption signal was not large (approximately 1 % of the

laser power), but the Unewidth was narrow (approximately 60 kHz

FWHM) and, using heterodyne detection, gave a background noise

that was near shot-noise limited. The Unewidth and noise-limited

signal-to-noise ratio gave a projected frequency stability of

3 X 10" ^*t~^'^. With this level of short-term stability, it may even be

possible to lock directly to the calcium resonance without the use of

any reference cavity.

The second calcium system that we constructed is a more tradi- tional atomic-beam optical Ramsey-fringe spectrometer. Although

the present system is not designed to be portable, it is reasonably

compact (total length -- I.Om), has good power efficiency (requiring

only 20 W for the beam source), and the vacuum is maintained with

a smgle 201/s ion pump. With this system, we have observed

four-zone saturated-absorption, optical Ramsey-fringes with high

sensitivity on the 657 nm line (Figure 3.4). To capture the narrow

Ramsey-fringe structure and at the same time display the whole

TN-65
CALCIUM SPECTROSCOPY WITH DIODE LASERS 89

Calcium Saturated Absorption

Ramsey Fringe

•

o

c

•

«

so

3

IE

-—

.

/"\ 40 KHz Jr^

\, -y \^ /

Expand^

(50 X) v^ vV/ ^^\ A^VKs^

8 MHz \ /

^^

\l^

Laser Frequenqf

FIGURE 3.4 Calcium Ramsey-fringes taken with a diode laser at 657 nm. The lower of the two traces is a broad scan over the entire calcium resonance in the atomic beam. The laser interaction region in the atomic

beam was configured in the usual way for four-zone, saturated-absorption

Ramsey-fringes. Expanding this same data set by a factor of SO along the horizontal axis produces the upper trace, where the Ramsey interference

fringes now becomes apparent. In this example, the width of the central Ramsey-fringe is 40 kHz.

Doppler-broadened lineshape this spectra was taken with a scan time

of 10 s but used a detection bandwidth of 10 kHz. Lower detection

bandwidths give very clean Ramsey-fringe lineshapes.

Higher spectral resolution is achieved in the traditional atomicbeam system than is obtained in the beam-cell system because of the

longer interaction time provided by the Ramsey interrogation

method. However, there is some penalty in the signal size. The

narrowest lines that we have observed up to now are 10 kHz FWHM,

TN-66
90 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

which is sufficient to resolve the photon-induced atomic recoil sphtting of 23 kHz. Unfortunately, as is well known, the Ramsey Hne

shape becomes quite complicated in the higher resolution limit where

the effects of atomic recoil, second-order Doppler, and Ramsey-fringe

resolution are all interconnected [29]. A very important simphfication of the spectrum (usually at the expense of a more complex

apparatus) can be achieved by eliminating one of the atomic recoil components as has been described in previous work [5, 11, 25, 30].

However, the limitation in the accuracy of this system will be the same as that previously realized in other fast atomic-beam systems.

The ultimate accuracy will likely be limited by imprecise knowledge

of the atomic velocity distribution and hence the second-order

Doppler shift and also by the atomic velocity-dependent opticalphase sensitivity of the Ramsey interferometer. Projected accuracy of

these systems is approximately 500Hz, (5v)/v~ 1 x 10"^^.

Real improvements in the frequency accuracy require low-velocity

atoms. Fortunately laser cooling and trapping of calcium has already

been demonstrated with dye lasers, and, recently, high-resolution

spectra of cold neutral atoms have been achieved [5, 6]. It is also now

feasible to do the trapping and cooling of calcium with frequencydoubled diode lasers. We have built a doubling system that uses KNbOj in a resonant ring-cavity. Starting with an 846-nm grating-tuned extended-cavity laser, we injection lock a 150mW, single-,

spatial-mode, diode laser. The resulting high-power beam is col- limated and sent through an anamorphic prism pair and optical

isolator before it is mode-matched into the ring build-up cavity. The

resonance of the ring is electronically locked to the laser frequency.

With 110 mW of 846-nm light incident on the ring we have been able

to generate as much as 45 mW of useful output at 423 nm. This

should be sufficient for laser cooUng and trapping of calcium. Thus

far, we have demonstrated one-dimensional transverse-cooling of the

calcium beam, which enhances the Ramsey-fringe signal by a factor

of two to three.

It is also interesting that some other transitions in calcium are

accessible with diode laser sources. Some of these may play an

important role in improving the performance of this standard in the

future. For instance, we have used a 672-nm diode in conjunction

with the 423-nm light to probe the calcium 'D(4s3d) to 'P(4s5p)

TN-67
REFERENCES 91

transition. This gives us additional information about (and may

enhance) the 423-nm coohng process and may also be useful to suppress the large background (657 nm) emission that is present in the cold trapped-atom systems. Other transitions in calcium are also

compatible with diode lasers, including the 612-nm transition that can be used to suppress a recoil component. Similarly, 423- or 444-nm light, from double diodes, could be used to improve the

trapping or to suppress a recoil component.

ACKNOWLEDGMENTS

Our thanks to A. Zibrov, L. D'Evelyn, H. G. Robinson, J. Aman and

J. Bergquist for important contributions to the results presented here.

REFERENCES

1. R. L. Barger, J. C. Bergquist, and D. J. Glaze, High-resolution Saturated

Absorption of the 'Sq-^Pi Calcium Transition in an Atomic Beam. J. Opt. Soc. Am. 68(11), 1634 (1978).

1 J. C. Bergquist, R. L. Barger, and D. J. Glaze, High resolution spectroscopy of calcium atoms. In Laser Spectroscopy IV (H. Walthcr and K. W. Rothc, cds. p. 120. Springer-Verlag, Berliii, 1979.

3. J. C. Bergquist, W. M. Itano, and D. J. Wineland, Laser stabilization to a siaglc ion, in Frontiers in Laser Spectroscopy (T. W. Hansch and M.

Inguscio, eds.), p. 359 North-Holland Publ., Amsterdam, 1994.

4. T. W. Hansch, Precision spectroscopy of atomic hydrogca At. Phys. 14,

63 (1993).

5. K. Sengstock, U. Sterr, J. H. Muller, V. Rieger, D. Bettermann, and W.

Ertmcr, Optical Ramsey spectroscopy on laser-trapped and thermal Mg

atoms. Appl. Phys. 859, 99-115 (1994).

6. T. Kisters, K. Zeiske, F. Richie, and J. Helmcke, High-resolution

spectroscopy with laser-cooled and trapped calcium atoms. Appl. Phys.

859, 89-98 (1994).

7. F. Nez, F. Biraben, R. Felder, and Y. Millerioux, Optical frequency

determination of the hyperfine components of the SSj^j-SDjj two

photon transitions in rubidium. Opt. Commun. 102, 432-438 (1993).

TN-68
92 HIGH-ACCURACY SPECTROSCOPY WITH SEMICONDUCTOR LASERS

8. A. Arie and R. L. Byer, Laser heterodyne spectroscopy of '^'I^ hyperfine structure near 532 nm. J. Opt. Soc. Am., B. 10, 1990-1997 (1993).

9. A. Clairon, O. Acef, C. Chardonnet, and C. J. Borde in Frequency

Standards and Metrology (A. De Marchi, ed.). Springer- Verlag, Berlin,

212-221, 1989; G. Kramer, C. O. Weiss, and B. Lipphardt, ibid, 181-186; M. A. Gubin, A. V. Nikulchm, and D. A. Tyunkov, ibid, 206-211; B. G. Whitford, ibid, 187-190.

10. J. L. Hall, Sub Doppler spectroscopy, methane hyperfine spectroscopy,

and the ultimate resolution limits. Colloq. Int. C.N.R.S. 217, 105-125

(1974).

11. C. J. Borde, New sub- Doppler interaction techniques, in Laser Spectroscopy III (J. L. Hall and J. L. Carlsten, eds.), p. 121-134. Springer- Verlag, Berlin, 1977.

12. C. J. Borde, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Saturated

absorption line shape; Calculation of the transit time broadening by a perturbation approach. Phys. Rev. A 14, 236-263 (1976).

13. C. J. Borde, C. Salomon, S. Avrillier, A. Van Lcrberghe, C. Breant, D.

Bassi, and G. Scoles, Optical Ramsey fringes with traveling waves. Phys.

Rev. A 30, 1836-1848(1984).

14. C J. Borde, The physics of optical frequency standards using saturation

methods. In Frequency Standards and Metrology (A. Dc Marchi ed.,). pp. 196-205, Springer-Verlag, Berlin, 1989.

15. L. Hollberg, R. W. Fox, N. Mackic, A. S. Zibrov, V. L. Velichansky, R. Ellingsen, and H. G. Robinson, Oiode lasers and spectroscopic applications. Int. Conf. Laser Spectrosc, 10th. p. 347 (1992).

16. Y. Yamamoto, ed.. Coherence, Amplification and Quantum Effects in Semiconductor Lasers. Wiley, New York, 1991.

17. K. Peterman, Laser Diode Modulation and Noise. Kluwer, Dordrecht,

The Netherlands, 1988.

18. M. Ohtsu, Highly Coherent Semiconductor Lasers. Artech House,

Boston, 1992.

19. H. R. Telle, Stabilization and modulation schemes of laser diodes for applied spectroscopy. Spectrochim. Acta Rev. 15, 301-327 (1993).

20. M. Zhu and J. L. Hall, Stabilization of optical phase/frequency of a laser system: Application to a commercial dye laser with an external stabilizer. J. Opt. Soc. Am., B 10, 802 (1993).

21. R. W. Fox, H. G. Robinson, A. S. Zibrov, N. Mackie, J. Marquardt, J. Magyar, and L. Hollberg, High-sensitivity spectroscopy with diode

lasers. Proc. —lnt. Soc. Opt. Eng. SPIE 1837, 360 (1992).

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REFERENCES 93

22. L. D'Evelyn, L. HoUberg, and Z. Popx5vic, A cpw phase-lock loop for diode-laser stabilization. IEEE MTT-S Int. Microwave Symp. Dig. San

Diego, p. 65 (1994).

23. R. W. Fox, L. D'Evelyn, H. G. Robinson, C. S. Weimer, and L. Hollberg,

Amplitude modulation on frequency-locked extended cavity diode

lasers. Proc. SPIE — Int. Soc. Opt. Eng. 2378, 58-62 (1995).

24. L. Hollberg, in Dye Laser Principles: with Applications (F. J. Duarte and

L. W. Hillman, eds. pp. 185-238. Academic Press, Boston, 1990.

25. T. Kurosu and A. Morinaga, Suppression of the high-frequency recoil component in optical Ramsey-fringe spectroscopy. Phys. Rev. A 45,

4799(1992).

26. A. S. Zibrov, R. W. Fox, R. Ellingsen, C. S. Weimer. V. L. Velichansky,

G. M. Tino, and L. Hollberg, High-resolution diode-laser spectroscopy

of calaum. Appl. Phys. B59, 327-331 (1994).

27. A. Celikov, F. Riehle, V. L. Velichansky, and J. Helmckc, Diode laser spectroscopy in a Ca atomic beam. Opt. Commun. 107, 54-60 (1994).

28. T. Kurosu, R. W. Fox, J. Ishikawa, and N. Ito, High-resolution diode

laser spectrometer for Ca 'Sq-^Pi transition. Proc. SPIE —Im. Soc. Opt. Eng. 2378, 236-244 (1995).

29. R. Barger, Influence of second-order Doppler effect on optical Ramsey

fringe profiles. Opt. Utt. 6, 145 (1981).

30. F. Riehle, J. Ishikawa, and J. Helmckc, Suppression of a recoil component in nonlinear Doppler-free spectroscopy. Phys. Rev. Lett. 61, 2092

(1988).

TN-70
Grating-tuned semiconductor MOPA lasers for precision spectroscopy*

J. H. Marquardt, F. C. Cruz, M. Stephens, C. W. Gates, L. W. Hollberg, J. C. Bergquist

National Institute of Standards and Technology

Boulder, CO 80303

D. F. Welch, D. Mehuys, and S. Sanders

SDL, Inc. 80 Rose Orchard Way, San Jose, CA 95134

ABSTRACT

A standard grating-tuned extended-cavity diode laser is used for injection seeding of a tapered semiconductor laser/amplifier.

With sufficient injection power the output of the amplifier takes on the spectral characteristics of the master laser. We have

constructed master-oscillator power-amplifier (MOPA) systems that operate near 657 nm, 675 nm, 795 nm, and 850 nm.

Although the characteristics vary from system to system, we have demonstrated output powers of greater than 700 mW in a single spatial mode, linewidths less than 1 kHz, coarse tuning greater than 20 nm, and continuous single-frequency scanning

greater than 150 GHz. We discuss the spectroscopic applications of these high power, highly coherent, tunable diode lasers as applied to Ca, Hg*, Ij, and two-photon transitions in Cs.

Keywords: diode lasers, tapered amplifiers, injection locking, high resolution spectroscopy, MOPA

Contribution of NIST and not subject to copyright

1. INTRODUCTION

Many scientific and technical applications of tunable diode lasers require higher powers than have been available from

semiconductor laser sources. Recent advances in tapered gain structures have opened a new frontier in single-mode, singlefrequency, tunable, semiconductor laser capabilities.' Tapered amplifiers (TA) can have broad gain-bandwidths, providing

tremendous potential for tunable lasers with high power. They provide roughly one order of magnitude more power than previous single-spatial-mode devices. However, these tapered amplifiers/oscillators usually operate with many simultaneous

longitudinal modes, which limits their usefulness for coherent and high-resolution applications. Using tapered amplifiers in extended cavities for wavelength control (such as optical feedback from diffraction gratings) allows good coarse tuning at high power,^ but it is difficult to maintain true single-frequency operation. Extended-cavity TAs often exhibit instabilities which can cause jumps among a few nearby longitudinal modes or result in lasing on a few modes simultaneously.

One powerful solution to these problems is to separate the function of the high-power generation from that of the highprecision single-frequency tuning. A few modem examples of this tyf)e of system can be found in the literature and include: distributed Bragg reflector (DBR) laser diode plus tap»ered amplifier,^ solitary diode laser plus tapered amplifier,* and

grating-tuned extended-cavity diode laser (ECDL) plus tapered amplifier. In this paper we describe the applications of

extended-cavity diode-laser plus master-oscillator power-amplifier (ECDL-MOPA) systems that are currendy under way at MST. The characteristics of these systems are discussed from a user's perspective, where our applications are primarily in high resolution spectroscopy. Other related systems and applications have been described by Zimmermann et al.^ and

Goldberg and Bums.*

2. EXPERIMENT

By using several different experimental setups we gain some insight into the general characteristics of injection-locked

MOPAs. A typical experimental setup is shown in Figure 1 ; it consists of a standard grating-tuned ECDL in the Littman34 I SPIE Vol. 2834 0-8 1 94-2222-3/96/$6.00

TN-71
Metcalf (grazing incidence) configuration, which acts as the master laser to inject the TA slave. The light from the master

laser is sent through an optical isolator and spatially mode-matched to the beam emitted from the back facet of the TA. Since

the front output aperture of the TA is very asynmietric (~ 1 |im by 100 pm), a cylindrical lens, in addition to the standard

spherical lens is needed to collimate the output beam. (In addition the output beam can have large astigmatism which may be

compensated.)

Extended Cavity

H>sr:

Isolator

Diode Laser

Tapered

Amplifier

Figure 1. General EGDL-MOPA set-up. The ECDL output is sent through an isolator and then mode-matched to the beam emitted from the rear facet of the tapered amplifier. The coUimating

optics consist of one spherical and one cylindrical lens.

0.6 0.8 1.0 1.2 1.4 MORA Current (A).6 1.8 iO 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 MOPA Current (A)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 MOPA Current (A)

Rgure 2. This figure shows the power versus injection current for three of our ECDL-MOPA

systems (a) 657 nm, (b) 674 nm, and (c) 792 nm. Each graph is shown with and without optical

injection power. Graph (a) and (b) show clearly a lasing threshold of the TA at high currents even

without optical injection. The thresholds of all of the systems are lowered, and the slope

efficiencies increase with increasing injection power. The optical injection power Pj used in these systems is (a) 1.3 mW, (b) 6 mW, and (c) 6 mW.

SPIE Vol. 2834 / 35

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With optical injection from the master laser into the TA, the threshold of the TA decreases, resulting in more emitted power

and the slope efficiency increases to as much as 0.7 W/A for the 674 nm and 792 nm systems (Figure 2). The MOPA output

power quickly saturates with injection power from the master laser. Figure 3 shows the output power of the MOPA as a

function of injected optical power. With good mode matching of the master into the TA, the output power saturates with

about 2-3 mW of injected power. The different ECDL-MOPA systems vary slightly in this characteristic but they all saturate with less than ~5 mW of injection power due to the high gain and strongly asymmetric nature of the TA.

550 — soo ^___^

^ ^ " T

Eo

450 ^

W"""^ ^

i f o

/^

e-. c

400

m/

o

u. J 350 4

300

1 2 3 4 5 6

Optical Injection Power (mW)

Figure 3. Dependence of output power with optical injection power for the 674 nm system. The

output power saturates quickly with as little as 2-3 mW (solid circles).

The isolation required between the master and the slave depends somewhat on system parameters such as master laser power, mode matching, and the power emitted out of the back of the amplifier. We often use another isolator on the output of the

amplifier to eliminate feedback into the high power amplifier. Although good quality isolators are needed between the master and the slave for relatively low injection powers (<5 mW), this requirement may be relaxed with higher injection powers. With optical injection from the master laser we have observed a decrease in temperature of the TA due to the large increase

in optical power and high efficiency of the TA.

i

in

665 nm 675 nm

Wavelength

685 nm

Figure 4. Optical spectrum analyzer trace showing the output of the ECDL-MOPA with and

without 6 mW of injection power. The vertical scale is 5 dB/div and the horizontal scale is 2

nm/div. The instrument resolution is 0.1 nm.

The MOPA output power can be quite high (up to 700 mW), in a single spatial mode, while retaining the spectral properties

of the master laser. Figure 4 shows an optical spectrum of the TA at 674 nm with and without injection. With injection the broad spectrum collapses into the single strong mode of the master laser. The single-frequency output takes power away

from nearby regions and rises 25-30 dB above the background pedestal as measured with a 0.1 nm resolution bandwidth. As

the master laser is tuned, the single-mode, coherent output of the MOPA follows exactiy.

36/SP/f Vo/. 2834

TN-73
The residual facet reflectance of the TA can significantly affect the tuning characteristics of the MOPA and varies somewhat

with each system. When injection current in the TA is brought above its own lasing threshold, the residual chip modes of the amplifier become important Since these chip modes tune with slave current and temperature, it is straightforward to reach

the desired wavelength and be centered on a "good" MOPA chip mode as well. When the TA shows no threshold behavior

(as for the 792 nm system), these chip modes can be suppressed by the optical injection. For those TAs that can operate well above their threshold, the modulation is always present. These characteristics represent two different operating regimes for

the MOPA: below the threshold of the TA the system acts like an optical amplifier, while above the threshold of the TA the system behaves like an injection locked laser. Using the 674 nm system near its own lasing threshold (-1.2 A) and with ~6

mW of injection power, we were able to scan continuously over 150 GHz with an output power of -100 mW.' As a demonstration of this capability, Figure 5 shows absorption of I2 near 674 nm. Although there is some modulation in the power, the sweep remains single mode for greater than 150 GHz. Even when the chip modes are strong, the system can be

scanned -20-30 GHz without mode jumps. This performance is comparable to that of many single-frequency tunable dye

lasers. For most high resolution spectroscopy, this scan range is more than adequate, but some applications, such as molecular spectroscopy, may need longer single mode scanning ranges. In addition, active control of the injection current of

the slave can be used to suppress the power modulation due to the residual facet reflectance.

Frequency

Figure 5. Absorption spectrum of I2 near 674 nm taken with an ECDL-MOPA system (adapted

from ref (7)). A specially designed long-scanning ECDL was used as the master oscillator to obtain this spectrum. The peak absorption was about 30% for a 5 cm long cell with a temperature

of about SOX.

3. APPLICATIONS

Applications of these ECDL-MOPAs provide "real-world" tests of the practicality and usefulness of these systems. The

following examples from our laboratory are used to illustrate the performance characteristics of these systems.

The first system at 792 nm is used to generate 194 nm light for use in a Hg* frequency standard. In this experiment Hg* ions

are held in electromagnetic traps and laser-cooled to temperatures on the order of 1 mK. Single-frequency radiation at 194 nm, required for laser-cooling the ions, is generated by sum-frequency mixing of radiation at 257 and 792 nm in an external build-up cavity. Radiation at 257 nm is obtained by frequency-doubling 515 nm radiation from an Ar* laser. Singlefrequency radiation at 792 nm is generated from the ECDL-MOPA system. More than 700 mW of light at 792 nm is generated with optical injection between 3 mW and 20 mW from the master laser. Greater than 90% of the slave laser power

can be mode-matched into the sum-frequency cavity, and negligible variation of the mode quality is observed as the slave

laser's output power or frequency is varied. The ability to couple such a high percentage of light into the external ring cavity

illustrates the excellent spatial mode these systems can provide. Two isolators (net isolation of about 60 dB) were used between the master and the slave laser, but no isolator was used on the output of the ECDL-MOPA. This high level of

isolation was required to prevent instabilities of the ECDL-MOPA caused by a small amount of optical feedback from the

SPIEVol. 2834/37

TN-74
build-up cavity.

Using the 792 nm system an experiment to check for the relative coherence between the injection beam and the TA output was performed. We split off part of the master laser beam, frequency-shifted it in an acousto-optic modulator (AOM), and

then heterodyned this beam with the output of the TA (Figure 6). The beat signal at the modulation frequency was then heterodyned with the signal driving the AOM, and the resulting E>C signal (proportional to the relative optical phase between

the master and the slave) was observed on an oscilloscope. In this way phase variations between the master and slave lasers were observed directly. Phase locking between the master and slave laser was observed. The phase difference never exceeded 7t rad for times of the order of minutes. Similar results have also been reported by Kikuchi et al.*

ECDL

A^

^

^Pr:

N

MORA \

V AOM

T

mixer ©

\

detector y

/

Figure 6. Schematic diagram of the method used to measure the relative phase coherence between

the master laser and the slave.

<«

>

calcium

beam

i

intens.

stab.

^

jh- MOPA-[Ol- ECDL#2

fiber

phase

lock

cavity

Figure 7. Calcium spectroscopy set-up. The solid lines represent the laser light and the dotted

lines represent the servo loops.

A good demonstration of the narrow linewidths and high optical resolution that can be achieved with these ECDL-MOPAs is provided by the 657 nm system we use for Ca spectroscopy. The system is shown in Figure 7. ECDLl is locked to an

ultra-stable high finesse Fabry-Perot cavity (fringe width - 50 kHz FWHM) using the Pound-Drever-Hall technique. The

beam transmitted through the cavity is used to phase-lock the 657 nm ECDL2-M0PA. This EODL-MOPA output is then

spatially filtered using an optical fiber which delivers the light to the Ca atomic beam system. In addition, the output of the

fiber is intensity-stabilized by active feedback control to the MOPA current This is done to compensate for the intensity fluctuations due to polarization changes and thermal drifts of the fiber system. The very high resolution achievable with this system is evident in Figure 8. This figure shows the optical Ramsey spectra of the 657 nm calcium line. The FWHM of

38/SPIEVol.2834

TN-75
approximately 1 1.5 kHz, with a signal-to-noise ratio of about 30 in a 1 Hz bandwidth, corresponds to what would be a noise- limited firequency stability 6v/v of about 8x10'^ x'"^ (where t is the averaging time). The resolution is limited here by the physicsd size of the windows on the atomic beam apparatus which limits the distance between interaction regions. Using the Ca lineshapc and the Fabry-Perot cavity as frequency discriminators we measure the residual FM noise of the ECDL-MOPA

to be £ 1 kHz dominated by the acoustical mode coupling between the laser table and the reference Fabry-Perot cavity (at about 1-2 Hz).

40 60 80 100 120 140 160 180

Relative 657 nm tuning (kHz)

Figure 8. Ramsey fringe of calcium using the ECDL-MOPA setup shown in Figure 7. The

FWHM of the fringe is - 1 1 .5 kHz, at an optical frequency of 456 THz.

20 40 60 80 100

Relative 674.1 nm tuning (MHz)

120

Figure 9. Fluorescence spectroscopy of the 6Sjyj, F=4 -> 12S,/2, F=5 two-photon transition in cesiimi (1 Hz bandwidth).

A third ECDL-MOPA system is used for high resolution and high sensitivity nonlinear spectroscopy in cesiimi atoms. The

674 nm system provides 500 mW of usable output power which is sufficient for two-photon spectroscopy on weak optical transitions without the need of a build-up cavity. The 674 nm hght is scanned over the 6S„2 "> ^^^m two-photon transition

in a cesium vapor cell heated to -80 °C; the transition is detected by the decay fluorescence from the 12S,;2 state to the 6P1/2 state at 541 nm (Figure 9). The nonlinear signal is quadratic in laser power, yet the signal-to-noise ratio is excellent (>1000

in a 1 Hz bandwidth). This demonstrates that the MOPA output has low AM noise.

SPIE Vol. 2834 / 39

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4. LIMITATIONS

This new technology is exciting and appears to have a bright future. However, there are some limitations. One limitation is that the ECDL-MOPA systems are roughly one order of magnitude more costly to build than the standard low power

counterparts. Although more expensive they are still an order of magnitude less expensive than many other high-power

tunable laser systems such as dye and Ti:Al203 lasers. As with low power diode lasers, these ECDL-MOPAs are very

susceptible to optical feedback and often require good quality isolators.

5. CONCLUSIONS

With these ECDL-MOPA lasers a new era in diode laser spectroscopy is opened. Power is increased by an order of

magnitude or more over conventional diode lasers while the systems retain the good spectral characteristics and tunability of

the lower power ECDL lasers. We have demonstrated the ability to use these lasers in several different experiments

including the high resolution spectroscopy of Ca, Hg*, Ij, and Cs. Although the systems have slightly different

characteristics, our experiments demonstrate that tunable, highly coherent, spatially single-mode, high power laser systems

are achievable. These lasers will undoubtedly play an increasingly important role in the high resolution spectroscopy and

nonlinear optics of the future.

6. ACKNOWLEDGMENTS

We acknowledge the support of the U.S. Air Force Office of Scientific Research.

7. REFERENCES

\. J. N. Walpole, "Semiconductor amplifiers and lasers with tapered gain regions," Opt. Quantum Electron., 28, pp. 623-645

(1996).

2. D. Mehuys, D. Welch, and D. Scifres, " 1 W CW, Diffraction-Limited, Tunable External-Cavity Semiconductor Laser," Electron. Lett., 29, pp. 1254-1255 (1992).

3. S. O'Brien et al., "Operating characteristics of a high-power monolithically integrated flared amplifier master oscillator power amplifier," IEEE J. Quantum Electron.. 29, 2052 (1993).

4. D. Mehuys, D.F. Welch, and L. Goldberg, "2.0 W CW, diffraction-limited tapered amplifier with diode injection," Elec.

Lett., 28, 19^ (1992).

5. C. Zimmermaim, V. Vuletic, A. Hemmerich, and T.W. Hansch, "All solid state laser source for tunable blue and ultraviolet radiation," Appl. Phys. Lett., 66, pp. 2318-2320 (1995).

6. Lew Goldberg and W. K. Bums, "Deep UV to mid-IR generation with laser diodes and non-linear frequency conversion,

in Proc. LEOS '95, edited by T. Fan, pp. 459-460 (IEEE, Piscatoway, NJ, 1995).

7. L. Hollberg, J. Marquardt, M. Stephens, and R. W. Fox, 'T>iode lasers and spectroscopy," in Proc. LEOS '95, edited by T. Y. Fan, pp. 327-328 (IEEE Piscatoway, NJ, 1995).

8. K. Kikuchi, C.-E. Zah, and T.-P. Lee, "Measurement and analysis of phase noise generated from semiconductor optical

amplifiers," IEEE J. Quantum Electron., 27, 416 (1991).

40 1 SPIE Vol. 283^

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4. SEMICONDUCTOR DIODE LASERS*

R. W. Fox and L. Hollberg

National Institute of Standards and Technology

Boulder, Colorado

A. S. Zibrov

Lebedev Institute of Physics

Moscow, Russia

4.1 Introduction

This chapter deals with the technology of applying semiconductor lasers to

scientific and technical fields. Diode lasers are prevalent in many applications

because of their well-known attributes: high reliability, miniature size, relative simplicity of use, and relatively low cost. These factors are important, but the use of diode lasers in technical fields is also increasing because of their unique

capabilities, such as: tunability, high efficiency, useful power levels, reasonable coherence, and excellent modulation capabilities. Volumes of information are already available on the technology of semiconductor lasers [1-8]. Their application to scientific fields has been discussed in a few review articles [9-13], and at least one special issue of a journal focused on the spectroscopic detection of atoms

and molecules using diode lasers [14]. As in any rapidly advancing field, this information becomes outdated quickly and will need to be supplemented with

current journal publications. We will concentrate here on the basic laser characteristics and general principles of operating single-frequency, tunable, diode laser systems.

4.2 General Characteristics of Diode Lasers

A wide variety of diode lasers are now commercially available. These range from low-power/high-speed communications lasers to high-power/wide-stripe de- vices that run multimode (both spatial and temporal) and are used mainly for pumping solid-state lasers. For most scientific applications it is much easier to use

Contribution of NIST, not subject to copyright.

77

EXPERIMENTAL METHODS IN THE PHYSICAL SCIENCES 1079-4042/97 $25.00

Vol. 29C

TN-78
78 SEMICONDUCTOR DIODE LASERS

single spatial-mode lasers, and we will concentrate on these devices here. In addition to the usual Fabry-Perot type lasers, distributed feedback (DFB) and

distributed Bragg reflector (DBR) lasers are now commercially available at some

wavelengths. These lasers have a more complex resonator structure that incorporates an optical grating fabricated within the semiconductor chip. Bragg reflection from the internal grating provides wavelength-selective optical feedback that forces single-longitudinal-mode operation at a wavelength within the reflection bandpass of the grating.

Figure 1 gives a rough sketch of the current (1995) distribution of commercially

available continuous wave (CW) single spatial-mode semiconductor lasers. There

are gaps in the wavelength coverage (and actual availability) and significant differences in performance across this distribution. Some typical characteristics of

semiconductor lasers are outlined in Table I. More details can be found in manufacturer's catalogs and an excellent recent handbook [15]. Another family of semiconductor lasers (outside the scope of the present

chapter) is based on group IV-VI elements (most common are Pb-salt lasers). These lasers span the wavelength range from 3.3 to 30 jim and operate at cryogenic

temperatures. The lead-salt lasers have not experienced the same degree of commercialization as the room-temperature devices, primarily because they are much

more expensive and they have poor mode quality and relatively low output powers

(<5 mW). However, high-quality devices using Sb-based semiconductors that operate at wavelengths that range from ~2 to 4.5 |im have been developed [16], These promising new devices, unfortunately, are not yet commercially available.

4.2.1 Tuning Characteristics

Often of paramount importance for scientific applications are the tuning characteristics of a laser. A diode laser's wavelength is determined by the semiconductor material and structure, and is a function of both temperature and carrier density. For a typical single-mode laser the wavelength increases monotonically with

increasing temperature and then suddenly jumps to another mode at a longer

wavelength. Although this jump is most often to the next cavity mode (-0.3 nm

cavity mode spacing), it is not at all unusual for one or several modes to be skipped.

The tuning range of each mode is typically on the order of 25% of the mode

spacing, but might vary by a factor of 5 or more. Subsequently decreasing the temperature causes the operating wavelength to shift downward with similar behavior, but hysteresis will be observed at the mode transitions. Details of the tuning characteristics are available in the general references [1-8] and [17]. Operating a simple diode laser at the wavelength of an atomic or molecular

transition usually requires iterative selection of injection current and temperature

settings. However, for any given laser the optimum tuning to a specific wavelength

cannot always be achieved. Possible alternatives include trying several lasers or

TN-79
GENERAL CHARACTERISTICS OF DIODE LASERS 79

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TN-80
80 SEMICONDUCTOR DIODE LASERS

Table 1 . Typical Semiconductor Laser Parameters"

Semiconductor (AlrGa|_,),Jn|_,P Al,-Ga|^,As Ga,ln|_,P,AS|_,, MORA

Wavelength 635-670 nm 750-850 nm 1.3-1.5 nm 670, 780-850, 980 nm

Output power (mW) 3-30 5-200 3-100 500-1000

Far-field divergence FWMI (degrees) 8x40 11 x33 30x35 0.3x35

Waveguide mode

dimensions (nm) 4x 1 3x1 1.25 X 1 1 xIOO

Astigmatism (|lm) -10 1-5 1-5 -500

Tiireshold current 30-90 mA 20-60 mA 20-50 mA -0.5 A

Operating current 50-120 mA 50-200 mA 40-120 m

-2.5 A

I^^,^^m--nm 70= 100 K 7o= 150 K To = 60 K

Slope efficiency (mW/mA)

Refractive index

0.5-0.7

3.1-3.5

0.7 3.3-3.60.2 3.2-3.51 3.3-3.6 Frequency vs. injection current (GHz/mA)

-5 -3 1

Frequency vs. temperature

Large-scale (nm/K)

Small-scale (GHz/K)

-0.2 -30-0.25 -30

-0.3 -10

Gain bandwidth (nm) 20 30 50 20

Typical linewidth (MHz) 200 5-20 100 Alpha factor (a) 3-6 4-8

"These values are representative examples and can vary significantly with structure and composition. The data

applies to index-guided single spatial- and spectral-mode Fabry-Perot lasers. Much of this information has been taken from various literature sources and manufacturer's catalogs and has not necessarily been verified.

using optical feedback techniques to control the wavelength. Extended-cavity

lasers (Section 4.3) allow tuning to any wavelength within the gain curve of the

laser. Another option is to place a small mirror near (-100 |im away) the laser's

facet, forming an etalon that acts as a mode selector [18]. An attractive alternative (but improbable for other than a few standard wavelengths) is to find a monolithic

DBR laser that operates at the desired wavelength.

4.2.2 Output Power

A typical output power vs. injection current (P-/) curve for a CW diode laser

is shown in Fig. 2. The slope of the P-I curve above threshold gives the laser's slope -efficiency (in mW/mA). Semiconductor lasers operate as forward-biased

diodes with the voltage drop fixed by the bandgap and an additional series resistance of about 2 to 50 Q. As expected for a semiconductor diode, the laser's

TN-81
GENERAL CHARACTERISTICS OF DIODE LASERS 81 LTO 26 AC Laser

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0)o

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0.5 r

0.4 '

0.3

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0.1

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10 40 50 60 70

Injection Current (mA)

80 90

Fig. 2. Output power vs. injection current for a typical AlGaAs diode laser operating near 780 nm. The vertical axis is photocurrent from the photodiode that monitors power out of

the laser's back facet. The solid dots show the P-I curve of the standard commercial laser as received (/,,, = 38 mA), while the open triangles show the P-I curve of the laser after we coated the front facet with an antireflectance (AR) coating (/,^ = 68 mA). As fractionally more power is coupled out the front facet, the slope efficiency of the back facet power is decreased.

operating characteristics are strongly temperature-dependent. Using a simple

model for a diode laser [3, 5] gives a threshold gain of

hh = aL + -ln

1

/?,/?2

and a total output power above threshold of

T1,/2V(/-4)

, Motal - - in egthL R,R,

(1)

(2)

where /?i and Rj are the facet reflectances, a^, is the loss internal to the laser, hv is the photon energy, / is the injection current, /,/, is the threshold injection current,

r\i is the internal quantum efficiency, e is the electron charge, and L is the laser length. The threshold will vary with temperature as I2 = /i exp [T2 - Ti)/Tq], where

TN-82
82 SEMICONDUCTOR DIODE LASERS

Tq is a characteristic temperature for the laser. A more precise theoretical treatment allows parameters in these equations to depend on wavelength, carrier density,

semiconductor material, and laser structure. If the injection current is increased to excessively high values, the P-I curve becomes sublinear, with the output power

eventually decreasing due to gain saturation, heating, or damage resulting from

high optical powers on the facets. Operation at overly high currents shortens the

lifetime and can seriously damage or destroy the laser. An important measure of a

laser's operating characteristics is the pumping rate, R = (I - I,i,)/I,h, which is the

injection current above threshold normalized to the threshold value. Generally in the safe operating region of temperature and current, the laser's characteristics improve with pumping rate: the power increases, the linewidth decreases, and the

relative amplitude noise decreases. Recent advances in diode laser technology have produced impressive results in high-power devices based on tapered amplifier designs. By starting with a narrowstripe single-mode waveguide and then expanding the width of the waveguide out

to larger dimensions, the output power can be increased while retaining single

spatial-mode operation. Thus, monolithic master-oscillator/power-amplifier

(MOPA) systems can be integrated into a single semiconductor chip [19]. The

increase in power obtained with tapered amplifiers scales roughly as the ratio of

the widths of the output to input waveguide dimensions. Single spatial-mode

devices with watt-level output powers are now appearing on the commercial

market. Obviously, high-power devices will open up many new possibilities. Of

particular interest will be their use with nonlinear optical materials to access other

spectral regions.

4.2.3 Beam Quality

The spatial mode produced by diode lasers depends on the laser structure and

the collimating optics. Since the output beam diverges rapidly from the small semiconductor waveguide, a high-numerical-aperture lens is needed to collect the

light into a collimated beam. Beam quality is not always what we might hope for, but at least in the case of single-mode lasers it can be corrected to be nearly

cylindrically symmetric Gaussian. Output beams are typically asymmetric, with a

larger divergence in the direction perpendicular to the junction (see Table I). Well

above threshold, most are strongly polarized with the electric field parallel to the

junction. The modes can also have astigmatism, which manifests itself as the apparent axial separation of the source of rays in the planes parallel and perpendicular to the junction. Astigmatic distances for Fabry-Perot lasers are generally

in the range of 1 to 10 |im, while for tapered amplifiers the astigmatism can be

~ 1 mm, about half the length of the chip. Left uncompensated, this aberration may

degrade the beam quality and result in an aberrated far-field intensity distribution. A cylindrical lens can be used to correct the astigmatism, while the asymmetry in

TN-83
GENERAL CHARACTERISTICS OF DIODE LASERS 83

divergence is often corrected with a pair of anamorphic prisms that are oriented to angularly magnify the smaller divergence and hence produce a nearly circular beam [20]. Alternatively, a cylindrical telescope can be used to correct the angular

asymmetry. In addition, there are sometimes small changes in the spatial mode

parameters with large changes in the pumping rate R.

4.2.4 Laser Amplitude Noise

An important attribute of semiconductor lasers is that they typically have much

lower amplitude noise then other tunable laser systems. For example, a singlemode laser operating well above threshold might typically exhibit amplitude

fluctuations that approach the shot-noise level for frequencies above ~1 MHz. The

noise does increases toward lower frequencies with an approximately 1// dependence. A common measure of the amplitude noise is the relative intensity noise: RIN = <AP2)/(P)2 ^ [2 . AfSp{f)]-/{P}\ where A/ is the detection bandwidth, S^(/)

is the spectral density of the power fluctuations, and (P) is the mean power. In general, RIN will decrease with increasing pumping rate. If the laser is operated

in a multimode regime, the amplitude noise may be much more pronounced,

especially when there are only a small number of modes oscillating. Optical

feedback can also cause increased amplitude noise.

4.2.5 Optical Feedback

The effects of optical feedback on diode lasers can be profound and depend on

a number of factors: the amount of feedback, the facet reflectance, the pumping

rate R, and the distance from the laser to the source of feedback (feedback time

delay). In some regions of this multidimensional space, the feedback can narrow

the linewidth and stabilize the laser's wavelength, while in other regions optical

feedback causes such instabilities as erratic mode jumping and coherence collapse

[5, 21-24]. In general, optical feedback (even small amounts /'feedback/^out - 10^^) from uncontrolled sources should be avoided. For many applications this simply means tilting optical elements to avoid direct reflections. In other cases we are forced to use Faraday isolators, which unfortunately tend to be bulky and expensive for wavelengths less than 1 |im. In some of the next sections we discuss ways

to use optical feedback to advantage.

Even though the terminology used to describe diode lasers is inconsistent and

imprecise, it may be useful to review some of the nomenclature. For some reason

the description "solitary laser" has come to mean a semiconductor diode laser that has not been modified by external effects such as optical or electronic feedback.

"External cavity laser," on the other, hand describes a system that lases only

because of optical feedback from external optical elements [25]. The name "ex- tended-cavity diode laser" (ECDL) has come to mean something between these

TN-84
84 SEMICONDUCTOR DIODE LASERS

two cases; that is, when the laser is operated in a regime where strong feedback

from one side of the chip (from an external element such as a grating) is used to control the laser's mode. Sometimes the nomenclature and jargon are more confusing than useful.

4.2.6 Laser Degradation

When properly protected from electrical damage, semiconductor diode lasers are reliable and long-lived. However, there are variations from laser to laser and some variations of laser characteristics with time. Quite a lot of research has been

done on the degradation of laser diodes (there is even a book on the subject [26]). However, we still lack detailed understanding of some aspects of laser aging, such

as the change in laser wavelength with time. Some characteristic modes of laser degradation are now recognized, including "dark line defect" and facet degradation (which can be caused by gradual photochemical effects or catastrophic optical

damage, COD). There seems little that users can do about these changes other than providing good electrical protection and a clean environment for lasers whose

facets are open to the air. High currents and high temperatures will increase the

rate of degradation. When treated properly, modern lasers have very long natural

lifetimes (-10,000 h), but unnatural lifetimes can be quite short!

4.3 Extended-Cavity Lasers

Tuning the wavelength of diode lasers and narrowing their linewidth can be

accomplished using some form of dispersive optical feedback [27]. Designs that employ relatively high optical feedback power, Pfeedback/^out ^ 005 (which is the power fed back into the laser's waveguide mode relative to the output power

without feedback), can have a large tuning range and be very stable. In addition to broad tuning, extended-cavity lasers typically have much narrower linewidths than

solitary lasers (fast linewidths -50 kHz as opposed to -20 MHz). Diffraction

gratings are the most commonly used dispersive feedback element, although

intracavity etalons, prisms, and birefringent filters have also been used successfully. Good-quality commercial extended-cavity diode laser systems are now avail- able from a few manufacturers, but distribution in terms of power and wavelength

are still somewhat limited. Because of special requirements or cost constraints, users may find it desirable to build their own extended-cavity systems. This can be done relatively simply, as described in a number of papers [7, 12, 28, 29] and

as we oudine below.

4.3.1 ECDL Construction

There are many good designs for extended-cavity lasers, but no particular

design that is optimum for all applications. In Fig. 3 we see five different configuTN-85
EXTENDED-CAVITY LASERS 85

a)

b)

/ ^

c)

AR/

"<0:

C^

d)

e)

Fig. 3. Various optical feedback configurations. The first design (a) is a two-sided exter- nal-cavity design, (b,c) are single-sided extended-cavity designs in Littrow configuration,

(d) is an extended-cavity laser that uses a grating in a grazing-incidence configuration, and

(e) is a resonant optical-locking configuration using a confocal Fabry-Perot cavity. Design

(b) is appealing because there is no movement of the output beam when the grating is rotated to tune the wavelength, and it can also be optimized to deliver high output power. On the other hand, it has the disadvantage that it requires a special laser package (or a

rather severe modification of standard laser packages) to gain unobstructed access to both

facets. In present usage, the two most common tunable laser designs are (c) and (d) because

they are relatively easy to implement using commercial lasers.

TN-86
86 SEMICONDUCTOR DIODE LASERS

rations of optical feedback that can be used to control diode lasers. For optimum

performance many of these designs require good antireflection coatings on the output facet of the chip (see Section 4.5). When designing a laser cavity, it is important to remember that the diffraction efficiency of typical gratings has a strong polarization dependence. For beams

polarized perpendicular to the rulings we expect high diffraction efficiency, while

for beams polarized parallel the efficiency can be significantly reduced. In the Littrow configuration (Fig. 3b,c), the number of grating lines covered by the laser mode is constrained by the focal length and numerical aperture of the collimating

lens, the orientation of the laser spatial mode, and the line spacing and corresponding cutoff wavelength of the grating. Since the beam from a laser waveguide is normally polarized in the direction parallel to the junction, in the far field the laser beam is polarized along the narrow dimension of the spatial mode. When the

laser's asymmetric mode is incident on a diffraction grating, there is a compromise

between high resolution and high diffraction efficiency. The user has very little freedom of design, which means that the resolution is sometimes not as high as we would like. In some cases it can be advantageous to use a half-wave plate

between the laser and the grating to decouple the polarization (hence diffraction efficiency) from the spatial mode orientation. An alternative approach is to use prisms to expand the small direction of the spatial mode [20, 24, 30]. With the one-sided Littrow configuration (Fig. 3c) there is also the disadvantage that the beam moves as the laser's wavelength is tuned. A remedy to the problem of beam

movement with tuning (present in the Fig. 3c configuration) is to use a mirror

mounted with its surface perpendicular to the grating surface so as to form a

retroreflector. Rotating both the grating and mirror together leaves the output beam

direction unchanged, although there will be some beam displacement if the axis of rotation is not defined by the intersection of the grating and the mirror. This

arrangement is not easily compatible with long continuous scans. Even with these limitations we often use the standard Littrow configuration

(Fig. 3c) because of its simplicity, and most of the time it works reasonably well. For many applications (atomic physics in particular) large tuning ranges are not very important. In practice one can achieve continuous scans of ~2 to 10 GHz by

simply arranging the grating pivot point so that the grating angle tunes synchronously with the laser's frequency as controlled by the extended-cavity length. Coarse tuning can be accomplished manually with a fine pitched screw. A typical

800-nm system might consist of an 8-mm focal length collimating lens (N.A. =

0.5), an 1800-line/mm grating in Littrow configuration with a cavity length of

about 5 cm. In a typical Littrow system we normally orient the laser mode so that the larger dimension is orthogonal to the direction of the grating rulings. This

orientation gives better resolution and better output power than the opposite

orientation.

TN-87
EXTENDED-CAVITY LASERS 87

Fig. 4. Diagram of a simple grazing-incidence grating-tuned extended-cavity diode laser. This extended-cavity system is constructed of three basic units: the laser mount, the grating

mount, and the feedback mirror. The diode laser, Peltier cooler, and collimating objective

are all integrated together in a stable laser mount that uses a flexure and fine-pitched screw

for precise focus adjustment. The feedback mirror and the angle of the grating are adjusted

relative to laser beam direction to provide just enough optical feedback power for stable single-mode operation.

The grazing incidence airangement (Fig. 3d) as proposed by Harvey and Myatt

[31] was shown to have the important advantages of significantly higher spectral

resolving power and no movement of the output beam when the laser is tuned. This

design, implemented with diode lasers by Harvey, is often called the Littman (or

Littman-Metcalf) configuration because they introduced the use of grazing-incidence gratings to control dye lasers [32]. Good discussions of the grazing inci- dence design have also been given by Day [33]. A simple mechanical layout for a grazing-incidence grating-tuned ECDL is shown in Fig. 4. In designing all of these systems we need to address a few basic requirements.

We need to precisely align the laser cavity, to tune the wavelength, and to precisely

control the laser chip temperature and extract excess heat. Care must be taken to ensure a stable thermal and mechanical structure by using good materials and

kinematic design principles. Ironically, ECDLs provide narrow spectral line- widths, but they are also much more susceptible to external perturbations than were the solitary lasers that we started with! For stable single-frequency operation,

ECDLs need to be isolated from vibrations and pressure fluctuations. A useful

principle to keep in mind in this design is: ifsomething can move, it will. Allowing

a large dynamic range of motion competes directly with stability. The simple optomechanical design sketched in Fig. 4 is an example of a

versatile system that satisfies most (but never all) of our basic requirements. It consists of a copper baseplate (not shown) that acts as a rigid backbone for the

laser resonator and at the same time serves as the heat sink for the temperature

TN-88
88 SEMICONDUCTOR DIODE LASERS

control system. A commercial laser is mounted in a small copper fixture that bridges the Peltier cooler and attaches to the laser base mount (also copper). The

base mount is then rigidly attached to one end of the baseplate. The collimating

lens is connected to the laser base mount by a stiff spring-steel flexure that is clamped in place using locating pins and multiple screws. The lens is mounted in an eccentric ring that is clamped in place after initial coarse alignment. The

transverse alignment can be set accurately enough with careful hand alignment and

visual inspection of the beam direction and shape. In the example of Fig. 4, the eccentric on the lens mount is used to adjust the vertical height of the lens, while

the horizontal position is set by the transverse displacement of the laser on the base mount. Critical adjustment of the focus is done with a high-quality fine-pitched screw that translates the lens against the restoring force provided by the flexure. We typically use 6.3-mm diameter screws with 3.1 threads/mm (1/4-80 screw).

The lever arm from the flexure pivot point (Fig. 4) gives further drive reduction. This simple design tilts the lens slightly as it is translated for focusing; however,

this is not a serious limitation because the lens can be set very close to the optimum

position before it is clamped in place. In constructing this system we tolerate the thermal expansion of copper in order to have the good thermal conductivity and

low mechanical Q. For very-high-frequency stability the cavity length can be

controlled with a PZT. For some high-power lasers we use water cooling in the

laser base mount. The water can be circulated without pump vibrations by using a simple thermal syphon.

One of the requirements for stable operation of ECDLs is to return sufficient optical feedback power to the diode laser waveguide mode. The optimal feedback

power depends on the characteristics of the laser and, in particular, the reflectance of the output facet. Typically feedback power rafios (Pfeedback/Pout) of from 5 to 50%

are appropriate. In grazing-incidence systems the feedback mirror and the angle

of the grating (relative to the laser beam direction) are adjusted to provide just

enough feedback power for stable single-mode operation (typical incidence angles

for the grating might be -75-85°). Good-quality high-numerical-aperture objectives (N.A. ~ 0.5) are recommended for the collimating lens. In most cases it is not necessary to correct for the laser's astigmatism for the laser to function

properly in extended-cavity mode. However, the output beam will have some

aberration if only spherical optics are used. Objectives lenses specifically designed

for diode laser collimation often assume that there is a thin window between the

laser chip and the lens. For best mode quality, the lens design needs to take into account any window on the laser mount.

4.3.2 Alignment

The optical alignment of extended-cavity lasers requires precision, but with

practice alignment can be accomplished in a simple common-sense manner. InfraTN-89
ELECTRONICS 89

red-sensitive cards that fluoresce in the visible are extremely useful when working

with near-IR lasers. Electronic IR viewers or CCD cameras can also be used. For

the initial alignment, the objective lens is carefully centered on the laser's output

so that the beam propagates in the same direction as the unperturbed laser emission. The beam should appear roughly collimated over a distance of several meters. The grating is then positioned so that the first-order diffracted beam returns to the

laser (taking care that the grating blaze is toward the lens). A card with a small

aperture held in front of the lens is useful to roughly position the returned beam

on the outgoing beam. Fine tuning of the focus and alignment will then be

necessary to obtain stable single-mode operation.

The method that we use most often to align ECDLs was derived from work

describing the output power-vs. -injection current characteristics of ECDLs [21 , 34,

35]. The method is simple and requires only monitoring the output power as a function of the swept injection current. Following the coarse alignment procedure

described above and with the laser operated near threshold, a triangular ramp is applied to the injection current. Monitoring the output power of the ECDL with a

large-area photodiode and an oscilloscope (synchronized to the triangular wave)

yields a classic diode laser P-I curve with no optical feedback (see Fig. 2). When

there is feedback from the extended cavity, there will be abrupt discontinuous

changes in threshold behavior. Iterative adjustment of the focus and extended-cavity alignment will result in oscilloscope traces similar to those in Fig. 5.

4.3.3 Tuning

The maximum tuning range of an ECDL depends on the design of the cavity

and on the detailed characteristics of the diode laser chip. Factors that affect the tuning include: the facet reflectances, the degree to which the spectral broadening

is homogeneous, the side-mode suppression ratio, the pumping rate /?, the spatial

mode control (how well the mode is index guided), and the propensity for nonlinear coupling between modes (for example, four-wave mixing). As users, the

facet reflectance is almost the only parameter that we have any control over. If the reflectance of the laser facet that faces the grating is very low (<10^), the maximum tuning range can be as large as the laser's gain curve (approximately

±20 nm for AlGaAs lasers and even larger for InGaAsP lasers). Continuous

single-mode scans over many nanometers require very low facet reflectance and

synchronization of the tuning of the grating passband with change in cavity length.

4.4 Electronics

The electronics required to operate semiconductor lasers are relatively straightforward and can be very simple if we do not require precise tuning. Since the

TN-90
90 SEMICONDUCTOR DIODE LASERS

CDo

Q.

k-0)

(A

CO

Time

Fig. 5. Output power of ECDL vs. injection current, which is swept near threshold with a

triangle wave. Three different P-I curves are shown for different cavity alignments; the curves have been offset vertically for clarity. The horizontal axis (labeled here as time) is synched with a triangle wave ramp, with maximum injection current corresponding to maximum output power. The characteristic features of the P-I curve are a good indicator of the quality of the extended-cavity alignment. As the focus of the collimating lens and

feedback from the grating are aligned, the output power increases in abrupt steps. The

rounded comers and noise on curve A corresponds to poor cavity alignment and are indicative of multilongitudinal mode operation. Curve B shows the type of abrupt jumps

that are indicative of single-mode operation. Curve C is near-optimum alignment, where

the injection current has very little effect on the laser's frequency and no mode jumps are apparent.

laser's output power and frequency depend sensitively on temperature and injec- tion current, we need to control both with some precision. The typical laser parameters in Table I can be used to estimate the stability and noise performance

that will be required of the current source and temperature controller for a given

application.

4.4.1 Current Sources

The most important requirement of current sources used for diode lasers is that they MUST BE FREE of electrical transients that can seriously damage the laser. CW narrow-stripe lasers require an injection current of about 20 to 200 mA and

have a forward voltage drop of about 2 V. In contrast, some of the high-power

devices—such as wide-stripe lasers, MOPAs, and diode laser arrays—might reTN-91
ELECTRONICS 91

quire a few amperes of injection current. The simplest diode laser current supply

is just a battery and a current-limiting resistor (or potentiometer). In practice we

usually want to do more than just turn the laser on, and so the current source becomes somewhat more complicated. A number of good diode laser current sources are now commercially available. These range from simple integrated

circuit chips that are designed for low-cost consumer electronics to very elaborate microprocessor-controlled systems. If a laboratory with a limited budget is planning on operating a significant number of precision diode laser systems, it can be

cost-effective to produce some simple circuit boards for current sources and

temperature controllers. Following this approach, we have found a few general

principles to be useful.

• When possible do not put the AC-to-DC power converter in the same box with

the current source electronics; very good filtering and regulation of the DC

supplies are also important.

• It is important to keep the diode laser current path, both to and from the laser, independent of other signal and return paths.

• Pay careful attention to avoiding spikes on startup, shutdown, and even power

failures. Before endangering a valuable laser, time is well invested in testing for transients (under all conceivable operating conditions) with an inexpensive

imitation laser load (such as 10 LEDs in parallel and these in series with a 1 Q. current sensing resistor to ground; you can also use one or more rectifier diodes

in place of the LEDs).

• To protect against damage caused by transients and operator errors, it is important to attach some passive protection near the laser chip (a typical protection

circuit is shown in Fig. 6). Protection circuits can also have adverse effects, such as slowing down modulation response and increasing thermal instability

due to diode leakage current. This last effect can be eliminated when necessary by controlling the temperature of the protection diodes by placing them on the

laser heat sink.

• Watch for potential ground loop problems, particularly when connecting multiple cables between the laser, current source, sweep source, temperature controller, optical table, detectors, oscilloscope, etc. Our approach has been to keep

the laser heat sink at ground potential but to isolate it from all other grounds

(including that of the box that we use to enclose the laser), except at the laser current source where there is a common ground.

• Look for other useful hints and examples in catalogs supplied by the laser manufacturers. An example of a good-quality diode laser current source is in Fig. 6. Other

examples can be found in the literature [36, 37]. This circuit is designed to have

good stability, low noise, and modulation capability.

TN-92
92 SEMICONDUCTOR DIODE LASERS I 1 II ^

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TN-93
ELECTRONICS 93

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4.4.2 Temperature Controllers

The high sensitivity of diode laser wavelengths to temperature (-30 MHz/mK)

places stringent requirements on their temperature control. For fixed- wavelength

operation, solitary lasers require better temperature stability than ECDLs. With

ECDLs the temperature stability is more of a concern because of thermal expansion of materials than it is because of the temperature sensitivity of the laser's gain. In practice the most difficult task in maintaining temperature stability is not the

electronics, but rather it is the design of the thermal environment. A stable ther- momechanical environment will reduce problems associated with such important, but often less obvious, perturbations as: beam-pointing stability (remember the angular magnifying properties of the short-focal-length collimating objective) and

fluctuations of even the small optical feedback that is invariably present. Putting

ECDLs in hermetically sealed containers greatly improves both thermal and

optomechanical stability. Important tradeoffs have to be balanced in designing temperature control sys- tems for diode lasers. For instance, we would like to have the thermistor very close

to the laser to accurately measure the laser's temperature, but we also want the thermistor close to the thermoelectric transducer so that the time delay in the servo

is small and the loop can have fast response and high gain. These considerations

indicate that a very small thermal mass should be used to support the laser. But the mount should also be mechanically stable and have a large thermal mass so that rapid temperature fluctuations (outside the loop bandwidth, e.g., from moving air) do not perturb the laser's temperature. For practical reasons we would also like the

entire system to be relatively light and compact. Obviously, compromises are in order. Figure 7 depicts an example of a temperature controller that uses a Peltier cooler

to control the temperature of a diode laser; others can be found in the literature [12, 29]. An excellent analysis of the use of Peltiers in temperature control systems

has been provided by Van Baak [38]. As with current sources, there are some basic design principles that are useful in constructing thermal control systems:

TN-94
94 SEMICONDUCTOR DIODE LASERS

THEJWilSTOR

-^v'W—I I i aSOnF

Fig. 7. Diode laser temperature controller. A precision thermistor (nominal value 125 kQ)

is used in a resistance bridge to sense the laser's temperature, and a Peltier (thermoelectric) cooler is used for cooling or heating. The servo-loop is a PID (proportional integral

differential) control that processes the error signal and then sends it to a driver amplifier

which provides sufficient power to run the Peltier cooler (typically a few volts and a few

amperes). This circuit is from reference [36].

Two-stage thermal control can be very effective in improving the stability of

ECDLs. One controller is used for the extended cavity and the other for the

laser chip.

Thermistors should be buried in holes below the surface (& 5 mm) to avoid

perturbations from temperature differences with the surrounding air

High-thermal-expansion materials (e.g., plastics, aluminum, copper) require

better temperature control to maintain mechanical stability and alignment. Invar and fused silica can be useful for some components.

TN-95
OPTICAL COATINGS ON LASER FACETS 95

• The combined thermomechanical properties of the materials and construction

must be considered. This includes the dynamic response of the material used

within the thermal control loop (aluminum, copper, and silver have large

coefficients of thermal diffusivity, which is good for control systems, but they

also have large coefficients of thermal expansion, which is bad for mechanical

stability).

• Peltier coolers are not very efficient, so a relatively large thermal reservoir may

be required to dissipate excess heat.

• Watch out for thermal drifts and emfs in the electronics. Even good-quality

resistors and capacitors can have significant temperature coefficients. Potenti- ometers can be particularly troublesome.

4.5 Optical Coatings on Laser Facets

Operating a diode laser in an extended-cavity configuration works best if the reflectance of the laser's output facet is very low. ECDLs are inherently coupled

cavity systems and are known to have operating regions of stability and instability

[21-23]. By reducing the reflectance of the output facet the performance of the ECDL is improved: the size of the stable operating region (in temperature, current, and feedback power) is increased, the usable output power is increased, and, most

importantly, the laser's tuning range is increased.

In Eq. (1) we see the strong dependence of the laser threshold current on the

reflectance of the facets. This is illustrated in Fig. 2, which shows the P-I curves of a laser before and after the output facet is antireflection (AR) coated. Almost

all commercial lasers come from manufacturers with coatings already on the

laser's facets. These coatings serve two purposes: first, they protect the facets from

degradation, and, second, they adjust the facet reflectance to optimize the output power. Since the early days of diode lasers, AI2O3 coatings have been used to reduce facet degradation and increase the lifetime of diode lasers. We typically find

that commercial low-power {P . 10 mW) AlGaAs lasers have single-layer coat- ings on both facets that are approximately Xl2 in optical thickness. In most cases we do not know with certainty what coating material has been used. Empirically we often (but not always) find that the laser coatings have an index of refraction of about 1.60, which is consistent with e-ht&m vapor-deposited AI2O3. Higherpower lasers (& 1 5 mW) typically have a similar coating on the output facet, except

that the thickness is approximately X/4 (which results in a reflectance of a few

percent). The back facet of the high-power lasers typically has a multilayer coating

with a reflectance of 90% or more. Most commercial lasers can be improved for use in extended-cavity configurations by reducing the reflectance of the output facet. The majority of laser manuTN-96
96 SEMICONDUCTOR DIODE LASERS

facturers are not interested in putting special coatings on diode lasers for those

users who need a few inexpensive lasers. In order to transform general-purpose

lasers into ECDLs, we have found it advantageous to develop some simple coating

capabilities in our own lab. Fortunately, the equipment needed to coat diode lasers

is readily available from the optical coating/semiconductor industry. For example,

inexpensive (can opener-like) tools are available for removing the caps from the standard hermetically sealed semiconductor packages. Otherwise, all that is really

needed is a simple vacuum coating system with electrical feedthroughs.

Our coating techniques are based on traditional dielectric coating methods but

are directed toward the specific problem of modifying the facet reflectance of

semiconductor lasers. We generally use common coating materials (e.g., AI2O3,

HfOi, SiO) and well-established techniques (thermal evaporation, electron beam

deposition, and RF sputtering). If one does not want to spend time characterizing

the unknown coatings on the lasers and carefully calibrating thickness monitors,

it is easiest to do the coatings by monitoring the change in threshold while the laser

is being coated. During the coating process the laser injection current is ramped

through threshold with a repetitive triangular sweep and the power out of the back

facet is monitored. Many lasers already have a monitor photodiode behind them

that can be used for this purpose. Diode laser coatings have been studied in detail, and good-quality AR and

mirror coatings have been developed. Some very useful information can even be

found in the published literature, but often details are lacking because they are proprietary in nature. The lowest-reflectance coatings that have been reported on

diode lasers range from 10^ to 10"^. These results have often been achieved by

laboratories working on optical amplifiers, in which case it is necessary to suppress

lasing altogether while maintaining very high optical gain.

Two relatively simple AR coatings that work reasonably well on commercial

lasers are: (i) thermally evaporated silicon monoxide and (ii) e-beam-deposited

Hf02 and/or AI2O3. Either of these coatings can achieve reflectances below 10"^, even on commercial lasers that already have some coating on their facets. Silicon monoxide is convenient because the equipment required for thermal evaporation

is relatively simple. It also has the useful (but challenging) property that changing

the oxygen pressure in the coating chamber changes the oxygen composition (x) in the film (SiO,), and hence the index of refraction from about 1.6 to 2.0. With

all coatings, but with SiO, in particular, the apparent index of refraction of the coating can change over time as the laser is exposed to and operated in air. An AR coating that we use regularly for semiconductor lasers is a dual coating

of AI2O3 and HfOi. We apply this coating using a standard electron beam evaporation source. Both of these materials produce good-quality optical coatings that are compatible with most of the commercial lasers that we have tested. To reduce

the facet reflectance of commercial lasers we first add AI2O3 (when needed) to bring the laser's base coating thickness to approximately ?i/2, and then we put

TN-97
DIODE LASER FREQUENCY NOISE AND STABILIZATION 97

down a A./4 layer of HfOT (deposited index approximately 1.89). The optical

thickness of coatings is monitored by watching the change in laser threshold while

the laser is being coated. This particular two-layer coating is relatively easy to monitor because the threshold reaches an extremum at or near the proper thickness

for both layers.

4.6 Diode Laser Frequency Noise and Stabilization

We draw a clear distinction between two aspects of laser frequency stabilization. The first concerns the reduction in the drift and low-frequency fluctuations

(jitter) of the laser's center frequency, and the second concerns the faster fluctuations that are responsible for the "fast linewidth" of the laser. The general aspects

of frequency stabilization of lasers are addressed in other chapters (Zhu and Hall,

Chapter 5 in this volume) and elsewhere. We will concentrate here on those aspects

particularly relevant to diode lasers [5-7]. An excellent discussion of the subject

is given by Telle [39].

First, the optical cavity of a solitary diode lasers is very small and the facet reflectance is not very high, which means that the Q of the resonator is low and

the resulting linewidth of the laser is relatively large (typically 10-200 MHz). In addition, a number of physical processes affect the spectral width of diode lasers. These include carrier density and temperature fluctuations, pump fluctuations, and

spontaneous emission. These effects can be amplified by the strong coupling

between the phase and amplitude of the lasing field. This coupling causes the linewidth of diode lasers to be increased above the fundamental SchawlowTownes limit by a factor of ( 1 -(- a-), where a (typically 3-10) is the ratio of the change in the real to the imaginary part of the susceptibility of the gain medium.

4.6.1 Electronic Control

An inexact but useful rule of thumb for frequency control servo systems is that the bandwidth of the servo needs to be somewhat greater than the linewidth of the

laser before the servo can actually reduce the laser's linewidth. Solitary lasers have

linewidths that are typically tens of MHz wide, which means that it is difficult, but not impossible, to achieve servo-loop bandwidths that are high enough to narrow

the linewidth. Even though the frequency of the laser light responds on nanosecond

time scales to changes in the injection current, other factors limit the loop response

time. Very fast electronics must be used, and the physical size of the system must

be small to minimize propagation delays. It is necessary to compensate phase shifts in the transfer function of injection current to laser frequency and also the time

delays inherent in the frequency discriminator (for example, a Fabry-Perot cavity).

TN-98
98 SEMICONDUCTOR DIODE LASERS

Extended

Laser

Blue out

Fig. 8. Frequency-doubled diode laser. In this system a grating-tuned ECDL provides

tuning and high spectral purity, which is then used to control the frequency of a higher- power diode laser by injection locking. Injection about 5 mW from the ECDL into the slave

laser provides about 1 50 mW of tunable output power. The spatial mode of the slave laser

is asymmetric (QJQn ~ 3) and has a small amount of astigmatism (about 3 |J.m); these are corrected by using an anamorphic prism pair and a cylindrical lens. After spatial mode

correction and passing through an optical isolator, there are about 105 mW remaining in the beam that is incident upon the ring buildup cavity that contains the KNb03 crystal. The

combined mode matching and couphng efficiency of this beam into the ring is about 75%.

Usable blue output powers as high as 45 mW are obtained in a good stable spatial and

temporal mode near 425 nm.

4.6.2 Optical Control

Resonant optical feedback from a confocal cavity (Fig. 3e) can be used to narrow the linewidth and simultaneously stabilize the center frequency of diode

lasers [2]. With this method optical feedback occurs only in the narrow spectral

windows defined by the confocal Fabry-Perot resonances. When the solitary

laser's frequency is tuned within the optical capture range of a Fabry-Perot

resonance, the resulting resonant feedback causes the laser to lock its frequency to the nearby cavity resonance. The laser's fast linewidth is thus reduced by a factor of about 1000 (to <10 kHz), and the center frequency is then automatically

stabilized to the cavity resonance. This system does not require modification of

the solitary diode laser and typically operates in the weak feedback regime,

Pfeedback/^out • 1 0"^. A limitation of this optical locking technique is that the tuning range of the laser is still restricted to those wavelengths accessible by the solitary laser alone. Although no active control is needed to optically lock a laser to a

TN-99
EXTENDING WAVELENGTH COVERAGE 99

cavity, electronic servos will be necessary for stable long-term operation at a

specific frequency.

4.6.3 Combined Optical and Electronic Control

As with most tunable lasers, the lasing frequency of ECDLs is controlled by a mechanical system (the grating angle and cavity length) that is susceptible to perturbation and drift. Active frequency stabilization can be done using some sort of frequency reference (such as a Fabry-Perot cavity or an atomic resonance) and

an electronic control system. The error signal from the frequency reference is processed by a loop filter and fed back to control the laser frequency. The main

feedback path is usually to a PZT that controls the laser cavity length. The

frequency stability that can be achieved using only a PZT loop is usually adequate

for most applications, but when linewidths less than about 50 kHz are needed it is relatively easy to use an additional feedback loop to the injection current (or to an

intracavity modulator) to further narrow the laser linewidth. These additional feedback paths have higher servo bandwidths because they are not limited in speed

by having to move the mass of a mirror or grating. With servo bandwidths of >1

MHz it is even possible to phase-lock a diode laser to a reference laser source.

4.7 Extending Wavelength Coverage

Present technology is now reasonably good at controlling the spectral characteristics of diode lasers, but these lasers may not be available at the wavelengths

that we require (Fig. I ). Fortunately, new wavelengths are on the horizon. There

are promising research results with blue lasers using ZnSe and GaN, and the Sb-based IR lasers also have great potential. In the meantime, we can use the

existing diodes and nonlinear optical techniques to extend wavelength coverage. Good results have been reported by using diode lasers and difference-frequency

generation (DFG) to produce single-frequency tunable infrared light [40]. The

chalcopyrite crystals AgGaS2 and AgGaSe2 and periodically poled lithium niobate

are well suited to this application because they have large nonlinear coefficients and they phase match for diode laser wavelengths. In fact, it appears that almost

the entire spectral region between 2 and 18 |im could be covered by using these

crystals and diode lasers as the input. In the opposite wavelength direction there is a need for good tunable lasers in the blue and UV based on solid-state sources. Fortunately, nonlinear crystals such

as KNb03, KTP, LiNb03, BBO, and LilO^ can be used for second-harmonic

generation (SHG) and sum frequency mixing of diode laser light [41]. With these techniques and materials the region between 200 and 500 nm is accessible. For

example, the SHG system developed in our lab by C. Weimer is diagrammed in Fig. 8. This system uses KNb03, which is a particularly good example because it

TN-100
100 SEMICONDUCTOR DIODE LASERS

has a large nonlinear coefficient, and it noncritically phase matches for AJGaAs

diode laser wavelengths. Starting with an injection-locked 150 mW diode laser, this system produces more than 40 mW of tunable light near 425 nm. An analogous

system that uses angle phase matching in LiI03 produces about 200 |iW of 405 nm light for an input power of 40 mW at 810 nm. From recent publications and conference proceedings we can anticipate that higher-power lasers will soon be available in many wavelength regions. As the technology improves we will be able to incorporate these lasers and MOPAs with

various nonlinear optical materials to greatly extend useful wavelength coverage.

Acknowledgments

Our thanks to V. L. Velichansky, C. W. Weimer, N. Mackie, T. Zibrova, H. G. Robinson,

J. Marquardt, S. Waltman, M. Stephens, and L. Mor for contributions to this work.

References

Given the length and general nature of this chapter, we provide only a very basic

list of references that might serve as a starting point for further study.

1. Kressel, H., and Butler, J. K. (1977). Semiconductor Lasers and Heterojunction LEDs. Academic Press, New York.

2. Casey Jr., H. C, and Panish, M. B. (1978). Heterostructure Lasers, Parts A and B. Academic Press, New York.

3. Thompson, G. H. B. (1980). Physics of Semiconductor Laser Devices, Wiley, New

York.

4. Yariv, A. (1989). Quantum Electronics, 3rd edition, Wiley, New York.

5. Petermann, K. (1988). Laser Diode Modulation and Noise, Kluwer Academic, Dordrecht, The Netherlands.

6. Yamamoto, Y, ed. (1991). Coherence, Amplification, and Quantum Effects In Semi- conductor Lasers. Wiley, New York.

7. Ohtsu, M. (1992). Highly Coherent Semiconductor Lasers, Artech House, Boston.

8. Zory, P. S., ed. (1993). Quantum Well Lasers, Academic Press, Boston.

9. Camparo, J. (1985). Contemp. Phys. 26, 443.

10. Ohtsu, M.. and Tako, T.'(1988). In Progress In Optics, Volume 25, E. Wolf (ed.), Elsevier, Amsterdam.

11. Lawrenz, J., and Niemax, K. (1989). Spectrochlm. Acta 44B, 155.

12. Wieman, C, and Hollberg, L. (1991). Rev. Scl. Instrum. 62, 1, and the references

therein.

13. Tino, G. (1994). Phys. Scrlpta. T51, 58-66.

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REFERENCES 101

14. Niemax, K.. ed. (1993). Spectmchim. Acta Rev. 15(5).

1 5

.

Suematsu. Y.. and Adams, A. R. , eds. ( 1 994). Handbook ofSemiconductor Lasers and

Photonic Integrated Circuits. Chapman and Hall. London.

16. Choi, H. K., Walpole, J. N., Turner, G. W., Eglash. S. J.. Missaggia, L. J., and

Connors, M. K. (1994). IEEE Photon. Tech. Lett. 6. 7. and the references therein. 17. Franzke, J.. Schnell, A., and Niemax. K. (1993). Spectrochim. Acta Rev. 15(5), 379-395; see also general diode laser references [1-7, 14]. 18. Bonnell, L. J., and Cassidy, D. T. (1989). Appl. Opt. 28, 4622-4628; Ruprecht. P. A., and Brandenberger, J. R. (1992). Opt. Comm. 93. 82-86.

19. Welch, D. F, Parke, R., Mehuys. D., Hardy, A., Lang, R., O'Brien, S., and Scifres, D. S. (1992). Electron. Lett. 28. 2011-2013.

20. Kasuya, T., Suzuki. T.. and Shimoda. K. (1978). Appl. Phys. 17. 131-136.

21. Lang, R., and Kobayashi, K. (1980). IEEE J. Quantum Electronics QE-16, 347-355.

22. Tkach. R., and Chraplyvy, A. (1986). J. Lightwave Tech. LT-4, 1655-1661.

23. Tromborg, B., and Mork. J. (1990). IEEE J. Quantum Electronics 26, 642-654; M0rk, J., Tromborg, B., Mark. J., and Velichansky, V. L. (1992). Proc. SPIE 1837,

and the references therein. 24. Zorabedian, R (1994). IEEE J. Quantum Electronics 30. 1542. and the references

therein. 25. Fleming, M. W,, and Mooradian. A. (1981). IEEE J. Quantum Electronics QE-17,

44-59.

26. Fukuda, M. ( 1991). Reliability and Degradation of Semiconductor Laser and LEDs,

Artech House, Boston.

27. Belenov. E. M., Velichansky, V. L., Zibrov, A. S., Nikitin, V. V.. Sautenkov, V. A., and

Uskov, A. V. (1983). Sov. J. Quantum Electronics 13. 792; Akul'shin, A., Bazhenov,

v., Velichansky, V., Zverkov, M., Zibrov, A.. Nikitin. V., Okhotnikov, O., Sautenkov,

v., Senkov, N., and Yurkin, E. (1986). Sov. J. Quantum Electronics 16. 912. 28. Boshier. M. G., Berkeland, D. J., Hinds, E. A., and Sandoghadar, V. (1991). Opt. Comm. 85, 355-359.

29. MacAdam. K. B.. Steinbach, A., and Wieman. C. (1992). Am. J. Phys. 60. 1098-1 111. 30. Duarte. F J. (1993). Laser Focus World, pp. 103-109. February. 31. Harvey. K.. and Myatt. C. (1991). Opt. Lett. 16. 910. 32. Liu. K.. and Littman. M. G. (1981 ). Opt. Lett. 6. 1 17; McNicholl. R, and Metcalf. H.

}.(\9S5).Appl. Opt. 24,2757.

33. Day. T., Luecke, F, and Brownell. M. (1993). Lasers Optronics, pp. 15-17. June; Day, T, Brownell, M.. and Wu, I.-Fan ( 1995). Proc. SPIE 2378. 37-41.

34. Velichansky. V. L., Zibrov, A. S.. Molochev, V. I., Nikitin. V. V, Sautenkov, V. A., Tyurikov. D. A., and Kharisov, G. G.. (1981). Sov. J. Quantum Electronics 11, 1165-1I7I.

35. Bazhenov. V. Yu.. Bogatov. A. P.. Eliseev. R G.. Okhotnikov. O. G.. Pak. G. T,

Rakhvalsky, M. R, Soskin, M. S.. Taranenko. V. B.. and Khairetdinov. K. A. ( 1982). IEEE Proc. 129( 1 ). 77-82.

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102 SEMICONDUCTOR DIODE LASERS

36. Bradley, C. C, Chen, J., and Hulet, R. G. (1990). Rev. Sci. Instrum. 61, 2097.

37. Libbrecht, K. G.. and Hall, J. L. (1993). Rev. Sci. Instrum. 64, 2133-2135.

38. Van Baak, D. A. (1992). Am. J. Phys. 60, 803-815.

39. Telle, H. (1993). Spectwchim. Acta Rev. 15, 301-327.

40. Simon, U., Waltman, S., Loa, I.. Tittel, F. K., and Hollberg, L. (1994). J. Opt. Soc. Am. B 12, 323-327; Petrov, K. P., Waltman, S., Dlugokencky, E. J., Arbore, M., Fejer, M. M., Tittel, F. K., and Hollberg, L. (1997). Appl. Phys. B, and the references therein,

to be published. 41. Risk, W. P., and Kozlovsky, W. J. (1992). Opt. Lett. 17, 707-709, and the references

therein.

TN-103

Part II

Tunable Laser Systems

Chapter 5

CW DYE LASERS

Leo Hollberg

National Institute of Standards and Technology

(formerly National Bureau of Standards)

Boulder, Colorado

INTRODUCTION 185

1.1. Overview of Characteristics 186

1.2. Brief History of the CW Dye Laser 186

1 .3. Other Related Laser Systems 188 BASIC SYSTEM DESIGN 190

2.1. Example Systems 190

2.2. CW Output Powers 191

2.3. Dye Characteristics 192

2.4. Pump Sources 197

2.5. Resonator Design 198 EXTENDED TUNING 203

3.1. UV Generation 203

3.2. IR Generation by Difference-Frequency Mixing 205 LASER-FREQUENCY CONTROL 206

4. 1 . Frequency-Selective Elements 206

4.2. Frequency-Stabilization Methods 214 SPECTRAL CHARACTERISTICS 225

5.1. Amplitude Fluctuations 225

5.2. Frequency-Fluctuations 228 SUMMARY 232 PROBLEMS 232 REFERENCES 233

1. INTRODUCTION

The CW dye laser is a well-established tool of optical science. It plays the

premier role as a source of tunable radiation in the visible and near-visible

regions of the spectrum. This laser has a unique set of capabilities that include broad tunability. high power, and the potential for extremely high

* I gratefully acknowledge the helpful discussions and contributions made to this chapter by

Dr. J.C. Bergquist, Dr. T.F. Johnston, Jr., Dr. J.L. Hall, Dr. S.L. Gilbert, and Dr. M.

Young.

Dye Laser Principles: With Applications 185 ISBN 0-12-222700-X

TN-105
186 Leo Hollberg

resolution. Because of these capabilities we overlook its high cost, sometimes complicated design, and the requirement of a high-power optical

pump. No other optical source can provide a comparable combination of

tunability, resolution, and power.

1.1. Overview of Characteristics

The most important attribute of the dye laser is its tunability, which gives

the user access to essentially any wavelength in the visible and near-visible spectrum. The spectral range of ion-laser-pumped cw dye lasers is essentially complete coverage from 365 to 1000 nm. It is even possible to extend

their cw tuning range by using nonlinear optical methods to generate

wavelengths further into the ultraviolet and infrared. With the addition of

these methods of nonlinear optical synthesis, the spectral range for complete coverage with cw radiation has been extended to 250 nm. Radiation

at even shorter wavelengths has been generated for special applications. In addition nonlinear methods have been used to generate radiation in the

2-5 /Ltm infrared region. This range of spectral coverage will certainly be

extended in the future. The power levels available from cw dye lasers are generally more than

adequate for spectroscopic applications. The output power of cw dye lasers varies with the type of dye, but typical cw systems produce between .1 and

1 watt of output power. As with most things, there are some applications

with almost unlimited demand for power. Special high-power cw-dye-laser

systems have been developed that can produce tens of watts of tunable

visible radiation.

With broad tuning ranges and narrow linewidths, single-mode cw dye

lasers can provide an impressively large number of resolution elements.

For example, a standard single-frequency dye laser (linewidth ~ 1 MHz)

operating with rhodamine 6G dye (tuning range = 100 nm or =10'"* Hz) is capable of resolving =10^ spectral elements across its tuning curve. If we

considered one of the special high-resolution lasers that have been demonstrated (linewidths less than 1 kHz) the number of resolution elements is = 10^\ probably more than any application can actually use and certainly one of the highest of any electromagnetic source.

1.2. Brief History of the CW Dye Laser

Historically, the development of the cw dye laser was an outgrowth of

research into the photophysics of dye-laser action in pulsed dye lasers (Schafer et al., 1966; Snavely and Schafer, 1969). The first flashlamppumped dye lasers were developed in 1967 (Schmidt and Schafer 1967; Sorokin and Lankard, 1967), just one year after the first successful pulsed

IN- 106
5. CW Dye Lasers 187

dye lasers, which were achieved using ruby lasers as the pump source (Sorokin and Lankard, 1966; Spaeth and Bortfeld, 1966; Stepanov et al. 1967). With flashlamp pumping, sufficient population inversion could be

attained with surprisingly long output-pulse lengths. The pulse lengths were longer than expected because the trapping of molecular excitation in the unwanted triplet states was less probable than expected. The other

important contribution that allowed cw operation was the development of

a system to flow the dye rapidly through the pumping region in order to reduce the optical inhomogeneities induced in the dye by heating from the cw pump laser. In 1970 Peterson et al. (1970) demonstrated the first cw

lasing of an organic dye. That laser used the dye, rhodamine 6G, with an

argon-ion laser as the pump. Two decades later, the combination of the argon-ion laser and the rhodamine 6G dye is the most common, and in some ways, the best cw dye-laser system that exists. That first cw dye laser appears extremely simple, but the design is very

clever in solving some of the serious technical problems. Figure 5.1 is a

simplified diagram of the type of laser design that was used in that first successful demonstration of a cw dye laser. This laser has the dye flowing

between two dichroic mirrors that form the laser resonator as well as part

of the containment cell for the dye. The argon-ion laser pumping beam was

injected coUinearly through one of the dichroic mirrors. The Peterson et al. (1970) laser of this type produced an output power of 30 mW in a spectral

width of 3 nm when pumped with 1 W of 514-nm (argon ion) laser light.

We can get some idea of the technological evolution of dye lasers by

Dichro

Mirrors

Dye In

>

Pump Laser Dye Laser Output

Dye Out

Fig. 5.1 Cross section of the type of dye laser used for the first successful cw operation.

The two dichroic mirrors serve the dual role of containing the dye fluid and acting as the

dye-laser resonator. The dichroic mirrors transmit the blue-green pump laser beam but are high reflectors for the reddish fluorescence from the dye. The pump-laser beam is derived from an Ar^ laser. A lens is used to focus the pump beam into the dye cell at the dye-laser resonator waist which is on the flat dichroic mirror. The dye flows rapidly through the cell to remove the excess heat and triplet state population. With this type of laser Peterson et al. (1970) achieved =30 mW of cw dye-laser output power at 597 nm when the laser was pumped

with =1 W of 514-nm lieht.

TN-107
188 Leo Hollberg

comparing these results with the performance characteristics of modern

lasers, which can produce 1 W of output in a spectral width of about

10"^ nm (=1 MHz) with a pump power of 6 W. More detailed discussion

of the early cw dye lasers can be found in Tuccio and Strome (1972).

Development of the cw dye laser since 1970 has been extensive and

continues in many labs around the world today. As in most technologies, progress in the development of the cw dye laser has involved a gradual

improvement in the design of each of its components, combined with a few

important discoveries that have significantly altered the basic system. The

important achievements will be discussed in later sections, but it is useful to have some historical perspective of the development. One of the important

developments that improved the performance of the dye laser was the

introduction in 1972 (Runge and Rosenberg, 1972) of the jet-stream dyecirculation system, which gave more reliable high-power operation. About

that same time techniques were developed that allowed frequency stabi- lization of these lasers and thus greatly enhanced their spectral resolving

power (Barger et ai, 1973, 1975; Liberman and Pinard, 1973; Schroder

etal., 1973, 1975; Wu etal., 1974, Hall and Lee, 1976b). The widespread

use of traveling-wave ring lasers started in the late 70s and improved both

the spectral characteristics and the power output from the cw dye lasers (Schroder et al. , 1977; Jarret and Young, 1979; Johnston et al. , 1982). The

incorporation of computer control has provided automatic long-range tuning and enhanced data-collection capabilities (Marshall et al., 1980; Williams et al. , 1983; Clark et al. , 1986). In addition to the continual improvement of laser dyes the '80s have seen the application nonlinear optical

techniques that extended the spectral coverage that was possible with cw

lasers into the UV and IR regions (Blit etal., 1977, 1978; Couillaud, 1981; Couillaud et al., 1982; Bergquist et al., 1982; Hemmati et al., 1983; T. F. Johnston, Jr., 1987; T. Johnston, 1988; Pine, 1974, 1976; Oka, 1988).

1.3. Other Related Laser Systems

Dye lasers are often the only choice or the best choice of laser for a given

application, particularly if it is necessary to tune to a specific wavelength.

In the dye laser's region of operation, only a few laser sources are competitive and those are only in limited parts of the dye laser's spectral region. A

few new tunable lasers are beginning to threaten some of the traditional domains of the dye laser. These include semiconductor, color-center,

Ti-sapphire, alexandrite, and a few optically pumped solid-state lasers. Other nontunable lasers exist that oscillate in the visible and near-visible

region of the spectrum; for example, the Kr-ion and Ar-ion lasers have

many useful lasing lines, and the optically pumped dimer lasers (sodium.

TN-108
5. CW Dye Lasers 189

lithium, iodine, etc.) have hundreds of Hnes, but the lines are relatively narrow and, even when combining all of these lasers, the actual fractional

coverage of the available spectrum is small. Semiconductor lasers are now available in some parts of the near-IR and

red regions of the spectrum. As of the late 1980s, in comparison with dye

lasers the semiconductor lasers generally have large linewidths and low

powers. But the characteristics of semiconductor lasers are improving and

their future looks quite bright.

The broad class of optically pumped lasers shares many of the characteristics of the CW dye laser-for example, color-center lasers (Mollenauer,

1985; Mollenauer and White, 1987). Two important, and relatively new

optically pumped solid-state lasers are the Ti-sapphire laser (Schulz, 1988)

and the LNA (Lanthamide hexa-aluminate) laser (Schearer et ai, 1986).

The designs of these lasers, as well as that of color center lasers, are very

similar to the designs of cw dye lasers. The Ti-sapphire laser is an interest- ing example of a laser competing for some of the domain dominated by the

dye laser (Ti-sapphire tuning range —700-1000 nm). These lasers use the same pumping source and essentially the same cavity design, but they

have the dye medium replaced by a solid-state material. Most of the design

features discussed here for dye lasers apply equally well to other optically

pumped lasers. True, some types of lasers produce higher power, and some

yield higher spectral purity, but the dye laser combines both of these traits with broad tunability and the ability to change dyes for even broader

spectral coverage.

This chapter is not intended to be a comprehensive review of cw dye

lasers but rather a description of the basic principles of some common cw

dye lasers. Keep in mind that the descriptions are simply examples and the

possible variations and extensions are large and often unexplored. This

material is but a glimpse at the field from one perspective, where I have

additionally chosen to cover in more detail those aspects that have been

neglected in other sources, and to give less emphasis to material that is covered well elsewhere. Effort is made to give reference to other sources of

material on cw dye lasers but the reference list is not complete. It is rather

a place to start for further study. In this light it is important to note some of

the review articles and books that are particularly relevant to the subject of cw dye lasers, including Shank (1975), Snavely (1977), Schafer (1977), Peterson (1979), and Mollenauer and White (1987). Of paramount interest

is the excellent article by T. F. Johnston (1987) which is a review of dye

lasers. Applications of dye lasers are discussed by Hansch (1976) and Hall

(1978). In addition, a great deal of useful information about the design and

characteristics of cw dye lasers can be obtained from the instruction manuals of commercial laser systems.

TN-109
190 Leo Hollberg

2. BASIC SYSTEM DESIGN

2.1. Example Systems

The years since 1970 have seen the development of a large number of cw

dye-laser designs. Two examples of dye-laser systems that have seen widespread use are the three-mirror folded-linear cavity and the four-mirror

unidirectional-ring cavity. These systems are diagrammed in Fig. 5.2. We

see some features that are common to both designs; for example, both use

a)

M2

./^P,

^2 FSE

^M3 —

s

r

26 /

/ y

Output

Coupler

3-Mirror Folded Dye Laser

b)

FSE UDD ^

r« ^ N. /Y'^ ^\K > ^^^^^\ ^^'^'^^^^

-Dye Jet

Pump^

4-Mirror Unidirectional Ring Laser

Fig. 5.2 Two popular cw dye-laser resonator configurations. The standing wave three- mirror resonator shown in (a) has a folded geometry with two short-radius curved mirrors (Ml and M2) and a flat output coupler, M3. The curved pump mirror. Mp. focuses the pump

beam on the dye jet, which is placed between Ml and M2 at the waist of the dye-laser resonator. FSE represents any frequency-selective elements that might be used inside the

laser's resonator. In (b), another flat mirror has been added and the resonator is transformed

into a figure-8-shaped ring. This resonator also has a unidirectional device, which ensures

that the laser oscillates as a traveling wave, propagating in only one direction around the ring.

TN-110
5. CW Dye Lasers 191

a free-flowing jet stream for the dye gain medium and a tightly focused

ion-laser beam for the pump source. The two mirrors with short radii of

curvature, which surround the dye jet, match the dye-laser cavity mode to the small pump spot. This strongly pumped region of the dye provides a high gain over a very short interaction length. The high gain allows flexibility in designing the other parts of the dye-laser resonator. The remaining

components of these two resonators are chosen for specific attributes or

applications and many variations of these basic systems are found. The

frequency-selective elements, FSE, and the unidirectional device, UDD,

in the ring laser, indicated schematically in Fig. 5.2, are components

that control the frequency and lasing direction, respectively, and will be

discussed in detail in a later section. Some of the early cw dye-laser designs (which have not survived the test of time) used glass cells to contain the gain medium. In almost all modern cw systems the dye cells have been replaced by free-flowing dye jets. The

introduction of the dye jet (Runge and Rosenberg, 1972) and its subsequent development (for example, Harri et al., 1982) has been a major

contribution to the success of the cw dye laser. The jets do not have the

problem of the pump laser burning the dye on the cell windows. Also,

much higher output powers can be obtained with dye jets, rather than cells, because more rapid flow rates are possible. Dye-cell lasers could have some advantage in low-power applications because they might have less frequency noise than the high-power dye-jet lasers. But in general the

problems outweigh the advantages of the dye cells.

2.2. CW Output Powers

In the beginning it is useful to have a rough idea of the performance

characteristics that can be expected from a modern cw dye laser. Curves

for laser output power as a function of laser wavelength are shown in Fig. 5.3. These outstanding results are obtained for single-frequency cwlaser oscillation using a number of dyes, pump-laser lines, and changes of

laser optics. One of the important things to notice here is that it is possible

to have reasonably high output powers and single-frequency operation

anywhere in the visible and near-visible spectrum (in fact from about 365 to 1000 nm). The broad spectral coverage demonstrates the versatility of the

dye laser. With different ion-laser pump sources and 11 different dyes it is possible to generate high-intensity, coherent radiation with powers of up to several watts. In exceptional cases output powers as high as 33 W cw have

been obtained from dye lasers (Anliker et al., 1977).

The portion of the spectrum covered by the cw dye laser extends for more than an octave. The requirement of a large number of dyes is usually

TN-111
192 Leo Hollberg

35K

WAVENUMBER (cm

25 K

ui 0,1 5o

—I—

I—I—I—I—

r

DOUBLED OUTPUTS

340 360 380 400 450 500 560 600 650 700 800 900 1000 WAVELENGTH (nm)

SINGLE FREQUENCY DYE TUNING SPECTRUM

Fig. 5.3 Tuning curves of single-frequency dye-laser radiation, including frequency- doubled and sum frequency mixed outputs. The vertical axis is single-frequency power output

displayed as a function of wavelength. The direct dye-laser output spans the spectral region from the blue end of the dye PP2 at =365 nm to the red end of the dye IR 140 at = 1 ^tm. The

outputs from the intracavity frequency doubled radiation extends from =395 to 270 nm. The

two curves at the extreme blue and end show the single-frequency power obtained by

intracavity sum-frequency-mixmg the R6G dye laser radiation with argon-ion laser lines at 488 and 477 nm. These curves are taken with permission from Johnston, T. F. (1987) and

have been modified slightly to include the results from Johnston, T. (1988) for the dye PP2

(polyphenl 2).

not a problem for most applications because spectroscopic studies usually

have spectral windows that are easily covered by one dye. In fact, with the high resolution (approximately one MHz) of a single-frequency dye laser,

there is often more spectroscopic resolution than is needed. Most of the UV outputs indicated in this figure (260-400 nm) are generated by using

the strong visible dye-laser outputs and nonlinear optical-mixing methods.

2.3. Dye Characteristics

2.3.1. Absorption and Emission Spectra

The basic design of the cw dye laser is naturally constrained in fun- damental ways by the photophysics and chemistry of the dye molecules. In

Fig. 5.4 we see the representative absorption and emission spectra of a common laser dye. One of the important things to notice here is that the emission band is lower in frequency (red shifted) and is nearly the mirror

image of the absorption band. In addition both the absorption and emission spectra are broadband features without sharp lines, indicative of a multitude of broadened mechanisms and overlapping energy levels. This is

TN-112
5. CW Dye Lasers 193

Singlet Absorption

2.5x10 5x10 7.5x10 Frequency (Hz) Typical Laser Dye Spectrum

Fig. 5.4 Representation of typical absorption and emission spectra of a laser dye. The

singlet emission spectrum is to the red and nearly the mirror image of the singlet absorption spectrum. Triplet absorption is smaller and typically extends even farther to the red than the

singlet emission spectrum.

characteristic of large organic molecules in the liquid state and is depicted

by a plausible energy-level diagram shown in Fig. 5.5. Here we see two

manifolds of states, the singlets and the triplets, as designated by the net

S2e =

1—^^

cg.

^^ ^— ^ o

CD S1^ ^= a. <

c

1

~\ _ LU ^ k -

O) ETO

0!

OJ =

_]

Q.E

CD

13 CL Q

t_ soi

=^

Singlets Triplets

Fig. 5.5 Schematic picture of the energy levels of a generic laser dye, showing the singlet and triplet manifolds of states. The double lined arrows represent the optical redistribution of

excitation by the pump laser, by the dye-laser emission (and dye fluorescence), and by

triplet-state absorption. The arrow labeled k^, represents the transfer of excitation from the

singlet to the triplet manifolds.

TN-113
194 Leo Hollberg

electronic spin. The transitions from the singlet manifold to the triplet

manifold have low probability because they require an electron spin flip. The large organic-dye molecules have many internal degrees of freedom

(vibration and rotation) that give rise to broad overlapping energy levels and spectra. The transfer of excitation within these energy bands can be

very rapid, with typical time scales on the order of a picosecond. This

energy transfer within a band is much faster than the spontaneous decay

rates for interband transitions which have nanosecond time scales. For laser oscillation the dye molecule's absorption band is excited by the intense pump laser from the lower part of the ground state, SO, to higher

energy regions of the first excited singlet state SI (Fig. 5.5). This excitation

energy is then rapidly redistributed within the SI state and reappears

predominantly as fluorescence photons as the molecule decays by an elec- tric-dipole transition from the SI state to the SO state. This transition in the singlet manifold from the first excited-electronic state SI to the upper

regions of the ground state SO is the lasing transition. It is obviously

advantageous to have efficient conversion of the pump photons into fluorescence photons and to avoid the loss of the pump energy to other

channels. The primary loss mechanism (indicated on Fig. 5.5) is the transi- tion from the SI state in the singlet manifold to the TO state in the triplet

manifold. This excitation, which reaches the triplet states, is detrimental

for two reasons. First, it is a loss of available energy from the lasing singlet

system. Second, the population in the Tl state can absorb photons by

making transitions to higher levels in the triplet manifold, thereby creating

additional loss for the laser system. The characteristic time scale for the

transfer of population from the SI state to the TO state is typically 100 ns. This needs to be compared with the time scales for other processes that

affect the excited-state population. These are the fluorescence lifetime for the Sl-SO transition (typically a few nanoseconds) and the time scale for transfer of population within the SI state (typically one ps). With the good

laser dyes available today, the conversion efficiency, in terms of fluores- cence photons (SI decays to SO) for pump photons, is in the range of 0.8 to

1.0. Note that this efficiency is not the energy-conversion efficiency because

of the difference in color between the pump and fluorescence photons.

2.3.2. Dye-Laser Gain and Threshold

Following the treatments of Shank (1975) and Johnston (1987) and

making some simplifying assumptions that ignore the actual spatial dis- tribution of the pump and the dye laser intensities we can write the

small-signal gain of the laser as

ant = ^—^ . (5-i) °

/zVp + /3p/p(l+^3,T)

TN-114
5. CW Dye Lasers 195

Here, /3p — o-pTcf)-, h is Planck's constant, Vp is the pump frequency, t is the

spontaneous emission lifetime and 4) is fluorescence efficiency. This ef- ficiency is the ratio of the fluorescence decay rate to the total decay rate for the SI state and is usually near 1 for most good laser dyes. The quantities o-p, o-g, and a^ are the singlet pumping, absorption, and emission

cross sections, respectively. A^ is the density of dye molecules, € is the

dye-jet interaction length, and /p is the intensity of the pump laser. The fac- tor /Cj, is the rate of transfer of population from the singlet to the triplet

manifold and multiplies the triplet absorption cross section cr, . Above

threshold the dye laser will show laser-intensity-dependent saturation as

is usual for a homogeneously broadened system; that is.

The saturation intensity I^ is a characteristic of the dye and is a function of

the pump intensity and limits the gain as the dye laser intensity 1^ increases.

For example, we can make the reasonable assumptions that the loss terms a^ (which represents absorption of the dye-laser radiation by the dye

itself) and A:^, (the singlet-to-triplet transfer rate) are small enough to be

ignored. Then Eq. (5.1) becomes

Nta„Ir,T(jp

^o€= , J\ \ . (5.3) hVp+ (7pIpT(l) The pump intensity at threshold can be estimated from Eq. (5.3) by

equating the gain to the resonator losses. We shall represent the total resonator loss as T, which is the sum of the output coupling transmission

and the actual scattering and absorption losses. The threshold pump in- tensity is then

hv,

The optimum transmittance of the output coupler for most cw dye lasers ranges from 1 to 15% and is almost always the dominant loss term for the

laser resonator. By using typical values for the dye rhodamine 6G and the parameters

in Eq. (5.4), we can estimate the minimum required pump intensity for

laser oscillation. For rhodamine 6G we expect 7—15%, €=.01 cm,

N-=W^cm-\ c7-e = o-p-l X 10"^^ cm^, i;p = 5.8x 10^'* Hz, T-3ns, and

(/)— 1. This gives a rough value for the pump intensity at threshold of

^p,th — 2 X 10^ W/cm^. Such high intensities can be obtained continuously

only at the focus of a strong pump laser. Actual operation of a cw dye laser

will often be at pump intensities that are several times the threshold value.

TN-115
196 Leo Hollberg

In these simple considerations we have neglected many factors that strongly influence the gain and tuning characteristics of dye lasers. Two of

the important omissions here are the spatial dependence of the pump and

dye laser modes (Tuccio, 1971), and the wavelength dependence of the gain and loss cross sections. A more complete discussion of dye-laser gain can be found in Chapters 1,3, and 7 as well as in articles by Peterson et al. (1971), Peterson (1979), Danielmeyer (1971), Snavely (1977), Shank

(1975), and Kuhlke and Dietel (1977).

Two conclusions that we can glean from this calculation are that with

practical pump powers the useful gain in laser dyes will be achieved in a very small active region and that the gain will be large. High gain is an asset

in that it allows design flexibility because the laser is relatively insensitive

to small amounts of extra loss. This, in part, is the reason that there are so many different dye-laser designs. Almost anything works if you have

enough gain. Thus dye lasers can be designed with characteristics optimized for specific applications. Even though high pump powers are often

needed to reach threshold with dye lasers, the high slope efficiencies that are possible result in laser-conversion efficiencies from pump power to dye-laser power that can be quite acceptable (even as high as 50% in some

cases). However, at the highest pump powers the effects of gain saturation

and dye heating limit the ultimate powers that are achieved.

2.3.3. Broadening—Homogeneous versus Inhomogeneous

The most important aspect of the gain of organic dyes is that it is spectrally broad. The processes that determine the spectral width are categorized according to whether they are homogeneous or inhomogeneous. Operationally there are important distinctions between the two

classes of broadening. Homogeneous broadening means that all of the gain medium can contribute power to the oscillating laser mode. In contrast, for inhomogeneously broadened systems, only a fraction of the total gain is available for a specific oscillating mode. The physics of a specific

broadening mechanism will determine whether the broadening is homogeneous or inhomogeneous. In the case of homogeneous broadening, all of

the excited molecules (or atoms, or excited carriers, etc.) are effectively

equivalent and can emit radiation at any frequency within the fluores- cence bandwidth. In inhomogeneously broadened systems, on the other

hand, the emission spectrum of a specific group of excited molecules is different from the emission spectrum of the system as a whole. When the broadening is inhomogeneous the molecules can be divided into groups

that have distinct absorption and emission spectra. The Doppler shift is the

best example of inhomogeneous broadening; atoms with different velocities have different emission spectra and hence contribute gain to a laser

TN-116
5. CW Dye Lasers 197

oscillator at different frequencies. On the other hand, the broadening due

to collisions (for example, in a dense liquid) is homogeneous broadening.

The homogeneous broadening of the gain of organic dyes is both a blessing and a curse. It is a blessing in the sense that most of the available

gain can be used for a single oscillation frequency and because the broad

emission spectrum provides the laser's tunability. It is a curse because the

broad spectral width means that the excited-state lifetime is short and

hence intense pump powers are required in order to achieve sufficient population inversion for laser oscillation.

2.3.4. Dye Lifetimes

An annoying characteristic of organic dyes is that the dyes have limited

productive lifetimes. (Unfortunately this is also the case for laser scientists!) The factors that Hmit the lifetime of laser dyes are thought to be the

chemical and photochemical degradation of the dye in solution. The life- time of the gain of a dye is often specified in terms of watt-hours, based on

empirical data. This power-lifetime product is a measure of the pump-laser

energy that has been used to excite the dye. Thus the degradation must be

at least in part due to thermally activated chemistry (resulting from the

pump-laser heating of the dye) and/or actual laser-induced photochemistry in the dye solution. The chemistry of the dyes can be quite complicated as is evidenced by the fact that the lifetime of the dyes' gain can even be affected by the type of metal plumbing components used in the

dye-circulating system. The lifetimes of the typical cw dyes range from

-75 W • hr (coumarin 480) to several 1000 W • hr (Rh6G). Obviously the

predicted lifetimes are estimates of typical performance and cannot be

depended upon without further specification of the conditions. For example, the lifetimes usually assume a typical dye-pumping system with ap- proximately one liter of dye solution.

2.4. Pump Sources

We require strong, broad fluorescence from the dye for broadly tunable cw laser operation. This in turn requires an intense optical-pump source tuned to some part of the absorption band of the dye. Incoherent optical

pumping of a cw dye laser to threshold has been demonstrated by Thiel

et al. (1987) using high-pressure arc lamps; but in order to have sufficient intensity for a practical system, the pump sources are almost always cw

ion-lasers. In practice, we are presently limited to the argon and krypton-ion

lasers. The obvious reason is that they are the only cw lasers that can produce

high enough power (>4 W, say) in a good single-spatial mode and in the

visible or UV region of the spectrum. Recall that the dye's emission band is to

TN-117
198 Leo Hollberg

Table 5-1

Powers Available from High-Power Ion Lasers

Wavelength (nm) Power (W)

Argon ion 528.7 1.5 514.5 10.0 501.7 1.5 496.5 2.5 488.0 7.0 476.5 2.8 472,7 1.2 465.8 0.75 457.9 1.4 454.5 1.0 Multiline visible 18-25

Multiline UV 5.0 351.1-385.8 3.0 333.6-363.8 5.0 275.4-305.5 0.6 Krypton ion Multiline —

752.5-799.3 1.6 647.1-676.4 4.6 520.8-568.2 3.6 468.0-530.9 2.5 406.7-422.6 1.3 337.5-365.4 2.0

the red of the absorption band; this means that for visible dye lasers we

need strong blue and UV pump lasers. As of 1989, we are stuck with the very inefficient high-power ion-lasers for dye-laser pumping. Some of the strongest lines that are available from high-power ion-lasers are listed in Table 5-1. To be useful as a laser dye, a compounds-absorption band must

overlap one of these strong ion laser lines. Other pump sources are cer- tainly possible. For example, dye lasers can be pumped with a HeNe laser

at 633 nm (Runge and Rosenberg 1972; Thiel et al., 1986) and also the future holds promise for pumping with high-power green light (532 nm)

obtained from frequency doubling the output of cw YAG lasers. There has

also been some progress in designing dye lasers that could be pumped with

concentrated solar radiation (Lee et ai, 1988).

2.5. Resonator Design

A good way to understand the performance characteristics of modern cw

dye lasers is to study an example laser that is typical of modern designs.

TN-118
5. CW Dye Lasers 199

Prism

Brewster Plate

Thin

Etalon

Pump

Fig. 5.6 Diagram of a frequency-stabilized ring dye laser. The basic laser resonator is formed with four flat mirrors and two short radius curved mirrors (=5 cm). The two curved

mirrors form a tight waist that overlaps the focused pump spot in the dye jet. The optical diode is made from a Faraday rotator and a thin quartz plate. It forces the ring laser to

oscillate in one direction as a traveling wave. The hierarchy of frequency-selective elements

are the prism (double passed for added dispersion) the thin etalon (driven with a galvo motor) and the air-spaced thick etalon (constructed from two Brewster prisms and scanned with a PZT, piezo-electric ceramic). The frequency of the laser is lock to the resonance of a stable reference cavity using the cavity side lock method. The resonance frequency of the stable reference cavity is scanned using an intracavity Brewster plate that is rotated by a galvo motor. To stabilize the laser's frequency the cavity lock feeds back to the galvo-driven Brewster plate, the PZT translated mirror, and the intracavity electro-optic crystal. This laser system can scan continuously for about 80 Ghz and has a linewidth of about one kHz. Figure

reprinted with permission from HoUberg (1984).

The goal of this reverse engineering is to understand how and why dye

lasers have evolved to their present state. We choose here a laser design

that has very good performance and is in regular use today.

Figure 5.6 shows a schematic diagram of a ring dye laser based on a six-mirror ring-cavity resonator. The two mirrors close to the dye jet have

short radii of curvature (—5 cm) in order to produce the small laser-cavity

mode that is necessary in the dye jet. The remaining mirrors are flat. They

close the optical cavity in a manner that also provides space within the resonator for other optical elements. The organic dye is dissolved in a

liquid solvent (for example, ethylene glycol) and squirted as a small ribbon

of liquid dye into the space between the two short-radius mirrors. The

TN-119
200 Leo Hollberg

pump radiation from ion laser is focused by the pump mirror to a small spot

size (Wq — 15 iJLm) on the flowing jet of dye. Because of the heat produced

in the dye by the focused pump laser and because of triplet-state trapping,

it is necessary to have the dye molecules traverse the pump spot very

rapidly, where "rapidly" in this case is determined by the heating rate and

by the rate of transfer of excitation to the triplet state (typically about

1 X 10"^ s). To avoid significant loss into the triplet manifold the dye fluid needs to traverse the pumping region at a velocity of about 10 m/s. Usually

the dye jet is a nearly rectangular ribbon with a cross section of 0.1 by

3 mm and is oriented at Brewster's angle (to minimize reflection loss) relative to the laser-cavity mode and near Brewster's angle to the pump

beam. The laser mode passes through the thin dimension of the dye jet. The concentration of the organic dye in the transporting fluid is chosen

to be high enough that the dye absorbs about 85% of incident pump

radiation.

2.5.1. Spatial Hole Burning

The first question we need to address about the design of the laser cavity

is why have we abandoned the linear three-mirror cavity of Fig. 5.2 in favor of the ring resonator of Fig. 5.6. The problem with the linear cavity

is spatial hole burning. This is easily understood by thinking about the

longitudinal mode structure of a linear dye-laser cavity. The dye laser's oscillating mode traverses the dye jet twice, in opposite directions; this sets up a standing wave field in the gain medium. The standing wave is a strong

periodic spatial modulation of the laser intensity across the gain medium.

Because of the intensity-dependence of stimulated emission, a singlefrequency laser mode is only able to use the gain that is available where the

field strength is high. But we recall that the pumping field is a traveling wave that provides gain throughout the jet. Thus gain at the nodes of the standing wave cannot be used by the single-mode oscillatory field. The laser can, and will, use this available gain by oscillating simultaneously at a different frequency so that the nodes of the new oscillating mode overlap

the antinodes of the original mode. The effect of spatial hole burning is to cause the linear standing-wave cavity to oscillate with more than one

frequency (longitudinal mode).

2.5.2. Unidirectional Ring Laser The problem of spatial hole burning can be alleviated by designing a

laser resonator that oscillates in a traveling wave rather than a standing wave. Both the effect of spatial hole burning and its solution have been

known for quite some time (Tang et ai, 1963; Danielmeyer, 1971; Pike, 1974; Green et ai, 1973; Kuhlke and Dietel, 1977), but it was not until about 1977 (Schroder et al., 1977) that the travelling-wave ring dye lasers

TN-120
5. CW Dye Lasers 201 ^ B — — ^ -^^^ ^' ^

^ — — ^

^Quartz

Plate

\ Faraday

Material

Unidirectional Device

Fig. 5.7 Cross-section diagram of a unidirectional device (optical diode). A stack of permanent magnets creates a strong magnetic field (a few kG) within its central bore which

contains Faraday material. The quartz "rotate-back" plate uses optical activity to rotate the

polarization of the laser field. Thus, the laser-propagation direction inside the quartz plate must be along the z-axis of the crystal. The configuration shown here is designed for minimum

loss with both the Faraday material and the quartz plate oriented at Brewster's angle relative to the laser-propagation direction. For the beam propagating in the direction shown, the net

rotation of the polarization is 0°, whereas the other direction has a net rotation of about 4°.

came into prominence (Jarrett and Young, 1979; Johnston etal. , 1982). An

interesting discussion of using prisms to create ring resonators for dye

lasers is given by Marowsky and Zaraga (1974).

To avoid lasing in both directions, the ring laser's cavity must have more

loss for one of the two propagation directions. This increased loss for one

direction is provided by a nonreciprocal loss element, depicted in Fig. 5.6

as an optical diode. This optical diode (or unidirectional device) provides

the directionally specific loss by using the axial vector nature of magnetic

fields. A typical unidirectional device is diagrammed in Fig. 5.7. The

device works by rotating the polarization of the propagating laser mode for only one of the two propagation directions. The rotated polarization en- counters extra loss in the remaining Brewster-angle elements of the ring

cavity. The rotation is made nonreciprocal by the Faraday effect of a

crystal or glass in a magnetic field (applied parallel to the direction of

propagation of the laser mode). The direction of polarization rotation due

to the Faraday effect is independent of the direction of propagation of the

light through the material. This Faraday rotation can then be combined

with a reciprocal polarization rotation to produce an optical diode that rotates the direction of polarization for a beam from one direction but has no net rotation for a beam from the other direction. The reciprocal rota- tion is easily obtained from the optical activity in a thin quartz plate. A

small differential loss of about =0.5% is sufficient for unidirectional operation of most ring dye lasers. This loss is achieved from a one-way polarization rotation of about 4° in a laser cavity that has six Brewster surfaces or more. The design criteria for unidirectional devices are discussed by

Biraben (1979) and by Johnston and Proffitt (1980).

TN-121
202 Leo Hollberg

Unidirectional ring lasers with traveling wave fields have advantages over standing-wave lasers because of more efficient use of the available

gain and better spectral characteristics. On the other hand, with ring lasers there is reduced gain per pass because the radiation field only traverses the gain medium once for each incidence on the output coupler. The net result

is that with sufficient pump power the traveling-wave ring dye lasers can

provide almost twice the single-mode output power of the standing-wave

lasers. For this extra power and mode stability ring lasers have the dis- advantage of slightly higher cavity loss because of the extra optical components. This means that the thresholds are typically higher for ring cavities. Some of the very low gain dyes actually work better in linear cavities because of their lower threshold.

From the gain arguments just given and knowledge of the pump powers

that are available, we know that the gain medium will occupy a small

volume (about 10"^ cm^). To optimally use the available gain the dye

laser's spatial mode is approximately matched to the pump-laser spatial

mode in the dye medium. "Approximately matched" here indicates that the optimal size of the pump and dye laser modes is actually a function of

the saturation of the gain medium and is thus a weak function of the pump

power (Suavely, 1977; Johnston. 1987). In practical cases, where the laser operates well above threshold, this dependence is weak and is usually not worth the trouble of readjusting the laser mode when the pump power is changed. We usually have a pump-laser spot size of about wq = 15 /xm,

which is consistent with the available pump powers and the threshold

intensity of the dye. We can then use Gaussian mode analysis to calculate the transverse mode structure for a laser resonator (Yariv, 1975; Siegman,

1986). This analysis can give us the information that is necessary to select the mirror spacings, orientations, and radii of curvature that will approximately match the dye-laser mode to the gain region.

2.5.3. Resonator Aberrations

Up to now we have naively assumed that the natural fundamental

transverse mode structure of the dye laser is the round TEMqo mode. But

in fact the orientation of the curved mirrors in the laser cavity relative to the incidence angle of the laser beam alters the transverse structure of the TEMoo mode. Having a laser beam incident on spherical mirrors at an

angle other than normal incidence causes the beam to be aberrated by

astigmatism and coma. The dye jet is also a source of astigmatism and coma because it intercepts the strongly focused Gaussian laser mode at an

angle. These aberrations distort the laser mode from the desired TEMoo

mode, and this degrades the resonator's stability and reduces the laser's conversion efficiency. In most modern designs the astigmatism is compenTN-122
5. CW Dye Lasers 203

sated by the appropriate choice of angles of the resonator's mode at the

curved mirrors or by the addition of other optical elements that introduce an astigmatism of the opposite sign. It is even possible to simultaneously

compensate for both astigmatism and coma. Details of the compensation

methods can be found in Kogelnik et al. (1972), Johnston and Runge

(1972). and Dunn and Ferguson (1977).

Using the geometry shown in Fig. 5.2a, we can follow the analysis of

Kogelnik et al. (1972), and Mollenauer and White (1987) to calculate the

astigmatism introduced by the two curved mirrors and the dye jet. The dye

jet with thickness t is located between the two short-radius curved

mirrors (Ml, M2) and is tilted at Brewster's angle B relative to the beampropagation direction. In this geometry there are two sources of astigmatism; the first is that due to the dye jet crossing the laser mode at an angle

and the second due to the curved mirror M2 that is tilted at the angle

relative to the laser-mode —propagation direction. Fortunately, the sign of

the astigmatism is opposite for these two sources, and the angles can be

chosen so that the mirror astigmatism cancels that of the jet. The condition

for zero astigmatism is

/(sin 0)(tan d) = t{n^ - 1) ^^^^^^, (5.5) n where /is the focal length of mirror M2 and n is the index of refraction of

the gain medium (Kogelnik et al.. 1972). Since the dye jets are quite thin

(—0.1 mm) and the mirrors have radii of about 5 cm, the angle 6 must be

small. These small angles are not always practical, so other methods have

been used to compensate the astigmatism. These includes lenses or

additional curved mirrors that are titled off normal incidence, a Brewster

plate between the dye jet and the short-radius mirrors, and rhombi with Brewster-cut surfaces that are placed in an auxiliary beam waist in the laser

cavity.

3. EXTENDED TUNING

3.1. UV Generation

Nonlinear optical methods can be used with dye lasers to extend the

already broad tuning range of cw dye lasers. If we look back to Fig. 5.3 we

see the U'V-tuning curves that were obtamed by T. F. Johnston (1987) and

T. Johnston (1988) using a high-power single-mode cw dye laser. This cw

single-frequency UV output is generated either by frequency doubling the

output of the dye laser or by sum-frequency mixing the output of the dye

TN-123
204 Leo Hollberg

laser with the output of a single-frequency argon-ion laser. Using these

methods, they have generated single-frequency cw UV radiation across the

frequency range between 260 and 400 nm. The excellent UV powers

obtained in these experiments were typically about 10 mW. Both the

doubling and the frequency mixing were done inside the resonator of a ring

dye laser. For the sum-frequency mixing experiments the two laser resonators were actually arranged to overlap at the nonlinear crystal. Thus the mixing occurred with buildup on both the input frequencies. Other systems

have been developed to generate cw ultraviolet light in this frequency

range and beyond (Frolich et ai, 1976; Blit et ai, 1977, 1978; Couillaud,

1981; Couillaud et al., 1982; Marshall et al., 1980; Bergquist et al., 1982; Hemmati et al. , 1983). The transparency of the nonlinear crystals limits cw UV generation to wavelengths longer than approximately 160 nm. That is not the case for UV generation in atomic vapors. Four-wave mixing has

been used in strontium vapor to generate —10 pW of broadband (—6 GHz)

cw UV radiation at 170 nm (Freeman et al., 1978).

Noteworthy among these efforts to generate single-frequency cw UV

radiation is the work of Bergquist and collaborators(Bergquist et al., 1982; Hemmati et al., 1983), who have combined the second harmonic of argonion laser radiation (fundamental = 514 nm) with tunable dye-laser radiation (=792 nm) to generate UV radiation at 194 nm. Other colors could

certainly be generated by these methods but the 194-nm radiation is of

particular interest for high-resolution spectroscopy of Hg ions. Their sys- tem is diagrammed in Fig. 5.8. It serves as good example of the techniques

and the 1980s state of the art for synthesizing single-frequency cw, UV

radiation. Their system uses the nonlinear crystal KB5 (potassium pentaborate) to generate the sum frequency of 792- and 257-nm radiation. The

792 nm radiation comes from a cw ring dye laser (LD700 dye), and the 257 nm radiation is from the frequency-doubled 514 nm argon laser. One

of the techniques they use to advantage is putting the nonlinear crystals in external ring buildup cavities. This enhances the optical power in the nonlinear crystals and avoids the problem of the crystal's loss in the laser resonator. A ring cavity containing a Brewster-cut ADP (ammonium

dihydrogen phosphate) crystal is locked to and enhances the power of the 514 nm radiation by a factor of —33. Thus 700 mW of 514 nm radiation

generates about 30-40 mW of 257 nm radiation. Then, as shown in Fig. 5.8, they use two buildup cavities around the KB5 summing crystal; one ring cavity builds up the 792-nm radiation and the second ring resonator builds up the 257-nm radiation. Both these cavities have buildup factors of =15. With input powers of =120 mW at 792 nm and =30 mW at 257 nm

they obtain =20 /aW of cw single-frequency radiation at 194 nm. The

output power at 194 nm is not limited by the availability of input powers

TN-124
5. CW Dye Lasers 205

I94nm

iD=24° 5 = 3 25"

KB5-Crystol

Double Tipping v'

Brewster Plates ^^^

792 nm 2"'^'°'® ^^^'0/

SINGlf

RING DYE

FfiEQUENCY LASER A

UV » AVV

11Uu^-^W^ %t^^ ^ ^

«\^

Poiorizotion Beom-Splitter

Plate

SERVO CONTROL

SINGLE FREOUENa

»R- ION LASER

515 nm

DOUBLING

RING CAVITY

257 nm

Fig. 5.8 Sum frequency generation of 194-nm radiation. This system, developed by Hemmati et al. (1983), and Bergquist (1989) uses the noniinearity of the KB5 crystal to generate

the sum frequency of 257- and 792-nm radiation. The power in both of these input beams is enhanced in ring buildup cavities whose waists intersect in the KB5 crystal. Servo-control

loops (using the polarization lock method) keep the two buildup cavities locked to their respective input beams. The 194-nm radiation leaves the KB5 crystal at a slightly different angle and thus escapes from the two buildup cavities. The 792-nm input radiation comes from

a frequency-stabilized ring dye laser, while the 257-nm is generated by frequency doubling the 514-nm radiation from a single-frequency argon-ion laser. The frequency doubling of the argon-ion laser radiation is done in a ring buildup cavity that is similar to the two used around

the KB5 crystal shown here. With input powers of =30 mW at 257 nm and 120 mW at 792 nm. this system generates up to 20 /xW of single-frequency radiation at 194 nm. Unpublished figure reprinted with permission from Bergquist (1989).

but rather by the effects of thermal blooming due to nonuniform optical

heating of the KB5 crystal. Another important technique of nonlinear

optics that is used in this system is electronic servo-control systems to maintain the resonance condition for the buildup cavities (see section 4 on

laser frequency control).

3.2. IR Generation by DiflFerence-Frequency Mixing

The useful tuning range of dye lasers can be similarly extended into the

infrared by difference-frequency mixing (Pine, 1974, 1976; Oka, 1988).

The technique is analogous to the sum-frequency generation, but now the

TN-125
206 Leo Hollberg

crystal's nonlinearity is used to generate the difference frequency between

an ion-laser beam and a tunable cw dye laser. Using LiNb03 as the

nonlinear crystal Pine (1974, 1976) has demonstrated that one can produce

narrowband ( — 15-MHz linewidth) radiation with wavelengths in the range

of 2.2 to 4.2 microns and with power levels of a few microwatts. The tuning

range can be extended by using other nonlinear crystals such as lithium

iodate (Oka, 1988). Somewhat higher power levels can also be achieved.

One problem with describing the late 1980s state of the art is that there is a tendency to report the best performances rather than what is typically

achieved. The output-power curves shown in Fig. 5.3 are an example of

what is possible with an optimized dye laser with very powerful pump

lasers. The performance that you should expect from a typical commercial

dye laser system is probably a factor of two less power than shown there. Nevertheless the record performances are always interesting, because re- search continues to expand our possibilities and the best results today are

indicative of the tools of the future. In addition, the extreme limits are often dominated by new and interesting science waiting to be explored.

4. LASER-FREQUENCY CONTROL

High-resolution dye lasers are common laboratory tools today because

of early research efforts in laser frequency control. The broad bandwidth of

the gain medium, combined with the mechanical instabilities of the rapidly

flowing dye jet. conspire to make frequency selection and stabilization a challenge. Nont<^heless, the technology required to control the frequency

of dye lasers has been developed. Many years ago, Soffer and McFarland (1967) demonstrated that the wide bandwidth of pulsed dye lasers could be compressed to a relatively narrow bandwidth by inserting an

optical grating inside the cavity. In addition to reducing the laser's line- width, the frequency selectivity of the grating allowed the laser's wavelength to be tuned. This demonstration of spectral compression, as well

as more recent techniques, takes advantage of the homogeneous broadening of the dye laser gain to produce a narrower spectral linewidth without

sacrificing output power.

4.L Frequency-Selective Elements

The laser's oscillation frequency can also be controlled by providing

frequency-selective loss inside the resonator. To achieve this frequencyselective loss, we have freedom to control both the spatial and polarization

boundary conditions of the resonator. Dispersive optical elements that create boundary conditions for the oscillating mode provide the appropriTN-126
5. CW Dye Lasers 207

ate frequency-selective loss. The dispersion can come from interferometry,

which is solely wavelength-selective, or it can be provided by polarizationsensitive elements which act on the vector nature of the optical field. Some

of the dispersive elements that have been used to control the frequency of

CW dye lasers include gratings, prisms, birefringent filters, and Fabry-Perot

etalons, as well as Michelson, Fox-Smith, and Mach-Zehnder interferometers (Smith, 1972).

Usually the addition of one frequency-selective element into a dye

laser's cavity is not sufficient to uniquely determine the laser's oscillation frequency. The conventional technique to achieve mode-stable singlefrequency operation is to use a hierarchy of frequency-selective elements

inside the laser's cavity. Most single-mode lasers use three separate levels of frequency selectivity to force the laser to oscillate on a specific longitudinal mode of the laser's cavity. Lacking this hierarchy of frequency

selectivity, the laser may oscillate with many modes, or it may oscillate with a single mode that is unstable to small perturbations and jump from

mode to mode as a function of time.

Due to the homogeneous broadening of the gain, once the laser starts to

oscillate on a specific mode, this mode quickly depletes the gain that is otherwise available for the other longitudinal modes. In a traveling-wave

ring dye laser the homogeneous broadening causes strong mode competition, which is usually enough to ensure that the laser will oscillate on a

single longitudinal mode. Unfortunately, without frequency selectivity in the cavity, the oscillating mode is unstable to small perturbations and will change in time. Thus even though the laser oscillates on a single mode,

additional frequency-selective elements inside the cavity are necessary to

select a particular frequency.

A typical hierarchy of frequency-selective elements might start on the

least selective end with a birefringent filter, which typically has a half- power bandwidth in the laser resonator of about 1800 GHz (60 cm~^). This

is usually followed by two etalons, with progressively higher resolution; for example, a thin etalon with a free spectral range (FSR) of 200 GHz and a

finesse of —3, then a thick etalon with a FSR of 10 GHz and again a finesse of —3. The overlap of the transmittance peaks of the three frequencyselective elements provides a net transmittance bandwidth that is narrow enough to uniquely determine a single mode for laser oscillation. The role of the various frequency-selective elements can be seen in Fig. 5.9, which

shows the transmission functions of these elements overlaid with the laser longitudinal mode structure. The resolving powers of the three levels of

frequency-selectivity are chosen so that the resolution of one level is sufficient to select a unique resolution element of the next higher level of

selectivity. Thus, the birefringent filter has enough resolution to select a

TN-127
208 Leo Hollberg

|a|

Ibl

- 300X SCALE EXPANSIOMFREQUENCY OFFSET IGH2I

Fig. 5.9 Filter transmission functions of the various frequency-selective elements of a single-frequency dye laser. The traces show the bandpasses of the frequency-selective ele- ments relative to the dye gain curve and the laser's cavity-mode structure. The upper half of

the figure has a broad spectral range and shows the birefringent filter and thin-etalon transmission functions. The lower half of the figure shows the thick etalons transmission

function relative to the longitudinal mode spacing (c/L with L = cavity round-trip length) of

the laser cavity. Also indicated are the losses created for radiation away from the central transmission peaks. This figure is reprinted with permission from Coherent Inc. and Johnston.

T. F. (1987).

specific thin-etalon mode, the thin-etalon selects a specific thick-etalon

mode, and the thick etalon has enough resolution to select a specific

longitudinal mode of the laser cavity. For the system to work in an optimum way, the bandpasses of these filters need to be at least roughly

centered on a specific cavity mode. Figure 5.6 is an example of a singlefrequency dye laser with a shghtly different hierarchy of frequencyselective elements, in this case a prism and two etalons. The frequency stability of such single-frequency lasers is now deter- mined by the mechanical stability of the optical elements, the gain

TN-128
5. CW Dye Lasers 209

medium, and the resonator's superstructure. We shall see in the spectral

characteristics section (5.2) that "single frequency" is a bit optimistic, in that the spectral linewidth of single-mode lasers can still be substantial. The birefringent filter is the most common coarse tuning element and is composed of quartz plates placed in the laser cavity inclined at Brewster's

angle relative to the direction of propagation (Bloom, 1974; Bonarev and

Kobtsev, 1986). The thickness of each plate in the filter is integrally related

to the others (for example, 1 :4: 16 for a common three-plate birefringent

filter). The quartz plates are cut with the optic axis parallel to the surface of

the plates. The design of the birefringent filter for a laser follows the

traditional Lyot filter design (Jenkins and White, 1957), with the important difference that the polarizers between the birefringent elements have

been removed. The role of the polarizers is played by the Brewster-angle

surfaces of the plates themselves and other Brewster surfaces in the cavity.

The optical frequency selectivity of this filter results from the birefringence

of the quartz waveplates combined with the polarization-dependent reflec- tion loss from the Brewster surfaces of the plates. The plates are mounted

together in the laser cavity so that they can be rotated about the normal to the plates, thereby changing the angle of the crystal axis with respect to the

laser polarization (parallel to the plane of incidence) while maintaining the

Brewster-angle orientation of the quartz surface relative to the laser mode

propagation direction. For a given plate thickness and orientation of the

optic axis, the plate will act as a wavelength-dependent waveplate, which in general changes the polarization character of the input laser mode. At some wavelength the polarization of the light that exits each plate will be

the same linear polarization (p-polarization) that entered and, thus, will pass with no loss through the subsequent Brewster surfaces. In general the

polarization of the beam will elliptical upon exiting each of the plates and

will therefore experience reflection loss at the Brewster surfaces that it encounters in traversing the rest of the laser cavity. Birefringent plates with

integrally related thicknesses can provide enough selectivity that lasing will be restricted to one color (a few cavity modes) within the dye gain curve. It

is interesting to note the frequency selectivity of the birefringent filter, in the laser cavity, is higher than that of a traditional Lyot filter with polarizers. The net spectral width of a cw dye laser with only a three-plate

birefringent filter can vary significantly depending on alignment; widths can vary from 1 to more than 100 GHz (Nieuwesteeg et al., 1986). The loss provided by a single Brewster surface for a beam incident with a polarization that is orthogonal to Brewster's polarization is

TN-129
210 Leo Hollberg

Here n represents the index of refraction of the Brewster plate, and the

loss is the fractional reduction in power of the transmitted beam. A net gain reduction of less than 1% is usually sufficient to suppress other modes

from lasing. A typical birefringent filter will have a free spectral range of — 100 nm. A dye laser with a three-plate birefringent filter has at least eight

Brewster surfaces (including the jet surfaces) that can provide a net loss of

—4% for a 200-GHz detuning (this corresponds to the FSR of the thin etalon, see Fig. 5.9).

Usually etalons provide the next two higher levels of frequency selectivity. These parallel plate interferometers have the standard Fabry-Perot

transmittance (Born and Wolf, 1964),

4/? ^ ^ 47rnL

where F = — —^ and 5 = cos d. Here R represents the power reflectance of the etalon's surfaces (assumed

equal), n its index of refraction. L its thickness, and 6 the angle between

the etalon normal and the optical propagation direction inside the etalon. A is the vacuum wavelength. A useful measure of the etalon's resolving

power is its finesse, S*, which is given by,

3= -77^. (5.8)

A cw ring dye laser might have one thin etalon (L = 200 /u,m with R - 30%) and one thick etalon (L = 1 cm and R = 30%), which, when combined with the birefringent filter, provide sufficient frequency-selectivity to force the laser to oscillate on a single longitudinal mode.

The frequency-selective components that we consider here are typical of

single-frequency dye lasers used in 1989, but other frequency-control sys- tems have also been developed. As noted earlier, the high gain of the dye

laser allows some experimental flexibility in testing ideas about laser design. The system with a birefringent filter and two etalons is the most

popular because of its dependability and relative ease of construction. That

is not to imply that this system is optimum. The tuning elements that are

alternatives to the birefringent filter are prisms and the tuning wedge that

is now rarely used. A variety of interferometric methods have also been

used to control the frequency of dye lasers. These include the Michelson,

Fox-Smith, and Mach-Zehnder interferometers and multiple implementations of these. Interferometers generally compete for the higher selectivity roles normally filled by the etalons.

TN-130
5. CW Dye Lasers 211

Optical Etalon Diode

Dye Laser

Output

Tipping Brewster Plates mi

Pump Beam M2

Biretringent

Filter PZT ^\hr

R2-*—

A *

R~50% v

HP

^

Fig. 5.10 Diagram of a single-frequency ring dye laser that uses a Mach-Zehnder inter- ferometer for longitudinal mode control. This laser also uses a birefringent filter and a thin etalon for frequency selectivity. An optical diode is used for unidirectional operation and

tipping Brewster plates are used for frequency scanning. The inset shows the structure of one

type of intracavity Mach-Zennder. This interferometer is constructed from two high-quality

optical flats. One piece has a 50% reflectivity coating on its front surface and a high reflectivity coating (HR) on the back surface. The partial reflecting surface splits the input beam into two

paths through the interferometer. The other optical flat is a high-reflectivity mirror and is mounted on a PZT translator so that the passband of the interferometer can be changed. The

Mach-Zehnder has two output ports (Rl and R2). If the reflectivity of the partial reflector is 50%, and the losses in the two paths through the interferometer are matched, the contrast in the output ports can be 100%. With good low-loss coatings, the net insertion loss of this device in the laser cavity can be very small. Figure reprinted with permission from Bergquist and Burkins (1984).

One of the most intriguing of the interferometric frequency selectors for use with dye lasers is the Mach-Zehnder system that was proposed and

developed by Bergquist and Burkins (1984). An example of one of the

several possible implementations is diagrammed in Fig. 5.10. The advantage of the Mach-Zehnder interferometer is that, in principle, it can provide the necessary frequency-selectivity with substantially less excess loss than that of a comparable etalon. The reason for the unavoidable loss with intracavity etalons is that it is necessary to tilt the etalons away from

normal incidence to avoid the disruptive effects of optical feedback on the

oscillating mode of the laser. Tilting the etalon ehminates the feedback but we pay the penalty that power is lost from the laser mode. In laser jargon,

this "etalon walkoff loss" results from the multiple reflections within the

tilted etalon that bounce laser power out of the spatial mode of the laser

TN-131
212 Leo Hollberg

cavity. A properly balanced Mach-Zehnder system does not have this limitation because the only additional optical output port (beam Rl in Fig. 5.10) has zero output under proper operating conditions. This occurs when the Mach-Zehnder interferometer is set for a interference maximum

on beam R2 (which corresponds to a minimum for beam Rl) and when the

interference maximum is tuned to a longitudinal mode of the laser cavity. In this case the only excess loss introduced by the Mach-Zehnder to the

laser is that due to the absorption and scattering from the optical coatings,

which can be made negligibly small. In practice the Mach-Zehnder system

has seen only limited application but appears to have great potential.

The most important attribute of dye lasers is their tunability. In addition

to reaching a particular wavelength, we frequently want to scan the fre- quency of the laser over some region near this wavelength. Depending on

the spectral resolution that is required, it may not be necessary for the laser

to oscillate on a single longitudinal mode. For example, the spectral

features observed in solid-state spectroscopy are relatively broad, which

often means that the resolution provided by multimode dye lasers is adequate. In this case a dye laser with only a birefringent filter provides

enough resolution, and the laser can be scanned simply by tuning the

bandpass of the birefringent filter. On the other hand, the technology

required to tune and continuously scan the frequency of single-mode

(single-frequency) dye lasers is complicated by the many frequencyselective elements. It is necessary to individually center and then scan all of

these elements synchronously. Such scanning systems have been developed

and some even actively optimize the centering of the bandpasses of the

frequency-selective elements. The actively controlled systems provide

long-term mode stability and repeatable scans. More sophisticated dyelaser control systems incorporate computer-controlled wavelength calibration, frequency scanning, and data acquisition (Marshall et al., 1980;

Williams et al., 1983; Clark et al., 1986).

For a deeper understanding of the methods of laser-frequency control we focus attention on a typical tuning system for a single-mode ring dye

laser (such as in Fig. 5.6). We assume that the frequency-selective ele- ments are able to force the dye laser to operate on a single longitudinal

mode of the laser cavity. The optical length of the cavity then determines

the fine tuning of the laser frequency. The laser frequency can be adjusted over a small range by using the piezoelectrically translated mirror, PZT (see

Fig. 5.6), and larger-frequency changes are induced by rotation of the Brewster plate. Changing the optical length of the cavity will scan the laser but only within the bandpass of the thick etalon. Since the thick etalon has

enough resolution to select a single mode it also limits the scan to less than

the laser cavity FSR. In order to achieve longer scans, the thick etalon

TN-132
5. CW Dye Lasers 213

must be scanned synchronously and likewise eventually the thin etalon

must also be scanned. Usually these etalons are scanned with a piezoelectric translator to change the spacing between the plates of the thick etalon

and by using a galvo-motor to rotate the thin etalon. The alignment of the thick-etalon transmission peak to the cavity mode

is critical and usually requires an automatic electronic servo to keep its bandpass properly aligned with the laser-cavity mode. This can be accomplished by using a conventional "modulation lock" which will be discussed

shortly. For long scans it is necessary to tilt the thin etalon to track the

thick etalon, but because of its low resolving power it is usually not necessary to have automatic feedback control —although such systems

have been developed (Biraben and Labastie 1982). Tracking of the thin- etalon bandpass to a scanning laser frequency is also complicated by the

fact that the bandpass of a tilted etalon scans approximately quadratically

as a function of the tilt angle (see Eq. 5.2). This nonlinearity can be

electronically compensated by using an electronic square-root-function

module. Centering the passband of the birefringent filter is usually done

manually by finding the maximum laser output power on a given mode.

Automatic control systems for the birefringent filter can also be made by

monitoring the polarization of the laser's output, which becomes slightly

elliptical when the birefringent filter's bandpass is not properly centered on

the cavity mode (Biraben, 1989).

A typical dye-laser scanning system thus consists of a Brewster plate

rotated by a galvo-motor, a piezoelectrically driven thick etalon to track

the specific cavity mode, and a thin etalon that is tilted by a galvo-motor to track the thick-etalon scan. All of these scanned elements are synchronized

by a master control circuit that thus controls the laser's frequency. Commercial single-mode dye-laser systems can be scanned continuously with direct electromechanical control over ranges of about 30 GHz. Longer scans are

certainly possible but they would put more stringent requirements on the

electromechanical stability of the tuning elements. For example, with

1-MHz resolution, a 30-GHz scan already provides 3 x 10'* resolution

elements, which is usually adequate for most applications. There are some limits to the mechanical and electrical stability, linearity, and reproducibility of the electromechanical transducers used to position the tuning

elements. Instability in these systems translates directly to laser-frequency

fluctuations. In practice it is difficult to achieve 10 parts per million resolution in the electromechanical positioning. One can reconstruct a broader

spectrum by computer-driven piecewise scans of about 30 GHz each. The

total scan is then limited only by the bandwidth of the dye. but care must

be taken to maintain some frequency reference in putting all of the separate scans together.

TN-133
214 Leo Hollberg

Pressure scanning of dye lasers is an alternative approach to mechanical

scanning. As of the late 1980s, pressure scanning is not very popular, but it has some advantages. For example, it does not require moving parts in the

laser. The idea is to enclose the entire laser inside a pressure-tight vessel so

that when the pressure is changed the optical path length changes (due to changes in the index of refraction of the gas) and this causes the laser's frequency to change. If the etalons are designed with an open air space

between the etalon surfaces, then when the pressure is changed, the etalons scan synchronously with the laser frequency.

4.2. Frequency-Stabilization Methods

The nature of the frequency fluctuations of lasers (as with other oscilla- tors) is such that the measured frequency-stability depends on the time

scale over which the measurement is made. The spectrum of dye laser frequency, fluctuations is strongly peaked at low Fourier frequencies and

then tapers down to a white noise level at high frequencies. In addition

strong resonant peaks in the spectrum of the frequency noise result from a

variety of technical problems (for example, noise at the AC line fre- quency). It is common practice to specify a laser's frequency-stability by a short-term "linewidth" and a longer-term center-frequency stability or

drift rate. The implicit assumption here is that short-term fluctuations of

the laser's phase determine the "linewidth," while slower fluctuations and

drift dominate the stability the laser's center frequency. This model of the

lasers frequency fluctuations has enough validity to be useful but it is far from the complete picture.

The frequency of the single-mode dye laser is determined by the boundary conditions imposed by the optical length of its resonator, which are

usually arbitrary and generally lack long-term stability. The solution to the problem of frequency instability and inevitable drift is to lock the

laser to a frequency reference such as a stable reference cavity or a molecular resonance. In principle the ultimate stability of the laser frequency

can match that of the reference cavity if the control system is properly

designed. Usually systematic errors degrade this performance considerably. Standard stabilized dye-laser systems have linewidths of —1 MHz

with a center frequency of —5 x 10^"* Hz. Typical drift rates are about

10 kHz/sec, which is adequate for most experiments. The best cavitystabilized laser systems have laser-frequency drift rates of about 1 Hz/s

(Salomon et ai, 1988; Hils and Hall, 1989; Helmcke et al., 1987). This

outstanding performance exceeds the precision that is required for all but

the most demanding metrology and physics experiments.

The other compelling reason to have a stable reference cavity is that it

TN-134
5. CW Dye Lasers 215

can act as a fast frequency discriminator with a very large signal-to-noise

ratio. The error signal derived from the cavity is then used in an electronic servo system to narrow the laser's linewidth and hence improve its resolution. The resulting linewidth of a laser stabilized to a reference cavity will depend on the laser's intrinsic frequency-fluctuation spectrum, the refer- ence cavity's resolution, the servo system's bandwidth, and even the

observation time. Some knowledge of the methodology of frequencycontrol systems is useful in developing an understanding of the operational characteristics of high-resolution dye lasers (see also Balykin et al. (1987) and Helmcke et al. (1982, 1987). Some of the common frequencystabilization techniques are outlined in the following section.

4.2.1. Cavity-Side-Lock

One of the easiest and most generally applicable frequency-control

methods is the cavity-side-lock system. It has been with us at least since the

early days of the dye laser. This system uses a spectrally sharp Fabry-Perot

transmittance peak to derive an electronic error signal that can be used to lock the laser to the side of the cavity resonance (see Fig. 5.11). The error

signal is the difference between the photocurrents of the cavity transmit- tance peak (signal channel detected by Dl) and the laser power (reference

channel detected by D2). The light levels are adjusted so that the output

from the difference amplifier is when the laser frequency is tuned to the

side of the cavity resonance. This provides a smoothly varying monotonic

frequency discriminator for laser frequency excursions less than 1/2 of the

Lock

Point :^A[

Laser

Servo

D2

Dl

Detector

<f: ,A

Reference

Cavity

Cavity Side Lock

Fig. 5.11 Laser frequency control by the cavity side lock method. Part of the laser's output beam is directed into a Fabry-Perot cavity and onto a photodetector DL A reference beam is directed onto detector D2 which measures the laser's power. The transmission

function of the Fabry-Perot cavity is shown schematically near Dl. The cavity acts as a frequency discriminator for the laser. The error signal is generated from the difference between the signals from Dl and D2, and is shown with the lock point indicated at zero

voltage. A servo amplifier uses the error signal to control the laser's frequency.

TN-135
216 Leo Hollberg

cavity-resonance width. Depending on the overall sign of the correction

signal, the laser frequency can be locked to one side of the fringe or the

other. The zero crossing of the error signal is set at the point of fringe half maximum by adjusting a variable attenuator in the reference channel. The

DC offset of the reference channel is derived from the laser power rather

than from a voltage reference for a good reason. This reference signal

generated by the laser power cancels laser-amplitude fluctuations that would otherwise cause an error in the lock signal. This is an important

correction because, as we shall see, the amplitude fluctuations on dye

lasers are often relatively large. Details of an advanced side-lock fre- quency-control systems can be found in Helmcke et al. (1982).

4.2.2. Modulation Lock

A second and very useful method of laser-frequency stabilization is the

modulation lock. This system incorporates frequency modulation and syn- chronous detection to generate an error signal that is then used to lock the

laser to the peak of a resonance. The resonance can be a Fabry- Perot

cavity transmission signal but it can equally well be an atomic or molecular

resonance. This method is very general and it allows us to stabilize any

variable parameter to the ma.ximum or a minimum of a response function.

Because of the simplicity of the method and because we often want to maximize (or minimize) some response, the technique is widely used in servo-control systems. We described this method in terms of locking the

oscillation frequency of a laser to the peak of a Fabry-Perot transmission fringe. The important features of the modulation lock are illustrated

in Fig. 5.12a, 5.12b. The various electronic signals are shown in Fig. 5.12b

where the Fabry-Perot transmission fringe is displayed as a function of the

laser frequency. If the laser frequency is sinusoidally modulated about

the peak of the cavity resonance, the transmitted light intensity varies as the

second harmonic of the modulation frequency. However if it is modulated

about the side of the cavity resonance, the transmitted power will vary at the modulation frequency with a phase that depends on which side of the

fringe the laser is tuned. There is a 180° relative phase shift of the modulation response on the two sides of the fringe. The power of the laser light

transmitted through the cavity is then detected and demodulated using a

lock-in amplifier. The lock-in output is then lowpass filtered to produce the

discriminator-shaped output (see Fig. 5.12b). This discriminator signal is used as the error signal for the servo-control loop. The phase reversal of

the error signal across the fringe changes the sign of the output from the

lock-in and produces an error signal that crosses at the peak of the resonance. For small-modulation amplitudes, the shape of the discriminator signal is approximately the first derivative (with respect to frequency)

TN-136
5. CW Dye Lasers 217

'%

Lock

Point

Servo *, Laser

Lock-in

•"Vj) Modulation

A

Reference .JV n Cavity Yl

V

Modulation Lock

Fig. 5.12a Laser frequency control by the modulation lock method. A Fabry-Perot refer- ence cavity is used as a frequency discriminator for the laser. The cavity's transmission

function is indicated schematically near the photodetector and amplifier. The signal from the detector goes to the lock-in amplifier where it is compared with the modulation signal that is used to modulate the frequency of the laser. The lock point is indicated on the error signal

that is shown schematically as the output of the lock-in. A servo amplifier uses the error signal

to control the laser's frequency.

Modulation Response

Sinusoidal —FM Averaged Demodulator Output

Modulation Lock Signals

Fig. 5.12b Signals used in the modulation locking method. The cavity transmission function and the modulation of the laser's center frequency are displayed on the left-hand edge of

the figure. The center of the figure shows the variation of the cavity's transmission due to the modulation and is displayed as a function of the laser's center frequency relative to the cavity resonance. The demodulator (lock-in) inverts the modulation response synchronously every

half-cycle of the modulation. Its output is shown at the bottom of the figure. When the demodulator's output is averaged for times that are long compared with the modulation

frequency, the result is an output signal that is approximately the derivative of the cavity transmission function. This output is shown at the bottom right of the figure and is displayed

as a function of the laser's center frequency.

TN-137
218 Leo Hollberg

of the transmission function. Similarly, high-order approximate derivative

signals are obtained by demodulating the transmitted power at harmonics

of the modulation frequency. For example, a third derivative locking signal

is obtained by demodulating at the third harmonic of the modulation

frequency and it has some advantages with respect to systematic errors. These frequency modulation-demodulation ideas are also useful for reducing noise and background problems in spectroscopy (e.g., laser derivative or FM spectroscopy).

4.2.3. rf-Optical Heterodyne Lock

Another laser stabilization system has been developed using rf heterodyne techniques (Drever et al., 1983; Hough et a/., 1984; Helmcke et al., 1987). Of all of the methods, this "rf-optical heterodyne"" locking system

has demonstrated the best performance, in terms of both center frequency

control and the narrowest linewidths. The method is similar to the modulation lock described previously, with the distinction that it uses radio- or microwave phase modulation on the laser's output to generate laser side- bands that lie outside the resolution width of the resonance of interest. The

high modulation frequencies are advantageous in suppressing noise, in achieving high-servo-control bandwidths, and in achieving good transient

response characteristics. An example of an optical heterodyne system used

for laser-frequency stabilization is diagrammed in Fig. 5.13. Here the system

consists of a laser, an electro-optic phase modulator {d) mod, made from a

crystal of ADP, ammonium dihydrogen phosphate), an optical directional

coupler (made from two polarizers and a Faraday rotator), a precision

reference cavity, a photodetector (det), some filters, a balanced mixer, and

a servo-control amplifier. The cavity resonance is detected in reflection by this heterodyne technique and can provide two types of signals. These

signals are derived from the two detection quadratures of the balanced

mixer (determined by the phase of the reference signal) and correspond to the cavity transmission and dispersion functions. The cavity resonance acts to alter the pure phase modulation that was imposed on the laser light by

the electro-optic modulator. This alteration of the phase modulation comes

from the transmittance and phase shift of the laser light by the cavity. The

cavity thus converts some of the phase modulation into amplitude modulation, which is then detected by the photodetector and subsequently demodulated by the mixer to generate a baseband (DC) response. The phase of

the reference signal (derived from the original modulation signal) that is applied to the mixer determines the detection quadrature and, thus,

whether we detect the effect of cavity transmittance or dispersion. Typical

response signals for the two detection quadratures are shown in Fig. 5.14. The discriminator shape of the dispersion signal provides an excellent error

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TN-139
220 Leo Hollberg

Fig. 5.14 Cavity signals generated by the rf-optical heterodyne locking method. The

output of the mixer (from Fig. 5 13) is shown as a function of the laser's frequency which is scanned. The upper trace shows the output when the phase of the reference signal (applied to the mixer) is set to detect the cavity's transmission. The multiple-peaked structure results from the carrier and sidebands being transmitted into the cavity when they come into resonance. The carrier (large peak in the center) and the two adjacent sidebands are separated by the modulation frequency. Small peaks due to the second-order sidebands are

also visible at a spacing that is twice the modulation frequency. The lower trace shows the output when the phase of the reference signal is shifted by -nil. It represents the effect of

cavity dispersion as seen by the phase-modulated laser beam. The dispersion signal has a steep discriminator shape that crosses when the carrier is tuned to the peak of the cavity resonance. This discriminator is used as the error signal in the frequency-control loop. This

figure is reprmted with permission from Drever et al. (1983).

signal for laser-frequency control. Some of the components in this system can be compared directly to those of the modulation lock; the phase

modulator serves the role of the laser FM, and the mixer replaces the

lock-in amplifier. One important advantage of the heterodyne system is that the high modulation frequencies and the detection of the cavity in reflection allow the time scales of the detection process to be very short. This allows the response time of a servo system to be shorter than the

characteristic response time of the cavity (Drever et al., 1983) while maintaining a good signal-to-noise ratio. This is an important consideration for the high-speed servo systems that are required for very narrow laser linewidths. This method has been used by Bergquist and collaborators

to observe — 50-Hz-wide mercury-ion resonances; this indicates that the

dye laser's linewidth and center frequency stability are at least that good

(Wineland etai, 1989).

TN-140
5. CW Dye Lasers 221

4.2.4. Polarization Lock

Noteworthy because of its good performance and simplicity is a related laser-frequency-stabilization method that was developed by Hansch and

Couillaud (1980). Analysis of the polarization state of the light reflected from the cavity is used to detect the dispersive nature of the cavity reso- nance. This method has the advantages that it produces a discriminatorshaped signal without modulation and it has a very large capture range. This results in a robust laser-locking method that is useful for laser- frequency stabilization and optical buildup cavities.

4.2.5. Postlaser Stabilization

An exciting and relatively new development in laser-frequency control is the implementation of a postlaser-frequency-correction system (Hall and

Hansch, 1984; Hall et al. 1988). The concept is that with the appropriate

acousto-optic and electro-optic transducers, we can correct the frequency

errors on the laser beam after the beam exits the laser. A system of this type is diagrammed in Fig. 5.15. The external frequency correction is implemented with an acousto-optic frequency shifter (driven by a voltagecontrolled oscillator) and an electro-optic modulator (EOM). The EOM

acts as frequency transducer through its ability to induce a time-dependent

optical phase shift via its electric-field-dependent index of refraction. In

this case the change in the laser frequency is proportional to the derivative

with respect to time of the applied electric field. Thus the circuitry for the

electronic feedback to the EOM is complicated by the fact that adding a

fixed frequency shift to the laser requires that a voltage ramp be applied to the EOM. The EOM used in this way operates as an optical phase shifter and hence only works well for removing high-frequency fluctuations. The

acousto-optic transducer is required for the low frequency fluctuations and

fixed frequency offsets. Another challenge is the fact that the time scales for the response of the acousto-optic and electro-optic transducers are very

different and appropriate crossover compensation must be designed. Clever

solutions to these challenges have been developed by Hall and Hansch

(1984). The error signal for this system can be derived from any of the

methods described previously, but perhaps the most appropriate is the

rf-optical heterodyne method. Impressive performance has been achieved

with these postlaser stabilization systems but, unfortunately, they are not

available commercially as of 1989. Starting with a single-mode dye laser that had an intrinsic linewidth of —1 MHz, the postlaser stabilization methods have produced linewidths on the order of 1 kHz. Even better performance can be anticipated. Another application of this method has

been to make an optical phase lock between a cw dye laser and a HeNe laser

TN-141
222 Leo Hollberg

ELECTRO-OPTIC

MODULATOR

ACOUSTO-OPTIC

MODULATOR

OUT

VOLTAGE

CONTROLLED

OSCILLATOR

SIGNAL

INPUT

Fig. 5.15 Laser-frequency control by the post-laser-stabilization method. In this system

the frequency of the laser's output is changed outside the laser by an electro-optic modulator and an acousto-optic modulator. A time rate of change of voltage applied to the electro-optic

crystal will change the frequency of the laser beam by a small amount. Larger frequency shifts are generated by the acousto-optic modulator which is driven by a voltage-controlled oscillator. To optimally use the two transducers the input error signal is first processed electronically

as indicated. Figure reprinted with permission from Hall and Hansch (1984).

that was used as the reference oscillator (Hils and Hall, 1989; Salomon

etal., 1988).

It is humbling for laser scientists to learn that many of the basic principles in these methods had been developed in the prelaser days by scientists working with rf and microwave systems. The techniques were subsequently

"reinvented" with laser technology.

TN-142
5. CW Dye Lasers 223

Up to this point I have outlined various general techniques for deriving an error signal from a resonance, but have not discussed the requirements

for a feedback loop that can use this error signal to control the laser frequency. The loop needs to process the error signal and drive the

appropriate transducers to correct the laser's frequency fluctuations. The

loop will thereby null (or attempt to null) the error signal. Common dye

laser frequency transducers are galvo-motor-driven Brewster plates,

piezoelectrically mounted mirrors, and electro-optic crystals (see Fig. 5.6).

Each of these transducers can change the optical path length of the laser cavity and hence the laser frequency. Typical commercial frequencystabilized dye-laser systems use a galvo-driven Brewster plate and a piezomounted mirror for their frequency-control transducers. These systems

routinely achieve laser linewidths on the order of one MHz. With faster feedback control and better reference cavities it is possible to achieve laser linewidths of about 20-100 kHz with a piezo-mounted mirror and a galvodriven Brewster plate. For very high resolution applications an electro- optic modulator (EOM) can be included in the laser cavity. With the EOM,

dye-laser linewidths on the order of 50 hertz have been demonstrated and

linewidths of one hertz or less are anticipated. These are truly impressive

high-resolution oscillators when we recall that the oscillation frequency is ~5 X 10'"* Hz. The narrow linewidths achieved with the intracavity EOMs

are due to the high-speed response of the crystal and the high servo bandwidths that are possible. In general the higher the servo bandwidth,

the narrower the resulting laser linewidth. The actual performance of the

frequency-stabilization system depends on the spectral density of the fre- quency noise on the laser and the characteristics of the servo loop. In

principle, and in some cases in practice, laser linewidths as narrow as you

desire can be achieved with late 1980s technology (Hils and Hall, 1989).

Often the limitation to the resolution is not the laser at all but rather the

spectroscopic sample of interest. Optimization of the filter characteristics of the feedback loop can be a

difficult task given the complexity of the system with the multiplicity of

transducers. In addition we need to take into account the spectrum of the

dye laser's frequency noise and the laser's dynamics. The simplest control

loops (termed proportional locks) use purely proportional control, where

the feedback is linearly related (by the gain) to the error signal. These

control systems are very stable but are lacking in both accuracy and

dynamic response. A significant improvement in performance is obtained

by integrating the error signal with respect to time before feeding back to the transducers. An integrating loop filter has gain that rolls off toward

higher frequencies at a rate of 6 dB per octave for each stage of integration. Even a single-stage integrating-loop filter has the advantage that is

TN-143
224 Leo Hollberg

guarantees zero error at DC and only a fixed, finite error for a ramping

error signal. In contrast, the proportional control loop will in general

always have a finite error. Adding some derivative feedback in the loop can

often improve the dynamic response. It is common practice to use some

combination of proportional, integral, and derivative feedback. These

systems are best optimized with careful system analysis, but empirical

adjustment of the gains and time constants is often productive.

As we have discussed, most of these laser-locking methods can be

applied equally well to stabilizing the frequency of lasers to a cavity or to atomic or molecular resonances. In the latter case the most applicable

techniques are the modulation lock and the rf heterodyne lock. The ability to stabilize the laser to an atomic resonance is important for some spec- troscopic applications and is crucial for high-accuracy metrology and

laser-frequency standards. The atomic and molecular resonances cannot

provide the same signal-to-noise ratio that is available from a cavity,

but their long-term (say, for times longer than a few seconds) stability

is generally much better. For dye lasers to have high resolution and high

accuracy, it is customary to lock the laser's frequency to a high-Q refer- ence cavity (to achieve the narrow Imewidths) and then to lock the cavity

to an atomic or molecular resonance (which then provides the long-term

stability).

The transformation of a broadband dye laser into a frequency-stabilized

narrow-linewidth laser adds considerably to the cost and complexity of the

laser system. There is also a penalty to be paid in the available output

power when we add intracavity optical elements (this typically amounts to about a factor of 2). If we use an electro-optic crystal, the upper power

limit may also be reduced due to the limited optical-power density that the

crystals can endure.

In summary, commercial stabilized dye-laser systems can provide high

resolution ( = 1 MHz) with tunability and good power levels. Their tuning

range extends throughout the visible and near-visible part of the spectrum.

These high-resolution systems are more than adequate for most spectroscopic applications. For applications that demand higher resolution, very narrow-linewidth dye-laser systems have been developed in a number of

research laboratories. The systems with the best reported resolution generally use optical heterodyne techniques and EOMs to achieve laser line- widths below 100 Hz. I see no reason that the hnewidths could not be

reduced further to below one Hz in the future. So while the performance

levels achieved in 1989 are truly impressive, they are merely a ghmpse of

the present state of the art and they will certainly be surpassed.

TN-144
5. CW Dye Lasers 225

5. SPECTRAL CHARACTERISTICS

The complexity of dye lasers encourages the user to have some diagnostic instruments to monitor the laser's output characteristics. Useful di- agnostic tools include power meters as well as wavelength- and linewidthmeasuring devices.

With dye tuning ranges of about 100 nm and linewidths of about

10"^ nm it is not a trivial task to determine, with precision, the lasing

wavelength of cw dye lasers. Many interferometric instruments have been

developed to measure the laser's wavelength relative to known standards;

these include the lambda or wave meter, the sigma meter, the Fizeau

wavemeter, calibrated Fabry-Perot interferometers, and dispersive bire- fringent filters (Juncar and Pinard, 1975; Kowalski et al., 1976, 1978; Hall

and Lee, 1976a; Woods et al., 1978; Snyder, 1980; Williams et al., 1983;

Licthten 1985, 1986; DeVoe et al., 1988). The accuracy of these inter- ferometers varies from 5 to 8 digits. Special standards-laboratory instru- ments are capable of 10 digits of accuracy in wavelength measurement. Also

extremely useful for general laboratory spectroscopy are the wavelength

tabulations that exist for molecular spectra of some simple molecules, such

as those for I2 (in the red) (Gerstenkorn and Luc, 1978) and Te2 (in the

blue) (Cariou and Luc, 1980). These tabulations can be used to determine

a dye laser's wavelength to about 3 x 10"^. We need certain mathematical and experimental tools to characterize

the spectral properties of lasers. These tools certainly include the fre- quency and amplitude-noise spectral densities and maybe the Allan vari- ance. The Allan variance was developed to quantify the frequency stability

of oscillators and can be applied directly to lasers. It is discussed here be- cause of its usefulness and its popularity in the literature and also because

it is not found in the usual textbooks.

5,1. Amplitude Fluctuations

The spectral distribution of amplitude noise in the output of a singlefrequency dye laser contains a great deal of useful information. It can be

measured directly by monitoring the laser light with a fast photodetector

and a rf-spectrum analyzer. The quantum theory of the laser predicts that the fluctuations in the power from an ideal laser source will be determined

by the statistics of the quantum mechanical generation of the photons

(Sargent et al.. 1974; London, 1983). In this model the ideal laser would

produce light with a time distribution of photons that is Poissonian. Upon

TN-145
226 Leo Hollberg

! I

W/^M^ll#Hi»^^

rr

4^

18 Frequency (MHz)

Fig. 5.16a Spectral density of the amplitude noise of a single-mode rmg dye laser. The

noise on the laser's output power is strongly peaked at the lower frequencies and finally reaches the shot-noise level at a frequency of about 4.5 MHz. The broad peaks in the noise come from small amounts of power oscillating in transverse modes m the argon pump laser. These pump-laser-related noise peaks extend out to hundreds of megahertzes but spectral regions can be found where the dye laser's amplitude noise is shot-noise-limited.

detection this photon distribution generates a Poissonian photoelectron

distribution and hence produces the usual "shot-noise" fluctuations in the photocurrent,

is^ = i2eiBW)'/\ (5.9)

Here / is the detected photocurrent, e is the electron charge, and BW is the detection bandwidth. The shot-noise distribution is spectrally flat. Figure

5. 16a shows the measured spectral density of the amplitude noise of a good

single-mode dye laser. The figure also indicates the expected shot-noise

level for the same average optical power on the detector. Clearly, there is more going on in real lasers than is predicted by the quantum mechanical

model of the ideal laser. Characteristically, the amplitude noise is very

large at low Fourier frequencies and decreases progressively to higher

frequencies until it reaches the shot-noise level at a frequency of approximately 4.5 MHz. We also see that there are many large resonant noise

peaks throughout the spectrum. These are due to various technical noise

TN-146
5. CW Dye Lasers 227

c

0) Q

o

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Fig. 5.16b Spectral ciensity of the amplitude noise of the same ciye laser as shown in Fig. 5.16a. but now with the aperture in the argon laser carefully adjusted to elliminate transverse modes. The dye laser's amplitude noise is improved, but the noise is still strongly peaked at low frequencies.

sources, the most important of which are the argon laser's intermode

beats that are transferred through the gain of the dye jet to the dye laser's power (these intermode beats are observed out to several hundreds of

megahertz). In Fig. 5.16b the spectral density of the amplitude noise of the same dye laser is shown but now with the argon laser resonator apertured

to eliminate transverse modes. This removes most of the resonant peaks in the noise (in this frequency range) and significantly improves the dye

laser's amplitude noise spectrum.

One of the important things we learn from the spectrum of amplitude

noise is that any measurements that are made with a detection bandwidth

centered at low frequencies (or near one of the resonant noise peaks) will be contaminated by excess noise on the laser. As seen in Fig. 5.16 this excess noise is not negligible. In this example there is =35 dB of excess

noise at a detection frequency near 100 kHz (resolution bandwidth was

3 kHz). The noise is even greater at lower frequencies. Not surprisingly the

signal-to-noise ratio can be improved by moving the center of the detection

bandwidth to higher frequencies by using high-frequency modulation

methods. If we look to high enough frequencies it is possible to reach the

TN-147
228 Leo Hollberg

shot-noise level in some limited-detection bandwidth. In fact, it is even,

possible to achieve noise levels below this shot-noise level by using nonlinear optical methods to generate nonclassical forms of light such as squeezed states. This regime of sub-shot-noise Hmited detection is a hot

topic in modern optics with two compilations of papers on this and related subjects ("Squeezed States," 1987).

5.2. Frequency Fluctuations

One method for determining the frequency stability and hnewidth of a dye laser is to monitor the laser's output with a high-resolution Fabry-Perot

cavity (optical spectrum analyzer). These instruments are available commercially. Using a scanning Fabry-Perot cavity to measure the spectral

distribution of light from a multimode standing-wave dye laser (with only a

birefringent filter as the tuning element) shows the optical power distri- buted in a large number of discrete longitudinal modes. The spectral width

of this array of modes can vary from 1 to 100 GHz. In this multimode case

the distribution of modes is often unstable.

If the dye laser is made to run on a single mode, a high-finesse cavity can be used to determine the laser's Hnewidth and the spectral distribution of

the residual frequency fluctuations. Another method for measuring the

frequency stability of a laser is to use a fast photodiode to observe the beat note between the unknown laser and a narrow-linewidth reference laser. There is also the "self-heterodyne" method, which uses a fiber delay-line

to measure the laser's Hnewidth.

The frequency noise spectrum of a single-mode laser can be measured

best by detecting the rf spectrum of the heterodyne beat note between two

lasers: the unknown laser and a reference laser that has a narrower spectral

width (Hough et ai, 1984). This heterodyne method is generally preferred

for the very high resolution systems but it requires an additional very stable reference laser to act as the local oscillator. A limitation here is that the

Hnewidth of the very best lasers must be determined by deconvolution of

two equally good lasers or by other methods (cavities or special narrow

spectral lines).

The Fabry-Perot cavity method of measuring a laser's frequency-noise

spectrum reHes on using the cavity's transmittance or reflectance function

as a frequency discriminator. By tuning the laser's center frequency to the

side of the cavity resonance and measuring transmitted power, the cavity

then acts to convert frequency fluctuations directly into amplitude fluctua- tions at the detector. A cavity (or a molecular resonance) can be an excellent frequency discriminator but care must be taken to avoid systematic

errors (for example, detection bandwidth limits, cavity response time.

TN-148
5. CW Dye Lasers 229

and laser amplitude noise). The literature is full of "outstanding" results based on improper measurements. A good example of a very popular

mistake is to lock a laser's frequency to some cavity or atomic resonance

(by the methods described previously) and then monitor the error signal

within the servo-loop to provide a measure of the residual frequency noise.

This appears reasonable at first glance, but usually the error signal is contaminated at some level by systematic errors (such as a ground loop).

These systematic error signals are then corrected by the servo system as if they were laser-frequency fluctuations. This puts these artificial errors

directly on the laser frequency. Any measurement of the error signal would

indicate that the laser's frequency fluctuations are small, because the servo loop is acting to cancel the error signal. This gives a misleading result when

the measured error signal is then used to calculate the laser's frequency

fluctuations. However, it is true that monitoring the residual error signal is useful in providing information about how well the servo electronics are working. It does not answer the question of how well the error signal

represents the laser's frequency fluctuations. To make a definitive state- ment about the frequency fluctuations of a stabilized laser it is imperative

to have a measure of the laser's frequency that is independent of the

stabilization system.

The self-heterodyne method of measuring a laser's linewidth uses a time

delay and a heterodyne detector to produce the autocorrelation of the

laser's frequency noise at a given time delay (Okoshi et ai, 1980). This

method compares the oscillation frequency of a laser at an earlier time with

its oscillation frequency now. Self-heterodyne systems are very easily implemented by sending some of the laser's output through a long fiber (for

the delay) and then combining this fiber-delayed output with the direct output on a fast photodetector to observe the beat note. In these systems one of the two beams is usually frequency shifted by an acousto-optic

modulator (for example, by 80 MHz) to avoid technical noise at zero frequency difference upon detection. It is difficult to make accurate measurements with this method if the laser has a very narrow linewidth,

and in general care must be used to avoid misleading results (Kikuchi and

Okoshi, 1985).

A spectrum of frequency fluctuations can be used to provide an effective laser linewidth (Elliot et al., 1982). In two limiting cases, which depend

on the analytical character of the frequency noise, the linewidth can be

calculated trivially. The important factor here is whether the Fourier

frequency of the dominant frequency fluctuations is high or low, compared

with the rms frequency fluctuations of the laser. That is. are the main

frequency excursions caused by low frequencies with a high modulation

index, or high frequencies with a low modulation index, where high and

TN-149
230 Leo Hollberg

low are measured relative to the laser's rms frequency fluctuations. For

example, if we make the assumption that the frequency-noise spectrum is rectangular with a bandwidth B, we can calculate the linewidth in these two

limiting cases. If the laser's rms frequency fluctuations are large compared

to the bandwidth of the frequency fluctuations, the lasers lineshape is Gaussian and the Hnewidth is given by

ApHM-2(2en2)'/2 6,^,. (5.10)

Here 6rms is the rms frequency deviation. On the other hand, when the

bandwidth of frequency fluctuations is larger than the laser's rms frequency

fluctuations, the laser's lineshape will be Lorentzian and the linewidth will be given by

Al^rmsJ //r 1 1 \ FWHM^-^ — (5.11)

Here we have again simplified the problem by assuming that the spectrum

of frequency fluctuations is rectangular in shape with a bandwidth B. In the more general case when the frequency fluctuations are not spectrally flat, with important contributions coming from both high and low Fourier

frequencies, the lineshape and linewidth could be determined from the spectrum of frequency fluctuations by numerical integration of the equations given by Elliot et al. (1982).

As with the amplitude noise, the spectrum of frequency fluctuations for dye lasers is large at low frequencies and then falls off at higher frequencies. There are often numerous large resonances throughout the spectrum.

Figure 5.17 shows the spectrum of frequency fluctuations of a single-mode

ring dye laser that was measured with a high finesse cavity and a rf-optical

heterodyne detection system. Also shown is the reduction in the frequency

noise that is achieved when the frequency-control loop is turned on. In this case, the servo is able to reduce the frequency noise (as measured by the servo-loop error signal) by as much as 50 dB. An independent frequency

discriminator would be required for an accurate determination of the

laser's linewidth.

A mathematical tool that is genuinely useful in describing the frequency

stability of lasers (and other oscillators) is the Allan variance (Allan, 1966; Allan et al. , 1974). It is the variance of the second difference of a series of

consecutive frequency measurements. The Allan variance is defined

1 / 1 '^-' \i/2

TN-150
5. CW Dye Lasers

REF -13.0 dBm ATTEN dB

SMPL

231

CENTER 1 1. 90 MHz

RES BW 1 KHz VBW 1 kHz

SPAN 1. 000 MHz

SWP 3. eec

Halletal Summary for IQEC - 88 Tokyo, Japan July 18-22, 1988

Fig. 5.17 Spectral density of the frequency noise of a single-mode ring dye laser with and

without fast frequency control. The frequency fluctuations are measured using the rf-optical heterodyne locking method (modulation frequency =12 MHz) diagrammed in Fig. 5.13. The

vertical scale displays the dye laser's frequency noise with a sensitivity of 10 dB/div. The

horizontal scale is 100 kHz/div and the data were taken with a resolution bandwidth of one kHz and a video bandwidth of one kHz. The largest peak shows the frequency noise on the

laser without fast frequency control. When a fast postlaser frequency control loop (of the type diagrammed in Fig. 5.15) is implemented, the frequency fluctuations are reduced. The three lower curves show the effect of incrementing the control loop gain by about 10 dB per step. The frequency noise remaining in the lowest trace is near the noise level of the measurement

system. It would correspond to a dye-laser linewidth of less than one Hz if the measurement

of the error signal was an accurate measure of the laser's frequency fluctuations. Figure is reproduced with permission from Hall el al. (1988).

Here M is the number of successive frequency measurements (assuming no

dead time between measurements), vq is the mean laser oscillation fre- quency, and Vi is the zth frequency measurement made during the sample

interval time r. The Allan variance can also be calculated from the power

spectral density of the frequency noise S(/) as follows:

r -(t) = 2 ^S(/)/sin2 77/7^2

vl (5.13)

TN-151
232 Leo Hollberg

One of the wonderful properties of this function is that it is well behaved

for common types of frequency noise, such as 1// noise. This is not true for the usual standard deviation which is often divergent. The Allan variance

serves as a one-parameter figure of merit for the frequency stability of

oscillators. Without measuring the spectrum, it can provide a diagnostic of

the type of frequency fluctuations that are present. For example, an Allan

variance that decreases as 1/t, where ris the averaging time, indicates that the frequency noise spectral density is white.

6. SUMMARY

Cw dye lasers are a unique source of laser radiation with broad tunability,

high spectral purity and good output-power levels. We have seen that these

lasers can provide complete spectral coverage from 365 to 1000 nm with

typical power levels that range from 0.1 to more than 1 W. Nonlinear

optical techniques have been used to extend this spectral coverage into the UV (260-400 nm) by harmonic generation and sum frequency mixing and

into the near-IR (2.2-5 microns) by difference frequency mixing. Other

specific wavelengths not included here have been generated by nonlinear

methods for special applications. Continued improvements in the pump

lasers, the dyes, and the nonlinear optical materials will undoubtedly

provide higher output powers and extended spectral coverage. The spectral characteristics of cw dye lasers are both good and bad: good

with respect to their linewidths and. hence, spectral-resolving capabilities,

but generally poor with respect to their amplitude noise properties. The

spectral density of amplitude noise on cw dye lasers is large for Fourier

frequencies below a few megahertz. Because of necessity, techniques

have been developed to alleviate the problems associated with this amplitude noise. Typical linewidths of cw frequency-stabilized dye lasers are = 1 MHz, which is more than adequate for most applications. The technology is available to reduce the dye laser's linewidth to =1 Hz for those

special applications that require it.

PROBLEMS

1. By making simple assumptions about the dye gain and available pump

power, design a three-mirror folded linear dye laser cavity of the type

shown in Fig. 5.2. For this cavity calculate the expected difference in frequency between the main longitudinal mode and the spatial hole- burning mode that could oscillate simultaneously.

2. Calculate the expected temperature rise of a laser dye (such as R6G in ethylene glycol) when it is pumped with 10 W of cw ion-laser radiation

TN-152

J
5. CW Dye Lasers 233

at 514 nm. Make reasonable assumptions about the optical and physical properties of the dye and the dye-circulation system.

3. Estimate the feasibility of pumping a cw dye laser with solar radiation.

For this estimate propose some simple and realistic design for the

laser.

4. Assuming the spectrum of frequency noise shown in Fig. 5.17 is an

accurate representation of the dye laser's frequency fluctuations, make

an estimate of the contributions to the laser's linewidth due to the various spectral regions of the noise. To calibrate the vertical scale, use

the fact that a perfectly coherent laser would produce a signal of

-3 dBm (at 12 MHz) when the laser's center frequency was tuned

to the half-power transmission point of the reference cavity. Note

that the rf-heterodyne detection method transfers the frequencyfluctuation information from zero frequency to the modulation fre- quency (12 MHz in this case).

5. Assume that the Fourier spectrum of a laser's frequency fluctuations is described by a simple power law dependence (that is. S(/) - H,, • /"";

a = 2. 3/2, 1. 1/2, 0, -1/2, and -1, and H„ is a constant).

(a) Find the functional dependence of the Allan variance on the

averaging time t. (b) Determine which simple power laws also give a standard deviation (using the usual definition) that is well behaved.

6. What sort of length stability is required for a Fabry-Perot reference

cavity that is used to stabilize the frequency of a visible laser to one Hz? Can length stabilities with this performance be achieved given

the physical properties of realistic materials?

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Laser Spectroscopy

Volume 64, Number 25 PHYSICAL REVIEW LETTERS 18 June 1990

Hyperfine Structure of the Metastable ^.^2 State of '^O Using an AlGaAs Diode Laser at 777 nm

G. M. Tino/"' L. Hollberg,^''^ A. Sasso/'^ and M. Inguscio^^'

European Laboratory of Nonlinear Spectroscopy (LENS), Largo E. Fermi 2, 1-50125 Firenze, Italy

M. Barsanti

Scuola Normale Superiore, Piazza dei Cavalieri 7, 1-56100 Pisa, Italy

(Received 12 February 1990)

By exploiting a narrow-linewidth diode-laser source we measure the hyperfine structure of the ^52

state of "O. Nuclear parameters can be calculated from the measured hyperfine structure. Recorded

collision-free linewidths allow an estimate of the lifetime of the levels involved in a new scheme proposed

for the cooling of atomic oxygen.

PACS numbers: 35.10.Fk,32.30.Jc

Nuclear effects in the spectrum of atomic oxygen are of great interest. Recently, a possible nuclear volume

effect on the isotope shift of optical transitions was observed. ' This effect is usually negligible in light ele- ments but it is enhanced in this case by the "doubly

magic" structure of the '^O nucleus which has both pro- ton and neutron closed shells. A deeper understanding

of these effects requires more detailed information about

the atomic structure. For example, information is re- quired about the electron density at the nucleus which

can be obtained from the analysis of the hyperfine structure. '^O is the only stable oxygen isotope which has

hyperfine structure since it has one neutron in the ds/2 orbital outside the doubly closed '^O nucleus; this pro- duces a nuclear magnetic moment of — 1.894/iyv-^ In

this paper we report the first measurement of the hyperfine structure of atomic oxygen performed by

high-resolution laser spectroscopy. In fact, the only existing data on the hyperfine structure for this atom were

obtained in a paramagnetic-resonance experiment on the ground state.

^ The level we have investigated is the excited 3 ^52 level (Fig. 1). The interest of this particular level is twofold.

First, it is the lowest in energy (9.14 eV) for the excited

configuration l5^2.y^2p^3.s, so stronger nuclear effects can be expected. Since optical transitions start from this

level, combined measurements of the isotope shift and

the hyperfine structure represent a stringent test for a

priori Hartree-Fock calculations, which are not easy for

this multielectron atom. Second, the 3^52 state is metastable (lifetime t~180 /is) and is connected to the

3*/*i,2.3 states by three strong transitions at X—777 nm;

as we discuss below, radiative cooling of atomic oxygen

could be achieved using these transitions and the subsequent decay of the cooled atoms into the ground state would produce very cold ground-state oxygen. This

metastable cooling is the only realistic cooling scheme

for oxygen since no allowed transition at visible wavelengths is available from the ground state. A critical pa- rameter for cooling is the lifetime of the upper 3^P state;

it determines the time required for the deceleration of

the atoms which must be shorter than the lifetime of the

3^S2 state. From the present results an estimate for the

3*/*-state lifetime is obtained, which supports this pro- posed cooling scheme. In addition, GaAlAs/GaAs het- erostructure diode lasers emitting at X.~780 nm are now

available with enough power to perform nonlinear highresolution spectroscopy. Interest in diode-laser spectroscopy has increased since the development of several tech- niques which improve these lasers' spectral purity and tu- nability^"* making them suitable for laser-cooling experiments. In this work a diode laser mounted in an extended cavity configuration is used to perform saturation

spectroscopy on the is^Sz-^p^Pj transition at 777.1 nm.The experimental arrangement is shown in Fig. 2. The laser we used was a commercial AlGaAs/GaAs

diode laser emitting at 780 nm at room temperature.

Coarse tuning over a range of more than 10 nm was

achieved using optical feedback from a 1 200-lines/mm

TRIPLET QUINTET

'h.

^ ^ ^D 'S 'p »D

\

6s'N605nm

-7—

'396nni

3p

.5s ^4d

'616nm

\

.''845nm

-'3s 7"

Anm

^(r-l80MS)

SINGLET \/"y

/

;558nm \ / 1^ 'nj(T-100s \ /

636nm "-- -A/

/

_\j3 (ground slate)

FIG. 1 . A simplified energy-level scheme of O I showing the

optical transition investigated in this work (solid line) and other transitions of spectroscopic interest (dashed lines). © 1990 The American Physical Society TN-159 2999
Volume 64, Number 25 PHYSICAL REVIEW LETTERS 18 June 1990

discharge

cell fffP+0

to recorder

FIG. 2. Scheme of the experimental apparatus. Laser fre- quency stabilization is achieved by optical feedback from a

grating which also acts as the output coupler. The beam is retroreflected through the sample cell to observe sub-Doppler

saturation spectra. Double-headed arrows represent lenses. A

Fabry-Perot interferometer (FPI) is used to monitor the laser's frequency.

ruled grating. The first-order diffracted beam was coupled back into the diode laser which had a reducedreflection coating on the output facet. The optical feed- back was strong enough to select a single mode of the

cavity. Tuning was achieved by changing the temperature and the injection current of the diode along with the grating angle. The zero-order reflection from the grating was used for the spectroscopy. The power available in the zero order was 6 mW in a single mode (jitter ~1

MHz). Light from an intracavity beam splitter (R

~20%) was used for diagnostics. Frequency scans of —5 GHz were accomplished by synchronously changing

the length of the cavity [with a piezoelectric transducer

(PZT)] and the injection current of the laser. The cali- bration of the frequency scan was provided by a FabryPerot cavity with a free spectral range of 310 MHz. The

low finesse of the cavity and feedback eff"ects on the laser frequency are the main cause of uncertainty in the ex- periment. Direct absorption could be detected using a photodiode to measure the intensity of the light transmitted through the discharge cell as the laser frequency was

scanned over the Doppler profile. The saturation dip

could be observed with good signal-to-noise ratio by

retroreflecting the laser beam (beam size —2 mmx4

mm) back through the cell at a small angle. A longfocal-length lens provided a better interaction of the probe beam with the saturating beam in the cell and

helped in separating the two after it. This simple

configuration has the advantage of exploiting all the

laser power to saturate the transition. Derivative saturation spectra were obtained by introducing a 20-kHz

modulation on the cavity length by means of the

piezoelectric transducer on the grating.

The fast sweep rate and low noise of the diode laser al- lowed us to detect saturated absorption signals in real time on an oscilloscope (detection bandwidth ~50 kHz).

S. _ zero lor derivative signal

av-1.6GHz

OL zero light level (tor absorption)

FIG. 3. Absorption profile of the 35 ^Si-^p ^Pi oxygen transition at 777. 1 nm observed in a natural-abundance sample us- ing the experimental configuration shown in Fig. 2. (a) The

saturation dip can be observed on the peak of the Doppler

profile, (b) The saturation signal is enhanced relative to the Doppler background with derivative spectroscopy using FM

modulation of the laser. The derivative signal is displayed with

arbitrary units on the vertical axis.

Also, the derivative spectra could be obtained rapidly,

limited only by the 1-ms time constant of the lock-in amplifier used for signal demodulation.

The radio-frequency discharge in which atomic oxygen

is produced has been described elsewhere.' As discussed

below, thanks to the higher sensitivity achieved in the

present experiment, lower pressure could be used both

for oxygen and for the buff"er gas (argon in this case). A

typical Oi/Ar pressure ratio was 1/20 and sub-Doppler

signals could be detected for total pressure ranging from

about 1 50 down to 0.6 Pa. For the measurement of the hyperfine structure, a 50% '^O/'^O enriched sample was

used. Natural abundances are '^0-0.04%, '^O -0.2%,

and the enriched sample enhances the relative signal

sizes. In Fig. 3(a) we show the absorption profile for the 3s^S2-3p^Pi 777.1-nm transition recorded in a nat- ural-abundance sample with the experimental configuration shown in Fig. 2. The small saturation dip can be

observed on the top of the broad Doppler profile. This

corresponds to the most abundant '*0 isotope and is easily observed because of the very low noise on the diode laser. In fact, this feature allowed us to detect ox- ygen in direct absorption at very low concentrations and

with a short (~2-cm) interaction length. However, observation of sub-Doppler spectra at very low pressures using enriched samples required an increase of sensitivity

and resolution. These were obtained by recording the

derivative of the absorption profile, as shown in Fig.

3(b). As described before, this was done adding a small

dither on the voltage tuning the grating position and us- ing the same dither as the reference signal for the lock-in

3000 IN- 160
Volume 64, Number 25 PHYSICAL REVIEW LETTERS 18 June 1990

1000 2000 v(MHz)

FIG. 4. Resonances of the three stable isotopes of oxygen as observed in an isotopically enriched sample. Hyperfine struc- ture of the '5: level is fully resolved for "O. Each of the five expected peaks also shows finer structure due to the upperstate hyperfine splittings, which are partially resolved. These

data represent a single scan taken with a l-ms time constant.

Inset: The '^O hyperfine levels (not to scale).

amplifier. The amplitude of the dither was optimized to reduce the amplitude of the broad Doppler signal relative to the saturation dip. In Fig. 4 we show such a spec- trum observed in an enriched sample. Besides the indivi- dual resonances of '^O and '^0, the spectrum shows that the five hyperfine components of the lower ^^2 level are

fully resolved for '^O. The hyperfine structure of the

upper ^Pj level is also almost resolved in this case, while

in previous measurements on transitions starting from

this level the hyperfine structure was unresolved for the

'^O resonance. The measured splittings for the ^^2 level are reported

in Table I. Comparison of these data with the theoretical expression Ef -Ej+ y hAK, with K -FiF+ 1 ) -/(/

+ 1 ) —JiJ + 1 ), gives a value for the magnetic coupling

constant of A —74.3(4) MHz. The quadrupole interaction is neglected because of the insufficient accuracy of

the data. The results we obtained are of interest for a deeper

understanding of nuclear effects on the atomic spectra.

From the measured A constant we can estimate the elec- tron density at the nucleus |^(0)p. We obtain ai

X I ^(0) p—0.12, where qq is the Bohr radius. A more

refined approach would require Hartree-Fock calculations, which are not presently accurate enough. Our ex- perimental results provide a useful test for such theoretiTABLE I. Measured hyperfine splittings of the '5: level of "O obtained by averaging over ten different recordings. Uncertainties correspond to I standard deviation.

Af.r

Measured hf splittings

(MHz)

A1/2, 3/2 I18.3±18

A3/2.5/2 172.0 ±22

A5/2.7/2 253.6 ±20

A7/2.9/2 342.0 ±18

cal calculations. The resonances recorded in this experiment are nearly

free from collisional broadening and correspond to a

linewidth of 60 MHz FWHM, a factor of 2 or 3 nar- rower than those previously obtained for different transitions by intermodulated optogalvanic'" or polarization'

spectroscopy with a dye laser. From measurements of

the linewidth as a function of pressure down to 0. 1 Pa we

can give a lower limit to the radiative lifetime r of the

3^Pi level of 3 ns. Taking into account the effect of

broadening due to residual pressure and saturation

effects, we estimate a radiative lifetime of 6 ns. In anti- cipation of the radiative cooling of oxygen this value is of

fundamental importance. In the scheme we propose, in fact, it is necessary that the deceleration time /deed is shorter than the lifetime of the lower 3^52 state. Assuming a starting velocity for O atoms of 4 x 10^ m/s and a

final velocity near zero, we get the necessary number of

cycles of laser absorption and spontaneous emission, A^ph

12000. The deceleration time is then /dccei'"2NphT

~150 us, which is within the time available of 180 fxs. This demonstrates the possibility of cooling a thermal

oxygen beam by resonant scattering of 777-nm radiation. Very cold oxygen atoms could be produced in the ground

state with a nonequilibrium distribution among the fine- structure levels populations. This opens the possibility of

performing experiments of metrological interest since the

ground state is connected by visible transitions to the

'Z)2 state, whose lifetime is ~ 100 s. Also of interest are

the magnetic-dipole fine-structure transitions in the

ground state at 63 and 145 ^m.

L.H. thanks the Scuola Normale Superiore di Pisa for

financial support for his visit. The authors also thank F. T. Arecchi for a critical reading of the manuscript and

E. Andreoni and P. Barnini of the Laboratorio of Scuola

Normale Superiore di Pisa for technical support. This

work was performed as part of a cooperation agreement

between LENS and the Scuola Normale Superiore di Pisa.

^*^Permanent address: Dipartimento di Scienze Fisiche dcirUniversita di Napoli, 1-80125 Napoli, Italy. ^'•'Permanent address: Time and Frequency Division, National Institute of Standards and Technology, 80303 Boulder.

TN-161

3001
Volume 64, Number 25 PHYSICAL REVIEW LETTERS 18 June 1990

CO 80303.

'L. Gianfrani, A. Sasso, G. M. Tino, and M. Inguscio, Opt.

Commun. (to be published).

2F. Ajzenberg-Selove, Nucl. Phys. A375, 1 (1982).

^J. S. M. Harvey, Proc. Roy. See. London A 285, 581

(1965).

'*M. W. Fleming and A. Mooradian, IEEE J. Quantum Electron. 7, 44 (1981).

5V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, Kvantovaya Elektron (Moscow) 10,

1232 (1983) [Sov. J. Quantum Electron. 13. 792 (1982)1. 6R. N. Watts and C. E. Wieman, Opt. Utt. 11. 291 (1986).

^B. Dahmani, L. Hollberg, and R. DruUinger, Opt. Lett. 12, 876(1987).

*M. Ohtsu, Opt. Quantum Electron. 20, 283 (1988), and

references therein. 'M. Inguscio, P. Minutolo, A. Sasso, and G. M. Tino, Phys. Rev. A 37, 4056(1988).

'°K. Ernst, P. Minutolo, A. Sasso, G. M. Tino. and M. Inguscio, Opt. Lett. 14,554(1989).

TN-162
Appl. Phys. B 59. 327-331 (1994) Applied

PnySICS D and Optic*

© Spnnger-Verlag 1994

High-resolution diode-laser spectroscopy of calcium

A. S. Zibrov*, R. W. Fox, R. Ellingsen**, C. S. Weimer, V. L. Velichansky*, G. M. Tino***, L. Hollberg

National Institute of Standards and Technology, Boulder, CO 80303, USA

(Fax: + 1-303 497-7845)

Received 16 November 1993/ Accepted 15 May 1994

Abstract. Saturated-absorption signals on the calcium

657 nm transition are observed by direct absorption us- ing diode lasers and a high flux atomic-beam cell. Linewidths as narrow as 65 kHz are observed with a high

signal-to-noise ratio. Prospects for using this system as

a compact wavelength/frequency reference are considered.

PACS: 42.55. Px, 32.30.Jc

The intercombination transitions of the alkaline-earth

atoms have been recognized as important optical

frequency/wavelength references. Prominent among

these, in terms of development effort, is the calcium

transition at 657 nm which has a 400 Hz natural line- width. Important advances in research on this system

have come from a number of laboratories including sat- urated-absorption signals [1], atomic-beam optical Ramsey fringes [2-6], resolution of photon recoil [7], observation of second-order Doppler perturbation of Ramsey

fringes [8], and suppression of one recoil component [9]. Laser cooling of calcium has also been demonstrated and

promises significant improvement in accuracy and precision in the future [10-12].

Recent experiments on very high resolution spectroscopy of laser-cooled magnesium atoms have provided

beautiful results that now demonstrate some of this promise [13]. In addition, diode-laser spectroscopy of

barium [14] and strontium [15] show optical resonances

with the potential to be used as wavelength references.

All of these alternative systems have inherent advantages

and disadvantages that could favor one for specific

applications.

* Permanent address: Lebedev Institute of Physics, Moscow,

Russia

** Permanent address: SINTEF DELAB. N-7034 Trondheim,

Norway

*** Pernmnent address: Dipartimento di Scienze Fisiche. Univ. di Napoli. I-Napoli, Italy

The reasons to choose the calcium (657 nm) transition are mostly well known; some are fundamental and others

are of a practical nature. These include relatively small

field shifts, no ground-state hyperfine structure, potential

for laser cooling, visible wavelength (hence, easy to use

for interferometry etc.), recognition by standards community [16], projected accuracy much higher than I2 stabilized lasers, and the expectation of an actual fre- quency measurement that will provide absolute calibration of frequency/wavelength [17]. A renewed interest in calcium is the result, at least in part, of its compatibility

with existing semiconductor diode-laser technology. This

technology will allow a significant reduction in size and

cost that may lead to construction of a compact portable

transfer standard. Not only are high performance diodelasers possible at 657 nm [18]. but high-power diode

lasers can also be frequency-doubled efficiently to produce the 423 nm light required for laser cooling [19]. In striving for high accuracy and stability in optical references we need unperturbed transitions with very narrow linewidths and high signal-to-noise ratios. The

quantum nature of atomic transitions results in a fundamental tradeoff between the linewidth and signal-tonoise ratio for spectroscopic measurements. This is readily apparent in trapped-ion experiments that use single

ions for the highest accuracy [20]. With neutral atoms we

can hope to achieve higher signal-to-noise ratios by using more atoms, but we must pay the very serious penalty of

limited observation time, and hence linewidth. Even us- ing laser cooling/trapping/fountain methods with neutrals has limitations that result from the perturbing ef- fects of the trapping fields. These cannot be ignored and

generally require that we turn off the trapping light. Present best-case neutral-atom fountains have unperturbed observation times of ^ 1 s; whereas trapped-ion

experiments have nearly unlimited observation times. We

anticipate that to achieve the highest accuracy laser cooling will be required, but we report here about a system in which ultimate accuracy is traded for short

term stability, compactness and the future potential for

portability. Such a system could serve as a relatively

TN-163
328 AS. Zibrov et al.

simple transfer standard of optical wavelength/frequency.

1 Experimental system

Our simple diode-laser saturated-absorption system is diagrammed in Fig. 1. To conserve the optical power we use a minimum number of components in the optical

beam path. In contrast to previous high resolution studies of calcium we have done the saturated-absorption in a high-flux hybrid beam-cell rather than in a traditional

low-density atomic beam. The idea here is to take advantage of the low amplitude noise on the diode laser by

detecting the absorption directly. The high-flux beam

provides narrow resonances and high signal-to-noise ratios and avoids the problems associated with buff"er gases. As usual, absorption has advantages and disadvantages compared to the common fluorescence detection systems. For fast calcium atoms the traditional

fluorescence detection methods have detection efficien- cies (signal-to-noise ratios) that are limited by the 20 cm

long decay length of the 657 nm fluorescence. The signalto-noise ratio of our absorption signal was limited by the diode's amplitude noise power which was within a factor of 5 of the shot-noise limit at the 1.5 MHz detection

frequency we chose.

Our high-flux beam is generated from calcium metal

that is heated in a stainless steel boat (internal dimensions 1 X 1.1 X 10 cm^). The boat is capped with a coUimating nozzle which is formed by a narrow channel

(480 |am wide) that is cut through a 4.5 mm thick stainless steel plate. A wire-EDM (Electric Discharge Machine) was used to cut the continuous channel in a pattern that forms a rectangular zig-zag across the surface

of the plate. The rectangular zig-zag pattern is contained

in an area of 3 mm wide by 8 cm long and consists of 106

interconnected parallel slots. The result is a net nozzle area of ^115 mm^. When the calcium vapor pressure is low (T<800K) the nozzle should produce an atomic

Calcium Qeam/Ce'

Fig. 1. Saturated-absorption spectrometer for calcium. The output

from an extended-cavity diode laser passes through a two-stage

optical isolator (isolation it 60 dB), beam-shaping optics and then on to the calcium beam cell. The return beam is deflected by the

isolator and detected with a photodiode

beam divergence (in the direction of the laser propagation) of about 12 degrees. With a smgle fill of calcium the beam-cell can be operated for about 15 h. Counter

propagating laser beams intersect the atomic beam

^ 3 cm downstream from the nozzle. The calcium beam

then condenses on a water cooled surface 3:4 cm beyond

the interaction region. Under normal operating conditions the source temperature is ^900 K and produces

a Doppler-broadened absorption of about 3%. In this case the calcium pressure in the nozzle is higher than

necessary for eff"usive flow; hence we observe a Doppler

width of about 700 MHz. The present beam-cell has a volume of about 4 1 and is now pumped with a turbo

pump, although ion pumping seems feasible. With some

minor design modifications of the nozzle and thermal/ vacuum enclosure the beam-cell should be portable and

have a much longer calcium source lifetime. In this experiment the extended-cavity diode lasers

[21. 22] use commercial index-guided lasers in conjunction with a special holographic optical selectors [23] for wavelength control. Although other good optical designs

are possible, the holographic selectors are attractive be- cause they provide both high diff"raction efficiency

(60-90%) and high resolving power ( ^3600 lines/mm).

In addition, and in contrast to traditional ruled gratings, the high diffraction efficiency is obtained when the laser polarization is parallel to the grating lines. To improve the single-mode tuning range and stable output power of the extended-cavity lasers it is important

to have good Anti-Reflectance (AR) coatings on the

laser's output facets [24-26]. Unfortunately, almost all of

the commercial laser manufacturers use optical coatings on the facets in order to insure long lifetimes, and to

tailor the laser's facet reflectance for optimum output

power. These coatings obviously constrain the perfor- mance of any additional AR coatings that we might add.

But even without removing the manufacturer's coatings we can achieve good AR coatings with a number of

different coating designs. For example, we commonly use

a two-layer coating that consists of AI2O3 plus Hf02 to achieve modal reflectance as low as 1 x 10"^. With these coatings we obtain good operating conditions of extended-cavity red lasers with coarse tuning within ± 10 nm of

the free-running laser wavelength. Starting with a 3 mW,

single spatial-mode, commercial laser, the extended-cavity systems typically provides * 1.5 mW of usable

power in a single spectral mode. These extended-cavity

lasers typically have a free-running fast linewidth of

about 30 kHz for a 10 cm extended-cavity length. Linewidths are determined by direct beat note measurements.

To further narrow the laser's linewidth we use the Pound-Drever-Hall [27] method to lock one of our red

lasers to a stable reference cavity. For fast electronic

control of this laser's frequency an ADP electro-optic

modulator is used inside the extended cavity. The use of

the electro-optic modulator helps to suppress the coupling of frequency modulation to amplitude modulation

in the diode laser system. When locked this laser has a

fast-linewidth of about 500 Hz and a residual frequency

jitter (due to vibrational perturbations of the reference

cavity) of about 5 kHz [18]. The laser Unewidth with

TN-164
High-resolution diode-laser spectroscopy of calcium 329

respect to the reference cavity may be decreased by ex- tending the servo bandwidth beyond the present 1 MHz.

Presently, the laser's linewidths do not contribute significantly to our observed calcium transition width

(5:65 kHz). Both the electronically stabilized laser and

unlocked, but long (^30 cm), extended cavity lasers give

calcium resonance widths that are similar. The observed

transition linewidth is presently dominated by transit and

wavefront curvature effects. We also note that Simonsen

[29] has reported an alternative laser narrowing scheme

that combines optical-locking with a grating-tuned ex- tended-cavity laser. As is usual for diode lasers the spatial mode is both

asymmetric and astigmatic. The mode also usually contains additional small aberrations that are caused by

imperfections in the beam path (the holographic selector

in particular). Some effort is then required to process this optical beam to obtain good quality optical wavefronts

for saturation spectroscopy. At present we use beamforming optics that includes: a cylindrical lens (f^4 m)

to correct astigmatism, two sets of anamorphic prisms to shape the beam, and two spherical lenses for collimation.

The resulting beam then has a nearly rectangular shape

4 mm X 6 mm with a wavefront flatness of about 1 fringe.

2 Results

For typical operating conditions with the beam-cell sys- tem the measured calcium saturation-dip is about 1 % of

the laser power, while the Doppler background absorption is about 3%. Using optical heterodyne techniques

[30] produces saturated-absorption signals with high signal-to-noise ratios as shown in Fig. 2. So far the nar1 1 MHz h"

Laser Frequency

Fig. 2. Calcium saturated-absorption signal observed using the system diagrammed in Fig. 1. The lineshape results from the optical-heterodyne detection method using frequency modulation of

the laser at 1 . 1 MHz. This example shows a calcium resonance with

a 100 kHz width with a nearly flat background. A good signal-to- noise ratio is achieved even using a 60 kHz detection bandwidth

rowest lines we have measured with our beam-cell system

are 65 kHz (FWHM) which corresponds to a resonance Qss 10^°. These signals are observed with about 1 mW of

optical power and provide a signal-to-noise ratio of

about 30 in a 40 kHz detection bandwidth.

If optimally used, the noise-limited-stability of

a diode laser locked to this resonance would be

ay(T)^3x lO"^"*!"'^. This estimate may be reasonable

for short and medium averaging-times (100|is<T<

100 s) but will not persist for long averaging-times

which will be limited by systematic effects. The time scale

at which long-term systematic perturbations become important has not yet been determined for this system.

Based on experience with similar systems, we might ex- pect the stability to degrade for averaging times larger

than a few hundred seconds. This projected stability of

the calcium beam-cell saturated-absorption resonance is excellent and comes from a system that is still far from

optimized.

With better quality optical beams we can anticipate

narrowing the single-zone saturated-absorption signal by

a factor of 2 or 3. This improvement of the spatial mode

will require higher quality windows and optics along the beam path as well as interferometric quality alignment in the interaction region. In the beam forming process a number of factors are traded against each other in order

to achieve spectrally narrow saturation signals while

maintaining a high signal-to-noise ratio. These tradeoffs include: limited optical power, poor initial spatial-mode

quality, and the desire to have a large spot size (because

of significant transit and wavefront-curvature broadening) [31, 32]. A preferred method may be to use the optical Ramsey-fringe technique proposed by Baklanov

et al. [33] and pioneered by Bergquist et al. [3,34]. These

methods have already demonstrated linewidths as nar- row as a few kilohertz [3,7,8]. The most significant factors that limit the resolution

and accuracy of non-cooled neutral-atom optical

frequency/wavelength references are velocity dependent

shifts such as residual Doppler, second-order Doppler,

transit and wavefront curvature effects. Other factors that will contribute smaller uncertainties include photon

recoil (23 kHz splitting), gas lens [35], coupling of laser AM and FM, quadratic Zeeman (10* Hz/T^) and Stark

[^ I Hz,(V/cm)-^] shifts. Many of these effects are complicated by their dependence on the system geometry and

atomic trajectories and will have to be evaluated in detail for any specific system realization. In particular the most

troublesome shifts are caused by the wavefront curvature and second-order Doppler effects that are determined by

averaging the atomic velocity distribution over the spatial distribution of the laser field. These effects will typically limit non-cooled optical frequency standards to an

accuracy of about 1 kHz [6,31]. The second-order Doppler shift for hot (T^900 K)

calcium atoms is significant (^2x 10"'- for the most

probable velocity of =i;740 m/s) and will have to be evaluated for any proposed standard. Fortunately, by using

the optical transitions the atomic velocity distribution can be measured with some accuracy. The second-order

Doppler shift can then be calculated and subtracted as

TN-165
330 AS. Zibrov et al.

IS done for cesium atomic frequency standards. For these microwave primary standards uncertainties of a few per- cent of the second-order shift are achieved, but the uncertainties will likely be larger for the laser saturated-absorption case. In evaluating the potential accuracy and precision of

calcium standards there are still other unresolved questions, one of which is the possibility of pressure shifts of

the 657 nm transition. While pushing towards the highest

accuracy frequency standards it has been discovered that

significant pressure shifts affect even trapped-ion systems

with pressures as low as 1 " * Pa ( Au/u ^ 2 x 1 ~ ^ ^ on an

rf transition of 303 MHz in Be) [36]. Similarly, Cs-Cs shifts have been measured in Cs fountain system (Au/u % 10" '^ for a cold Cs density of ^3 x lO'cm"^) [37]. In unpublished

data, Barger measured pressure shifts of the 657 nm saturated- absorption transition due to argon and krypton collisions. The measured shifts were ^ 68 kHz/Pa (9 MHz/Torr) at low

pressures. Unfortunately, the corresponding pressure shifts are not known for calcium perturbed by calcium, or other

atoms that might be found in a typical vacuum system. The

density of calcium atoms in the interaction region of our

high flux beam is about 10' ^/cm^ ( ^ 10"^ Pa) with a background gas pressure of about 7 x 10"^ Pa. If, for purposes

of discussion, we assume a Ca-Ca pressure shift of the same

magnitude as the measured argon shift, our present system

would have a pressure shift of^ 1 kHz. Linewidths measured as a function of calcium beam flux and system background pressure from 10" * Pa to 10~* Pa show no indication of pressure broadening. This limited diagnostic gives some indication that pressure shifts are not playing a signifi- cant role at our present resolution (65 kHz), but these will have to be evaluated in future higher accuracy systems.

3 Summary and future prospects

Using diode lasers for high resolution saturation spec- troscopy of calcium demonstrates the potential for a frequency/wavelength reference in the visible that could

achieve very high precision with transportability. The

calcium system should compete favorably with iodine

stabilized lasers (scatter in frequency accuracy of good

iodine cells is about 10 kHz) [38]. These initial results on

calcium saturated-absorption in a beam-cell provides narrow linewidth signals with high signal-to-noise ratios. We can expect very high short-term stability from this system. Careful evaluation of all possible systematic effects, and intercomparisons of various system designs,

will be required to determine the ultimate accuracy of the calcium saturated-absorption resonance.

It is clear that cold (low velocity) atoms will be re- quired to achieve the ultimate resolution and accuracy. We are presently a long way from the 400 Hz naturallifetime-limited resolution that is possible on the 657 nm

transition, but we expect that this will be achieved even

with an all-diode-laser system. The 423 nm cooling transi- tion in calcium is a very fortuitous match for frequencydoubling high-power diode lasers. Using KNbOj in a

ring build-up cavity and a 1 50 mW diode laser at 846 nm, we have produced a usable beam of 35 mW at 423 nm

[19]. To improve the long term stabihty and tuning of the blue hght, we have injection-locked the 150 mW diode

laser using an extended-cavity diode laser (output power

%23 mW) as the master oscillator. The injection locking narrows the high-power laser hnewidth and allows continuous scans of about 7 GHz. The power and stability

of the blue light which we have achieved should be

adequate to test the fundamental resolution limits for calcium.

Acknowledgements. For their significant contributions to this effort on calcium and precision diode lasers we would like to thank J.C. Bergquist, J.L. Hall, R. Barger, F. Riehle, and J. Helmcke. We also thank N. Mackie and T. Zibrova for the excellent coatings on the diode lasers. This work was supported in part by the Air Force

Office of Scientific Research.

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Phys. Leu. 34, 850(1979)

8. R. Barger: Opt. Lett. 6. 145 (1981)

9. F. Riehle, J. Ishikawa, J. Helmcke: Phys. Rev. Lett. 61, 2092

(1988)

10. N. Beverini, F. Giammanco, E. Maccioni, F. Strumia, G. Vissani: J. Opt. Soc. Am. B 6, 2188 (1989) ll.T. Kurosu, F. Shimizu: Jpn. J. Appl. Phys. 29, 2127 (1990)

12. J. Helmcke, F. Riehle, J. Ishikawa, A. Witte, Th. Kisters, L.-L.

Liu, X. Yuan: In Light-Induced Kinetic Effects on Atoms. Ions and Molecules, ed. by L. Moi (ETS Editrice, Pisa 1991)

13. K. Sengstock. U. Sterr, G. Hennig, D. Bettermann. J.H. Miiller, W. Ertmer: Opt. Commun. 103, 73 (1993)

14. A.M. Akulshin, A. A. Celikov, V.L. Velichansky: Opt. Commun. 93, 54 (1992)

15. G.M. Tino, M. Barsanti, M. de Angelis, L. Gianfrani, M. Inguscio: Appl. Phys. B 55, 397 (1992)

16. CCDM (Comite Consultatif pour la Definition du Metre) now

recognizes the 657 nm transition as a working standard; Comite

International des Poids et Mesures, Report of the 81st Meeting, tome 60 (1992)

17. J. Helmcke, A. Morinaga, J. Ishikawa. F. Riehle: IEEE Trans. IM-38, 524(1989)

18. R.W. Fox, H.G. Robinson, A.S. Zibrov, N. Mackie, J. Marquardt, J. Magyar, L.W. HoUberg: SPIE Proc. 1837, 360 (1992)

19. P. Gunter: SPIE Proc. 236, 8 (1980)

G.J. Dixon, C.E. Tanner, C.E. Wieman: Opt. Leu. 14, 732

(1989) A. Hemmerich, D.H. Mclntyre, C. Zimmerman, T.W. Hansch:

Opt. Leu. 15, 372 (1990) G.P. Barwood, CS. Edwards, P. Gill, H.A. Klein, W.R.C.

Rowley: SPIE Proc. 1837, 271 (1992) CS. Weimer, J.H. Marquardt, R.W. Fox, H.G. Robinson, L. HoUberg: Proc. CSOISSA Summer School. Kiev (1993), in Special Issue of Ukr. Phys. J. (in press)

TN-166
High-resolution diode-laser spectroscopy of calcium 331

20. W.M. Itano, J.C. Bergquist, D.J. Wineland: Science 237. 612

(1987)

21. C. Wieman, L. Hollberg: Rev. Sci. Instrum. 62, 1 (1991) and

references therein

22. M. Ohtsu: Highly Coherent Semiconductor Lasers (Artech

House, Norwood, MA 1992)

23. M.S. Soskin, V.B. Taranenko: Sov. J. Quant. Electron. 7. 298

(1977)

24. P. Zorabedian, W.R. Trutna Jr., L.S. Cutler: IEEE J. QE-23,

1855(1987)

25. M.G. Boshier, D. Berkeland, E.A. Hinds, V. Sandoghdar: Opt.

Commun. 85, 355 (1991)

26. R. Fox, G. Turk, N. Mackie, T. Zibrova, S. Waltman, J. Marquardt, A. Zibrov, C. Weimer, L. Hollberg, M.P. Sassi: In Solid

State Lasers: New Development and Applications, NATO ASI

Ser. (Plenum, New York) (in press)

27. R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford,

A.J. Munley, H. Ward: Appl. Phys. B 31, 97 (1983)

28. L. Hollberg, R. Fox, N. Mackie, A.S. Zibrov, V.L. Velichansky.

R. Ellingsen, H.G. Robinson: In Proc. Tenth Int'l. Conf. Laser

Spectroscopy (World Scientific, Singapore 1992) p. 347

29. H.R. Simonsen: SPIE Proc. 1837, 250 (1992)

30. J.L. Hall, L. Hollberg, T. Baer, H.G. Robinson: Appl. Phys.

Lett. 39, 680(1981)

31. J.L. Hall: In Methodes de Spectroscopic sans Largeur Doppler

de Niveaux Excites de Systemes Moleculaires Simples, ed. by

J.C. Lehmann (CNRS, Paris 1974) p. 105

32. C.J. Borde, J.L. Hall, C.V. Kunasz, D.G. Hummer: Phys. Rev. A 14, 236 (1976)

33. Ye. V. Baklanov. B.Ya. Dubetsky V.P. Chebotayev: Appl.

Phys. 9. 171 (1976)

34. J.C. Berquist, S.A. Lee, J.L. Hall: Phys. Rev. Lett. 38, 159

(1977)

35. R. Felder: Metrologia 23, 101 (1986)

36. D.J. Wineland, J.C. Bergquist, J.J. Bollinger, W.M. Itano, F.L. Moore, J.M. Gilligan, M.G. Raizen, D.J. Heinzen, C.S. Weimer, C.H. Manney: In Laser Manipulation of Atoms and

Ions, ed. by E. Arimondo, W.D. Phillips, F. Strumia (NorthHolland, Amsterdam 1992)

37. K. Gibble, S. Chu: Phys. Rev. Lett. 70, 1771 (1993)

38. J-M. Chartier, S. Picard-Fredin, A. Chartier: In Tenth Int'l. Conf. Laser Spectroscopy. (World Scientific, Singapore 1992)

p. 106

TN-167
JOURNAL OF MOLECULAR SPECTROSCOPY 168, 416-428 ( 1994)

Sub-Doppler Frequency Measurements on OCS at 87 THz (3.4 jum)

with the CO Overtone Laser

A. Dax,*' J. S. Wells,* L. Hollberg,* A. G. Maki,*'^ and W. URBANf

"'Time and Frequency Division, National Institute ofStandards and Technology, Boulder, Colorado

80303; and f Institut fur Angewandte Physik der Universitdt Bonn, Bonn, D-53I15 Germany

Sub-Doppler frequency measurements have been made on three transitions of OCS in the 87- THz region (near 2900 cm"' ). The CO overtone laser was used as the saturating laser. Polarization spectroscopic techniques utilizing optical heterodyne detection were used to observe the features and subsequently provide the discriminant for locking the overtone laser to the OCS transitions. A CO2 laser synthesizer was used to measure the frequency of the CO overtone laser and thereby measure the frequencies of the OCS lines. The resulting frequencies of the three new measurements

are: lO^l-OCO ^(27), 87 117 278.496(50) MHz; 11 '-^1-01 '-^0 7?(14), 87 222 001.143(70) MHz

for OCS; and for the OC^^S lO^l-OO^O P(9), 87 010 586.667(75) MHz, where the numbers in parentheses are the uncertainties in the last digits. These new numbers have been fitted along

with more than 5700 other data points in our OCS data bank and improved constants have been

obtained. These latest constants are used to calculate updated calibration tables containing values with much smaller uncertainties; three such tables are included. © 1994 Academic Press, inc.

INTRODUCTION

The wide acceptance of the tunable diode laser (TDL) by the spectroscopic community in the late 1970s pointed to the need for frequency calibration standards to achieve the full potential of these devices. Since 1979, we have been involved in a major effort to provide frequency /wavenumber calibration standards based on het- erodyne frequency measurements (7, 2).

Our heterodyne frequency measurement activity came to a temporary halt when

we reached the 61.76-THz (2060-cm~') region, the upper limit of our Au = 1 CO

laser (i). Some measurements at sUghtly higher frequencies were possible based on a doubUng of the CO2 laser {4). It was the development of the DC discharge overtone CO laser at the Institut fur Angewandte Physik (lAP) in Bonn [W. Urban and co- workers (5)] that made further progress possible. The most recent reports (6, 7) suggest

the potential usefulness of this laser with over 330 transitions observed in the 2.6 to

4.1 ^m region. A long standing NIST-IAP collaboration was renewed in Bonn, where

TDL-based heterodyne measurements were made on some OCS features in the 11 ' ^l01 '^0 and 1 1 '^1-01 '^0 bands at 87 THz (3.4 ^lra){8). Between 1979 and 1990, our measurements were all Doppler-limited with the exception of some measurements on CO (9) and N2O (70). In a separate effort, Fayt et al. {11) have made sub-Doppler

measurements on those OCS transitions that are near the 9-Mm CO2 laser transitions. These mostly Doppler-limited frequency measurements formed the foundation for the publication of a calibration atlas (2) which spans much of the region from 486 to 3 120 cm"' plus another small region (407 1-4352 cm"' ). The atlas has a spectral map

' Guest researcher from Institut fiir Angewandte Physik der Universitat Bonn, Bonn, D-53 1 1 5 Germany.

2 Address: 15012 24th Ave. SE, Mill Creek, WA 98012.

0022-2852/94 $6.00 416

Copyright © 1994 by Academic Press, Inc. All rights of reproduction in any form reserved.

TN-168
SUB-DOPPLER OCS MEASUREMENTS 417

and facing table format which we intend to update from time to time. Since a deliberate

effort was made to keep the atlas at a manageable length, about three-quarters of the

possible frequency entries were not included. The diskette in NIST Standard Reference

Database 39 includes these omitted values (72). These calibration data will also be

available next year in the over the world wide electronic network.

In order to further improve the atlas, more accurate frequency measurements are required. Consequently, we have begun sub-Doppler frequency measurements at 3.4 ^m. Our initial emphasis was on OCS, and we hope to include N2O later. Our colleagues

in Bonn have also made sub-Doppler frequency measurements on OCS near 5 nm

(13). Both this paper and Ref ( 14) describe our first OCS sub-Doppler experiments

and results at NIST.

SUB-DOPPLER EXPERIMENTS WITH THE CO OVERTONE LASER

Two different experimental approaches were investigated in order to find the tech- nique that is best suited to making measurements of OCS transitions near 3.4 fim. The first involved a normal saturated-absorption technique (15-23), which is much

simpler to use and is potentially more accurate for frequency measurements (77)

(provided that the transition moment of the molecule is sufficiently large). The second

technique used polarization-selective optical saturation techniques (24-35) and pro- duced a much better signal-to-noise ratio (SNR). However, it was considerably more

cumbersome. For clarity concerning sub-Doppler spectroscopy and frequency measurements at 3 ^m with a CO overtone laser, we discuss elsewhere (14) both types of

experiments showing the advantages, limitations, and additional details of each. Be- cause of the weak transition moment involved and some technical problems in obtaining a clean modulation signal for third-derivative detection (27, 22), the saturated- absorption technique was shelved for the time being. In our NIST laboratory, we have developed a CO overtone laser similar to the one

developed in Bonn (5). Our 1.87-m-long laser has a 450 line/mm grating and a 10 m radius output coupler. The LN2-cooled gain section is about 1 .09 m long, and the bore i.d. is 12 mm. The operating partial pressures of the He, N2, air, and CO are

essentially the same as the Bonn papers indicate. (We can attest to the wisdom of

using an aluminum storage cylinder for the CO to avoid problems (6, 7) arising from

Fe(CO)5 in older iron cylinders.) The Bonn versions employ coupling from the laser utilizing the zero-order output of the grating. We chose to take the output from a

dielectric coated ZnSe coupler. This compensated coupler (the second surface of the coupler is curved) minimizes the spreading of the output beam. In an effort to minimize

the laser linewidth, we have inserted convection barriers to enclose the air path between

the resonator optical elements and the Brewster windows of the gain tube. We have

also inserted a surge reservoir between the mixing valves and the gas inlet to the laser tube to reduce pressure fluctuations caused by the flow meters.

CONSIDERATIONS OF OPTICAL HETERODYNE POLARIZATION SPECTROSCOPY

The polarization spectroscopy method was invented by Wieman and Hansch (24)

in 1976 for making sub-Doppler measurements. Since then, this versatile method has

been used not only for several laser spectroscopic measurements, but also for laser stabilization (25-33, 35). The principle of operation is that a strong pump beam

introduces an anisotropy in a sample; that is, the sample becomes dichroic and bire- fringent if the pump frequency is near a molecular resonance. A weak probe beam at

TN-169
418 DAX ET AL.

the same frequency will suffer a change in its polarization if it interacts with the same

molecules as the pump beam. By use of an appropriate selection method, we can

observe this change in polarization at the low power levels necessary to avoid saturating

the detector. The possible variations concerning the polarization of the pump and

probe and the offset angle of the analyzer from a predetermined orientation produce

different signal shapes and intensities for molecular Q, R, and P transitions (24-30). Because of the problems with the saturated absorption technique, we selected the

optical heterodyne polarization spectroscopy technique ( 20, 24, 30). Its physical principle is extensively explained in (i/). The main advantage of this technique is that a weak signal can be considerably enhanced by heterodyning the signal wave ( amplitude

£5) with a much stronger local oscillator wave (amplitude Eo), as long as £"0 (which

can also contribute noise) is selected appropriately. To use this technique, we apply an intensity modulation to the pump beam and detect the modulation transfer to the probe beam. The result is a low-noise dispersion-shap>ed signal which can be symmetric

about the molecular transition. The /-dependence of similar dispersion signals is cal- culated in Refs. (20. 24. 27. 30).

Since both birefringence and dichroism can contribute to the signal here, the most

difficult problem is to obtain a line shape that is symmetric about the true line center

(24. 32, 33). The local oscillator wave £"0 can be obtained most conveniently from

the probe beam itself by slightly uncrossing the analyzer with respect to the polarizer

by an angle (p. An improper choice of may be accompanied by asymmetries in the dispersion signal.

Excluding noise sources originating from the environment between the laser and

detector for a moment, the SNR for this type of experiment increases as 1 / n, where

^ is the extinction ratio of the analyzer (20, 24). This is limited by the laser power

noise 7^0 (where Pq is the laser output power) and the detector noise D^. One can show (14. 34) that for 7/^01 <^ A,

SNR^a, = const.A/-^. (1)

A small extinction ratio of the analyzer is essential for a good signal-to-noise ratio. In the visible spectral region, extinction ratios of 10"^ are often cited (24. 35). Our

Rochon-type analyzer had a theoretical extinction ratio of | = 10"' (36). In practice

it is not quite that good, depending on the optical beam path through the crystal. By

using a two-stage analyzer, we have improved the extinction ratio considerably.

By using the Jones formalism (37) we have calculated the contributions to the detector response /det and find, by using linear approximations,

/de, = Ce-''<^^El{i,^2 - lie' - l2«' + e' - e^oAZ^, + 0t + <t>xko^b, - e^KkoL + (piAnkoL + \[klAnLAbr + klAKLAb^] + \[(koAnL)- + (koAb,)' + (AKkoL)' + (koAb-y]}, (2)

where C is a proportionality constant, k is the susceptibility (k = k+ + k-), ko = 2t/

X, X is the wavelength of the probe beam, and L is the estimated overlap length of the crossed beams within the cell. The symbols |i and ^2 represent the extinction ratios for the first and second analyzer, respectively, e is the ellipticity of the polarization

after the polarizer, and Ak = k+ — k- and An = n+ — ri- are the susceptibility change

and refractive index change of the anisotropic medium in the circular basis, respectively.

TN-170
SUB-DOPPLER OCS MEASUREMENTS 419

Ak describes the dichroism and has a Lorentzian lineshape; An describes the birefrin- gence and has a dispersion hneshape; (/)i is the deviation from the crossing angle of

the first analyzer; and Ab^ = bt — br (the real part) and A^i = bt — b^ (the imaginary

part) describe the anisotropy of the cell windows under vacuum stress (20, 21, 30).

Since both extinction ratios have similar values between 10"" and 10"^, the term

^1^2 is negligible. The same is usually true for all terms containing «' since we have

found experimentally that f < 10"^. The signal term can be expressed as (jiyEoiEoAnkoL), showing the heterodyning of the signal amplitude EoAnkoL and the

local oscillator amplitude (piEo (31). The terms Ak, (Ak)'^, and {An)^ may lead to asymmetry of the signal, and the remaining terms are responsible for the background.

EXPERIMENTAL DETAILS

The overtone laser is the starting point of our description of the block diagram in

Fig. 1 . The output of the overtone laser was directed by several mirrors to a wedged

uncoated ZnSe beam splitter where the transmitted portion was used for the saturating

beam. The beam reflected from the front surface was used for the linear probe beam,

and the beam reflected from the back surface was directed through an acousto-optic

modulator to the IR frequency synthesizer. Even if the frequencies of the CO laser and the OCS line did not overlap, it was sometimes possible to shift the laser to the required frequency by placing the acousto-optic modulator ( AOM ) in the laser beam

before it reached the beam splitter.

As indicated in Fig. 1, the probe beam's polarization was rotated by 7r/2 by the

five-mirror variable rotator and was then focused by mirror 1 onto a reflecting wedged

germanium plate polarizer (23, 38). The beam was recollimated by mirror 2. This

increased the polarization purity of the beam from 2000: 1 at the laser output to greater

than 650 000: 1. A four-mirror polarization conserving half-wave plate (2i, 39) returned

the polarization back to horizontal. The probe beam traversed the OCS cell at a small

angle with respect to the cell axis and was focused by mirror 3 onto a second reflecting

wedged germanium plate polarizer which acted as the first stage of the analyzer. Only

the component polarized perpendicular to the plane of incidence was reflected by this L unit along the detection path. The local oscillator wave was generated by tilting the base of this device to the offset angle 0|. A similar one-stage analyzer can also be

found in Refs. {25, 34). These collinear signal and local oscillator beams were focused on the Rochon analyzer by mirror 4 and mirror 5 focused them on the detector. Before considering the path of the pump beam, we point out that instead of the usual X/4 plate, we have used a two-component scheme to achieve circular polarization.

Our two-component scheme has three advantages. First, and most important, it is possible to have some control over the degree of polarization (similar to using a Babinet

Soleil compensator); second, it is nearly wavelength-independent; and, third, the device

is purely reflective. The path (shown in Fig. 1) of the saturating beam through our two-component

device starts where it emerges from the ZnSe beam splitter. The beam then had its polarization rotated by a three-mirror variable polarization rotator (40) to some ar- bitrary value, say <l> (the difference between a three-mirror rotator and a five-mirror

rotator is that the latter conserves the polarization quality much better (23)). The

beam was focused by mirror 6 onto a titanium plate, which affords an adjustable angle

of incidence relative to the incoming beam. The physics involved in the phase shift on reflection from the titanium plate is described in ( 2i ) and is more or less simply

the physics of Fresnel reflection on a metal surface (41). A measured polarization

TN-171
420 DAX ET AL.

Si oj 912

2<r

iJ-a 9 a

_ o -~

-1 go

^^A^

J3 POoI

C/5 U

o

Q.a

oQ

TN-172
SUB-DOPPLER OCS MEASUREMENTS 421

<

w

co

P(27) .

- - -1 -

Frequency

Fig. 2. Dispersion signal of the saturated P(27) transition. The center frequency is 87 117 278.496(50) MHz and the peak to peak linewidth is about 700 kHz. The width of the scan shown here is about 45 MHz.

quality of 99.5% was achieved for the saturation beam by iterative adjustment of the

angles, $ and O. It is essential to have a good circular polarization quality here; otherwise, the pump wave can be considered to be composed of a circular and a linear part where dichroism can be accompanied with this linear pump wave. According to Ref. (25), such a dichroism changes the azimuth angle of the probe beam's linear polarization. This, in turn, increases the Lorentzian shaped contribution to the signal

thus giving greater asymmetry to the detected dispersion signal. The saturation beam

traversed the cell at a small angle with the cell axis. The crossing angle between the two beams was estimated to be about 1 mrad.

The elimination of stray light was tedious and is detailed in Ref (14). When this was accomplished, we were able to measure three OCS transitions which had accidental

overlaps with the CO overtone laser or its AOM shifted sidebands. Some of the data

from the experiment on the P{21)A line of OCS at 3.4 ixvn are shown in Figs. 2 and

(/3

(/3

••is < J-

-0.5 MHz +0.5 MHz

Frequency

Fig. 3. Spectrum analyzer display of the time-averaged (100 scans) beatnote between the CO overtone

laser which was locked to the ^(27) line and a reference from the infrared frequency synthesizer. The center frequency is 1 171.900 MHz, the video bandwidth is 30 kHz, and the sweep time is 62.56 msec.

TN-173
422 DAX ET AL.

3. Figure 2 shows the dispersion signal which was used to lock the CO overtone laser. The signal appears fairly symmetric.

In order to obtain a symmetric lineshape, we rotated the second analyzer (Rochon

crystal) of our two-stage system relative to the first analyzer. Offset angles of 02 < 5° were enough to achieve symmetric signals. Since the polarization of the probe beam

after the first analyzer is elliptical, this technique bears some resemblance to the method

employed by Delsard and Keller (26). They used a linear pump beam and a circular probe beam, and found that it was possible to change the signal continuously from

an absorption shape to a dispersion shape simply by rotating their analyzer 45°. Our quantitative description does not demonstrate that we can symmetrize the

signal without changing the real zero-crossing of the Lamb dip. To do this would

require the inclusion of a valid model which describes the cell windows under stress as well as our offset angle 02. However, not only do the dispersion signals appear

symmetric, but also another measurement using a different technique produced a

result which agreed to within 20 kHz with our result for the same S.B-^m OCS transition (13.42).

Referring again to Fig. 1, the third beam from our wedged ZnSe beamsplitter was

focused by mirror 8 on the AOM, and the shifted beam was recollimated and sent to the input of the infrared frequency synthesizer. The frequency synthesizer consists of

two CO2 laser frequency standards, a microwave oscillator, a MIM diode, and a spec- trum analyzer along with a marker oscillator. (See Ref (2), pp. 17-21, or Refs. (i,

4, 8).) Reference (14) contains details of the latest improvements of the CO2 laser systems.

Figure 3 shows the time averaged beatnote between the locked CO overtone laser and a reference synthesized from a combination of two C02-stabili2ed laser standards. Aside from the frequency, which is the primary goal, two features are significant. The

first is that the linewidth of the laser is about 100 kHz, which is considerably less than

the 700-kHz saturation feature. The relative phase and amplitudes of modulation of

the reference lasers were adjusted to minimize the beatnote linewidth; hence, the

linewidth here is an upper limit on that of the CO laser. The second feature ( not

discernible here) is the SNR of the beatnote which was generally observed to be between

25 and 30 dB, and hence suitable for stabilizing the overtone laser to the synthesized

reference. This makes it an ideal reference for use in a heterodyne measurement to measure the linewidth of TDLs and to use in frequency offset control in an alternate scheme with a line-narrowed TDL (43).

Dispersion signals similar to that in Fig. 2 were obtained for two other transitions. These measurements were made at pressures of about 1.3 Pa (10 mTorr) with an

estimated overlap pathlength of about 1 m in a 1.5-m-long absorption cell. The measurements were all made with the same sample of gas at room temperature. No iso- topically enriched samples (^''S for example) were used in the measurements.

RESULTS AND ANALYSIS

Table I gives the three saturated-absorption frequency measurements made through

the use of this polarization spectroscopic technique. Of course, this technique is limited

to the measurement of transitions that are within the small tuning range of the CO

laser lines, or within the range of the sideband produced by the acousto-optic modulator.

The CO2 laser frequencies used to calculate the observed frequencies given in Table

I were taken from a recent reanalysis of the CO2 laser frequencies (44) and, for the

lines used for this work, only differ from the frequencies given by Bradley et al. {45)

TN-174
SUB-DOPPLER OCS MEASUREMENTS 423

TABLE I The Measured Transition Frequencies for Carbonyl Sulfide

CO

Trans.

OCS Transition Obs. Freq.'' (MHz) CO2 Freq. Stds.'= Beat Freq. (MHz)

^26(9) Pill)

P2,(8) R(U)

P^(\Q) P(9f

10"! -00"0

ll"l-01'f0

lO"! -00°0

87 117 278.496+0.050

87 222 001.143+0.070

87 010 586.667+0.075

2x;?(8)I+«(12)I -1261.908 2xP(28)l + /'(32)II -1056. 507^

2x/?(28)I + P(24)I -412.438

^ For the CO laser designation the subscript indicates the lower state vibrational quantum number and the number in parentheses is J"

The OCS observed frequency is given by the sum of the CO, laser frequencies and the beat frequency.

'^ For the CO, laser designation the I indicates the 10 /xm band and the II indicates the 9 nm band.

'^ For the measurement of the R(H) line of the 1 1"1 -01"0 band a microwave frequency of

10 999.988 MHz was added to the CO, laser frequencies.

^ This transition is for ''O'^C^S; the other two are for "O'^C^S.

by a few kilohertz. The uncertainties in the measurements were about 30 kHz for the absolute frequencies of the synthesized references, or about 10 kHz for each of the

three CO2 laser harmonics. The remaining contribution to the uncertainty was that due to locating the line center. This depended on the ratio of asymmetry of the dis- persion signal to the signal amplitude with an additional contribution due to the noise. These measurements have been combined in a least-squares fit with the many other

measurements on OCS that were used in Ref. (2). In addition, some more recent FTS

TABLE II

The Rovibrationai Constants (in cm"') Used to Fit the Data

state S, D xlO' //.xlO'" i,,xlO"

00''0 Ol'O

10°1

ll'l

oco

iCl

0.202 856 740 854(398)" 4.340 677 1(1187) -0.326 19(1452) 0.203 209 834 843(1006) 4.411 511 2(1497) -0.256 97(1803) 0.201103 238 50(5499) 5.137 499(5107) 86.768(2420) -7.9212(5145)" 0.201516 185 28(6599) 4.774 825(3871) 13.797 9(8046) -0.429 90(5429)

0.197 898 035 007(3272) 4.141 187 4(6101) -0.351 71(8951) 0.196 197 685 12(10560)5.000 256(7002) 68.962(1599) -2.680 3(1161)

State (7,xlO^ fy.jXlO'" q,„-x\Q"

">0'2C"S

Ol'O 2.121938 676(253)

ll'l 2.377 549(462)

1.424 123(492) 10.916 3(2087)0.057 395(2118)

3.090 4(2204)

Vib. Transition "o

'o''c"s

">o'^c"s

lO^l -oo''o ll'1-Ol'O

10°l-00"0

2918.105 066 6(248) 2903.717 546 5(144)

2906.045 274 8(75)

The estimated uncertainty (one standard deviation) in the last digits is given in parentheses. The fit of the 10"1 level of "0"C"S also included M, = 4.467(+0.484)x 10"'' cm"' and

/V, = -1.110(±0.166)xl0-"cm-'.

TN-175
424 DAX ET AL.

measurements were included in the fit in such a way as to allow the heterodyne measurements to determine the vibrational energy levels. The FTS measurements were

necessary to determine the values of the higher order vibrational terms, i.e., the L„

terms. Table II shows the vibrational constants that resulted from this fit. Enough

digits are given for the constants to allow for correlation among the constants and to ensure that the observed frequencies (actually their deviations) are correctly calculated. The least-squares analysis made use of the term equations

E, = G, + B,JiJ+ \)- D,[J{J+ I) - l']^ + H,[J{J + 1)-/-]^ + L,[J{J+ I) - l^]^ + M,[J(J + I) - I-]' + N,[JiJ + 1)-/-]' (3)

and

i^o - G'v — G'v. (4)

TABLE III Wavenumbers (cm"') Calculated for the IO°l-00°0 Band of "O'^C'-S

P-Branch J' R-Branch P-Branch J" ^-Branch

2918.507 273 (49)^ 2898.038 623 (32) 42 2932.195 776 (34) 2917.699 353 (50) 1 2918.905 971 (49) 2897.484 749 (33) 43 2932.444 165 (35) 2917.290 134 149) 2 2919.301 159 (48) 2896.927 304 (34) 44 2932.688 887 (36) 2916.877 410 (49) 3 2919.692 836 (48) 2896.366 284 (35) 45 2932.929 936 (37) 2916.461 181 (48) 4 2920.081 000 (47) 2895.801 689 (36) 46 2933.167 308 (38) 2916.041 448 (48) 5 2920.465 649 (46) 2895.233 517 (37) 47 2933.401 000 (38) 2915.618 211 (47) 6 2920.846 780 (44) 2894.661 765 (37) 48 2933.631 009 (39) 2915.191 471 (46) 7 2921.224 392 (43) 2894.086 432 (38) 49 2933.857 330 (40) 2914.761 227 (44) 8 2921.598 482 (41) 2893.507 516 (39) 50 2934.079 960 (42) 2914.327 479 (43) 9 2921.969 047 (39) 2892 925 016 (40) 51 2934 298 895 (44) 2913.890 226 (41) 10 2922.336 085 (37) 2892 338 931 (42) 52 2934.514 131 (46) 2913.449 469 (39) 11 2922.699 591 (35) 2891.749 257 (44) 53 2934.725 666 (48) 2913.005 206 (37) 12 2923.059 564 (33) 2891.155 995 (46) 54 2934.933 496 (51) 2912.557 436 (35) 13 2923 416 000 (31) 2890.559 143 (48) 55 2935,137 617 (55) 2912 106 158 (33) 14 2923.768 895 (29) 2889.958 699 (51) 56 2935.338 027 (58) 2911 651 371 (31) 15 2924.118 246 (26) 2889.354 663 (55) 57 2935.534 721 (62) 2911.193 074 (29) 16 2924.464 049 (24) 2888.747 032 (58) 58 2935.727 697 (66) 2910 731 265 (26) 17 2924 806 301 (21) 2888.135 807 (62) 59 2935 916 952 (71) 2910.265 943 (24) 18 2925.144 996 (19) 2887.520 985 (66) 60 2936.102 482 (75) 2909.797 105 (21) 19 2925.480 133 (16) 2886.902 566 (71) 61 2936.284 285 (79) 2909.324 751 (19) 20 2925.811 705 (14) 2886.280 549 (75) 62 2936.462 357 (83) 2908.848 877 (16) 21 2926.139 710 (11) 2885.654 932 (79) 63 2936.636 695 (88) 2908.369 482 (14) 22 2926 464 142 (09) 2885.025 716 (83) 64 2936.807 297 (91) 2907.886 565 (11) 23 2926.784 998 (06) 2884.392 898 (88) 65 2936,974 159 (95) 2907.400 122 (09) 24 2927.102 273 (04) 2883.756 478 (91) 66 2937,137 279 (98) 2906.910 151 (06) 25 2927.415 963 (03) 2883.116 455 (95) 67 2937.296 65 (10) 2906,416 650 (04) 26 2927.726 062 (04) 2882.472 829 (98) 68 2937.452 28 (10) 2905.919 618 (03) 27 2928.032 568 (06) 2881.825 60 (10) 69 2937.604 16 (11) 2905.419 051 (04) 28 2928.335 475 (08) 2881.174 76 (10) 70 2937.752 28 (11) 2904 914 946 (06) 29 2928.634 778 (11) 2880.520 32 (11) 71 2937.896 64 (11) 2904.407 303 (08) 30 2928.930 474 (13) 2879.862 27 (11) 72 2938.037 25 (11) 2903.896 117 (11) 31 2929.222 557 (16) 2879.200 62 (11) 73 2938.174 10 (11) 2903.381 387 (13) 32 2929.511 023 (18) 2878.535 35 (11) 74 2938.307 17 (11) 2902.863 111 (16) 33 2929.795 867 (20) 2877.866 48 (11) 75 2938.436 49 (11) 2902.341 285 (18) 34 2930.077 086 (22) 2877.194 00 (11) 76 2938.562 03 (11) 2901 815 908 (20) 35 2930.354 674 (24) 2876.517 91 (11) 77 2938.683 81 (11) 2901.286 976 (22) 36 2930.628 628 (26) 2875.838 22 (11) 78 2938.801 81 (11) 2900.754 488 (24) 37 2930 898 942 (28) 2875.154 91 (11) 79 2938.916 03 (11) 2900.218 442 (26) 38 2931.165 613 (30) 2874.467 99 (11) 80 2939.026 47 (11) 2899.678 834 (28) 39 2931.428 636 (31) 2873.777 46 (11) 81 2939.133 14 (11) 2899.135 663 (30) 40 2931.688 007 (32) 2873.083 32 (11) 82 2939.236 02 (11) 2898 588 927 (31) 41 2931.943 721 (33) 2872.385 57 (11) 83 2939.335 11 (11)

The estimated uncertainty in the last digits (twice the standard deviation) is given in parentheses.

TN-176
SUB-DOPPLER OCS MEASUREMENTS 425

TABLE IV

Wavenumbers (cm"') Calculated for the 1 1 "l-Ol'lD Band of '^O'^C^S

P-Branch J" /f-Branch P-Branch J" 7;-Branch

1 2904.520 724 (28) 2883.746 229 (61) 42 2917.994 773 (61) 2902.900 922 (28) 2 2904.917 267 (27) 2883.198 259 (61) 43 2918.251 229 (61) 2902.487 570 (28) 3 2905.310 444 (26) 2882.646 898 (61) 44 2918.504 195 (62) 2902.070 859 (27) 4 2905.700 255 (25) 2882.092 144 (61) 45 2918.753 668 (62) 2901.650 790 (26) 5 2906.086 697 (23) 2881.533 995 (62) 46 2918,999 643 (62) 2901.227 363 (25) 6 2906.469 769 (21) 2880.972 448 (62) 47 2919.242 116 (62) 2900.800 579 (23) 7 2906.849 469 (19) 2880.407 503 (62) 48 2919.481 083 (62) 2900.370 440 (21) 8 2907.225 795 (17) 2879.839 156 (62) 49 2919.716 541 (62) 2899.936 944 (19) 9 2907.598 746 (15) 2879.267 407 (62) 50 2919.948 484 (62) 2899.500 092 (17) 10 2907.968 319 (12) 2878.692 252 (62) 51 2920.176 909 (62) 2899.059 885 (15) 11 2908.334 512 (10) 2878.113 691 (62) 52 2920.401 811 (63) 2898.616 322 (12) 12 2908.697 323 (07) 2877,531 721 (62) 53 2920.623 188 (63) 2898.169 404 (10) 13 2909.056 749 (05) 2876.946 339 (63) 54 2920.841 033 (64) 2897.719 131 (07) 14 2909.412 789 (04) 2876.357 545 (63) 55 2921.055 344 (64) 2897.265 502 (05) 15 2909.765 440 (05) 2875.765 336 (64) 56 2921.266 116 (65) 2896.808 517 (04) 16 2910.114 699 (08) 2875.169 711 (64) 57 2921.473 346 (66) 2896.348 175 (05) 17 2910.460 563 (11) 2874.570 666 (65) 58 2921.677 028 (67) 2895.884 477 (08) 18 2910.803 031 (14) 2873.968 201 (66) 59 2921.877 160 (68) 2895.417 421 (11) 19 2911.142 098 (17) 2873.362 313 (67) 60 2922.073 736 (69) 2894.947 007 (14) 20 2911.477 763 (20) 2872.753 000 (68) 61 2922.266 753 (70) 2894.473 235 (17) 21 2911.810 021 (23) 2872.140 260 (69) 62 2922.456 207 (71) 2893.996 104 (20) 22 2912.138 871 (27) 2871.524 092 (70) 63 2922.642 094 (72) 2893.515 612 (23) 23 2912.464 309 (30) 2870.904 494 (71) 64 2922.824 410 (73) 2893.031 759 (27) 24 2912.786 332 (33) 2870.281 463 (72) 65 2923.003 150 (75) 2892.544 544 (30) 25 2913.104 936 (36) 2869.654 998 (73) 66 2923.178 312 (76) 2892.053 966 (33) 26 2913,420 119 (39) 2869.025 097 (75) 67 2923.349 889 (77) 2891.560 024 (36) 27 2913.731 877 (41) 2868.391 757 (76) 68 2923.517 880 (78) 2891.062 716 (39) 28 2914.040 206 (44) 2867.754 978 (77) 69 2923.682 279 (80) 2890.562 041 (41) 29 2914.345 103 (46) 2867.114 757 (78) 70 2923.843 084 (81) 2890.057 999 (44) 30 2914.646 564 (48) 2866.471 092 (80) 71 2924.000 289 (81) 2889.550 587 (46) 31 2914.944 587 (50) 2865.823 982 (81) 72 2924.153 890 (82) 2889.039 804 (48) 32 2915.239 166 (52) 2865.173 424 (81) 73 2924.303 885 (83) 2888.525 648 (50) 33 2915.530 299 (54) 2864.519 418 (82) 74 2924.450 269 (83) 2888.008 119 (52) 34 2915.817 982 (55) 2863.861 960 (83) 75 2924.593 037 (84) 2887.487 215 (54) 35 2916.102 211 (57) 2863.201 049 (83) 76 2924.732 186 (84) 2886.962 933 (55) 36 2916.382 982 (58) 2862.536 684 (84) 77 2924.867 712 (86) 2886.435 272 (57) 37 2916.660 291 (59) 2861.868 861 (84) 78 2924.999 610 (88) 2885.904 232 (58) 38 2916.934 134 (60) 2861.197 580 (86) 79 2925.127 878 (92) 2885.369 809 (59) 39 2917.204 508 (60) 2860.522 839 (88) 80 2925.252 509 (99) 2884.832 002 (60) 40 2917.471 409 (61) 2859.844 635 (92) 81 2925.373 50 (11) 2884.290 809 (60) 41 2917.734 832 (61) 2859.162 967 (99) 82 2925.490 85 (13)

a T-u„ „„*: *_j .

. . The estimated uncertainty in the last digits (twice the standard deviation) is given in parentheses

In addition, for the / terms

1 states, the /-doubling was taken into account by adding the

±[q.J{J+ 1) q,,jjHJ+ \? + q,jjJHJ \y (5)

where the upper sign ( + ) was used for the /levels and the lower sign ( — ) was used

for the e levels. As discussed by Maki et al. {46), there is a weak resonance between the 10*^1 and

04 °1 states and a similar resonance between the 1 1

' 1 and 05 ' 1 states. This resonance

has been investigated in more detail by Fayt {47, 48). It causes the effective values of

the //i-, Li;,Mi,. and A^^. terms to be much larger than in the ground state; consequently,

it was necessary to include those constants in the least-squares fits. Although it is surprising that an N^. term should be so large that it is needed to fit the data, the value

that we find for the 10°1 state is not as large as that predicted by Fayt et al. {49) from

their analysis.

TN-177
426 DAX ET AL.

TABLE V

Wavenumbers (cm"') Calculated for the lO^l-OCO Band of '^O'^'^S

P-Branch J" /{-Branch P-Branch J" A-Branch

2906.437 670 (15)^ 2886.483 94 (10) 42 2919.807 87 (10) 2905.649 479 (15) 1 2906.826 663 (14) 2885.944 16 (10) 43 2920.050 78 (101 2905.250 283 (15) 2 2907.212 253 (13) 2885.400 90 (10) 44 2920.290 12 (10) 2904.847 689 (14) 3 2907 594 438 (11) 2884.854 15 (10) 45 2920.525 874 (99) 2904.441 696 (13) 4 2907.973 216 ( 9) 2884.303 90 (10) 46 2920.758 040 (99) 2904.032 305 (111 5 2908.348 586 ( 7) 2883.750 170 (99) 47 2920.986 614 (98) 2903.619 516 ( 91 6 2908.720 544 ( 5) 2883.192 940 (99) 48 2921.211 593 (98) 2903.203 329 ( 7) 7 2909.089 089 ( 4) 2882.632 214 (98) 49 2921.432 972 (97) 2902.783 745 ( 5) 8 2909.454 218 ( 5) 2882.067 989 (98) 50 2921.650 749 (97) 2902.360 761 ( 4) 9 2909.815 928 ( 8) 2881.500 263 (97) 51 2921.864 919 (96) 2901.934 379 ( 5) 10 2910.174 217 (12) 2880.929 034 (97) 52 2922.075 479 (96) 2901.504 597 ( 8) 11 2910.529 080 (16) 2880.354 301 (96) 53 2922.282 426 (96) 2901 071 414 (12) 12 2910.880 516 (20) 2879.776 063 (96) 54 2922.485 756 (95) 2900.634 829 (16) 13 2911.228 519 (25) 2879.194 318 (96) 55 2922.685 467 (95) 2900.194 840 (20) 14 2911.573 087 (29) 2878.609 065 (95) 56 2922.881 555 (94) 2899.751 447 (25) 15 2911.914 216 (34) 2878.020 302 (95) 57 2923.074 018 (93) 2899.304 647 (29) 16 2912.251 902 (39) 2877.428 030 (94) 58 2923.262 853 (93) 2898.854 438 (34) 17 2912.586 141 (44) 2876.832 247 (93) 59 2923.448 058 (92) 2898.400 820 (39) 18 2912.916 928 (48) 2876.232 953 (93) 60 2923.629 630 (91) 2897.943 789 (44) 19 2913.244 259 (53) 2875.630 147 (92) 61 2923.807 567 (91) 2897.483 343 (48) 20 2913.568 130 (58) 2875.023 828 (91) 62 2923.981 867 (90) 2897.019 480 (53) 21 2913.888 536 (62) 2874.413 997 (91) 63 2924.152 528 (90) 2896.552 197 (58) 22 2914.205 472 (67) 2873.800 653 (90) 64 2924.319 546 (91) 2896.081 492 (62) 23 2914.518 934 (71) 2873.183 796 (90) 65 2924.482 922 (92) 2895.607 363 (67) 24 2914.828 917 (75) 2872.563 426 (91) 66 2924.642 652 (94) 2895.129 805 (71) 25 2915.135 415 (79) 2871.939 543 (92) 67 2924.798 734 (96) 2894.648 817 (75) 26 2915.438 424 (83) 2871.312 147 (94) 68 2924.951 17 (10) 2894.164 396 (79) 27 2915.737 939 (86) 2870.681 238 (96) 69 2925.099 95 (10) 2893.676 538 (83) 28 2916.033 955 (89) 2870.046 816 (99) 70 2925.245 08 (11) 2893.185 240 (86) 29 2916.326 466 (91) 2869.408 88 (10) 71 2925.386 55 (11) 2892.690 500 (89) 30 2916 615 467 (94) 2868.767 43 (11) 72 2925.524 37 (12) 2892.192 314 (91) 31 2916.900 954 (96) 2868.122 47 (11) 73 2925.658 52 (12) 2891.690 679 (94) 32 2917.182 921 (98) 2867.474 00 (12) 74 2925.789 01 (13) 2891.185 592 (96) 33 2917.461 362 (99) 2866.822 01 (12) 75 2925.915 84 (13) 2890.677 049 (98) 34 2917.736 27 (10) 2866.166 51 (13) 76 2926.039 00 (13) 2890.165 048 (99) 35 2918.007 65 (10) 2865.507 49 (13) 77 2926.158 49 (13) 2889.649 59 (10) 36 2918.275 48 (10) 2864.844 96 (13) 78 2926.274 30 (13) 2889.130 66 (10) 37 2918.539 77 (10) 2864.178 91 (13) 79 2926.386 43 (13) 2888.608 26 (10) 38 2918.800 51 (10) 2863.509 34 (13) 80 2926.494 88 (14) 2888.082 40 (10) 39 2919.057 70 (10) 2862.836 25 (131 81 2926.599 64 (1.4) 2887.553 06 (10) 40 2919.311 32 (10) 2862.159 63 (14) 82 2926.700 70 (16) 2887.020 24 (10) 41 2919.561 38 (10) 2861.479 50 (14) 83 2926.798 07 (18)

^ Tile estimated uncertainty in the last digits (twice the standard deviation) is given in parentheses.

The new constants are not very different from the previously determined constants

(2, 46, 49) because the one accurate heterodyne measurement for each vibrational

transition does not change any one constant by very much, but rather changes all the constants by a small amount. However, those new constants, with the new variancecovariance matrix elements, can now be used to calculate more reliable transition frequencies and their uncertainties. Tables III, IV, and V give new tables of OCS absorption line wavenumbers that can be used for calibration. Even though the table lists uncertainties that are twice the

standard deviation, experience has shown us that they should be treated as if they were a single standard deviation. It would not be unusual if subsequent measurements

of the high-y transitions changed the numbers by two or three times the uncertainty

given in the table. In order to further improve the reliability of the calibration numbers

for these bands, it would be useful to make at least one more sub-Doppler frequency

measurement for these bands at J values that differ from the present measurements

TN-178
SUB-DOPPLER OCS MEASUREMENTS 427

by at least 1 5 units. Until more sub-Doppler measurements are made, the calculated wavenumbers for transitions with 7 values more than 10 units from the measured /

values should be treated with skepticism.

In the least-squares fit for the most abundant isotopic species over 5700 transitions were included although many of those transitions did not involve either the upper or lower state of the transitions measured in this work. For the OC^'^S species, far fewer

frequency measurements have been made, but again, all the data used in Refs. (2, 46) were included in the present fit along with some more recent FTS measurements.

ACKNOWLEDGMENTS

This work was supported in part by the NASA Office of Upper Atmospheric Research. The authors thank M. Winnewisser and co-workers for providing the FTS spectrum of OCS in this region. A. Dax was funded

by the Deutsche Forschungsgemeinschaft and the Graduiertenkolleg "Wechselwirkung in Molekulen" in Bonn, Germany. The Institut fiir Angewandte Physik provided a large quantity of optics for this experiment.

We thank B. Nelles and his co-workers from Carl Zeiss for polishing the Ti-mirror, and Mr. Koch from the Deutsche Titan GmbH Dusseldorf for making the substrate available to us. We also thank S. Gilbert of NIST for valuable suggestions regarding the paper.

RECEIVED: June 23, 1994

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(1993).

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10. C. R. Pollock, F. R. Petersen, D. A. Jennings, J. S. Wells, and A. G. Maki, J. Mol. Spectrosc. 107,62-71 (1984).

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Reference Data, NIST Bldg 221 /Room A32, Gaithersburg, Maryland 20899, or telephoning (30!

)

975-2208]

13. T. George, M. H. Wappelhorst, S. Saupe, M. MOrtz, W. Urban, and A. G. Maki, / Mol.

Spectrosc, in press.

14. A. Dax, J. S. Wells, L. Hollberg, A. G. Maki, and W. Urban, NIST Tech. Note No. 1365, 1994.

15. V. P. Chebotayev, Phys. Rep. 119, 75-1 16 ( 1985).

16. A. Clairon, O. Acef, C. Chardonnet, and C. J. Bord6, in "Frequency Standards and Metrology"

(A. DeMarchi, Ed.), Springer, Berlin, 1989.

17. M. D. Levenson, "Introduction to Nonlinear Spectroscopy", Academic Press. New York, 1982.

18. B. CouiLLAUD, in "Progress in Atomic Spectroscopy" (W. Hanle and H. Kleinpoppen, Eds.), Part C, Plenum Press, New York, 1984.

19. Murray Sargent III, Phys. Rev. A 14, 524-527 (1976).

20. R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hansch, SPIE 113, 80-87 ( 1977 ). 21. W. DemtrOder, in "Laser Spectroscopy: Basic Concepts and Instrumentation," Springer, Berlin, 198 1. [See for example, pp. 494-499.]

22. F. Bayer-Helms AND J. Helmcke, PTB-Bericht Me-17. Braunschweig. Germany, 1977.

TN-179
428 DAX ET AL.

2J. A. Dax, Ph.D. thesis. Institut fur Angewandte Physik. Universitat of Bonn. Germany, 1992.

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37. R. M. A. AZZAM. "Ellipsometry and Polarized Light," North-Holland, Amsterdam, 1977.

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42. J. S. Wells, a. Dax, L. Hollberc, and A. G. Maki. / .\fol. Spectrosc. in press. 43. M. MOrtz, M. Schaefer, M. Schneider, J. S. Wells, W. Urban, U. Schiessl, and M. Tacke.

Opt. Commun. 94, 551-556 (1992).

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214(1994).

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46. A. G. Maki, J. S. Wells, and J. B. Burkholder, / .\fol. Spectrosc. 147, 173-181 ( 1991 ). 47. A. Fayt. Ann. Soc. Scl. Brus.sels 82, 101-1 12 ( 1968).

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TN-180
JOURNAL OF MOLECULAR SPECTROSCOPY 170, 75-81 (1995)

Sub-Doppler Frequency Measurements

on OCS near 1689 and 1885 cm~^

J. S. Wells, a. Dax, ' L. Hollberg, and A. G. Makj^

Time and Frequency Division. National Instiiure of Standards and Technology. Boulder. Colorado 80303

We have used an optical polarization heterodyne technique to measure the frequencies of two OCS lines, one near 5.3 ^"1 and the other near 5.9 ^m. These sub-Doppler measurements gave

56 533 766. 1 25 ± 0.035 MHz for the 2i/2 + C3 ^(16 ) transition and 50 627 632.01 3 ± 0. 100 MHz

for the 2j'3 P(A%) line. The F( 16) measurement is in excellent agreement (20 kHz) with a new

result obtained with an alternate technique by a group at the University of Bonn. The Iv-^ measurement was combined with other frequency measurements to produce an improved calibration

table for the Iv-^ OCS band near 1 700 cm"' . These and other sub-Doppler frequency measurements

in different spectral regions give improved frequencies for a number of OCS bands. These new

frequencies will soon be incorporated into calibration data that will be available over the Internet. ® 1995 Academic Press. Inc.

INTRODUCTION

The first phase ofajoint NBS/NASA program ( which began in 1979 (7)) to generate

infrared frequency standards for the users of tunable lasers culminated in 1991 with

the publication of a calibration atlas, NIST SP 821 (2). Although other new atlases (with some complementarity in frequency coverage) have recently been published (i, 4), the NIST atlas is the only one in the mid-infrared based primarily on infrared

frequency measurements. The NIST atlas has a spectral map/ facing table format, and

the facing table information is also available in the form of computer diskettes in NIST Reference Data Base 39 (5). About four times as many other frequencies (of

transitions too weak and numerous to be included in the atlas proper) are included

in the diskettes. A text (6), intended as a companion to Data Base 39, contains ref- erences and other relevant information that also appears in the atlas. The frequency

measurements used for the generation of tables in this atlas were based primarily on

Doppler-limited spectra. The frequency measurements were based on CO2 lasers used

as frequency standards. Phase two of this on-going effort features three new developments, an ever increasing

number of sub-Doppler frequency measurements, a revision of CO2 laser frequencies,

and the dissemination of the atlas material on the new information superhighway.

Sub-Doppler frequency measurements on OCS include contributions in the 9-Mm

region by Fayt el al. ( 7). More recently Urban's group at the Institut fiir Angewandte

Physik in Bonn have extended their CO frequency measurement techniques at 5 ^.m

(5) to include OCS (9). The first NIST sub-Doppler measurements on OCS were made at 3.3 ^im ( 10). The initial measurements at 5 and 3.3 fivn relied on accidental

coincidences between OCS and CO laser lines (both Au = 1 and Au = 2 transitions)

' Guest Researcher from Institute fiir Angewandte Physik der Universitat Bonn, Bonn, D-531 15 Germany.

^ Present address; 15012 24 Ave. S.E., Mill Creek. WA 98012.

75 0022-2852/95 $6.00

Copyright © I9Q5 by Academic Press. Inc. All rights of reproduction in any form reserved.

TN-181
76 WELLS ET AL.

or on coincidences that were possible after shifting the CO frequency with an acoustooptic modulator ( AOM).

The number of such accidental coincidences is rather small and the revolutionary

development of a new frequency measurement system featuring tunable sidebands on

a CO laser at the Institut fur Angewandte Physik (Bonn) eliminates the need for coincidences. Many high quality new measurements are pending publication ( //, 12)

and others are being planned.

The precision of these sub-Doppler frequency measurements is quite high ( uncertainties down to tens of kilohertz), and a new set of more accurate CO2 transition frequencies makes possible absolute frequency measurements with accuracies commensurate with this precision. This new set of CO2 laser frequencies was determined

by a refit of all the frequency measurements for CO2 and its isotopomers by Maki et al.{ 13). It is based on the most accurate frequency measurements currently available. These new CO2 frequency values have been used in the sub-Doppler OCS frequency

measurements on OCS. While the new OCS results are within the uncertainties of the frequencies listed in SP 821, they represent improved frequency values with much

smaller uncertainties. The results of new measurements are continually being added to the data bases used to calculate frequencies of transitions in the atlas, and the development of the information superhighway will permit the dissemination of the newly calculated fre- quencies to everyone in a more timely fashion. This first update of the calibration

atlas will be available in 1995 on the Internet. In the following, we describe two new sub-Doppler frequency measurements of

OCS absorption lines, one at 5.3 ij.m the other at 5.9 ^m.

EXPERIMENTAL DETAILS

These 5-6 ^m experiments were an extension of experiments at 3.3 nm ( 70) . Again, we have used the optical heterodyne polarization technique invented by Wieman and

Hansch (14). The essence of this technique is that a strong pump /saturation beam

introduces anisotropy in a sample; that is, the sample becomes dichroic and birefringent

when the pump beam frequency is near a molecular resonance. A counterpropagating

probe beam will undergo a change in polarization orientation as the laser frequency

approaches the vicinity of a molecular resonance. Under appropriate conditions one

can detect the orientation changes in polarization and use the resulting dispersion

signal as a discriminant for locking a laser frequency to the absorption frequency of

a molecule of interest. One can divide a laser beam into several portions and use them

for saturation and probing of a sample, and have a third portion for frequency measurement. The basic scheme for the 5.3-^lm experiment is shown in Fig. 1. The starting point

is a liquid-nitrogen-cooled, flowing-gas CO laser which has been converted from 3.3 Mm (Ai; = 2) operation to Au = 1 operation by substituting a 240 line/mm grating

and appropriate coupler for those used earlier. About 400 mW were available from

the PgiS) transition, and polarization purity of the output beam was about 2000:1 as

it left the laser. The beam from the CO laser was directed to an uncoated ZnSe beam

splitter, and the transmitted beam as well as two reflected beams were used in the experiment.

The transmitted beam was passed through a novel two-stage device (equivalent to a quarterwave plate) which produced the circularly polarized saturating beam. This

reflective device has a throughput of about 60% and produced a circularly polarized

TN-182
SUB-DOPPLER OCS MEASUREMENTS 77

Two COj Lasers (u, . uj

Infrared Frequency mim

Synthesizer (5^

Us = {u, ± m-U2i rru^ Diode MO = [1 -f C + m + n] ^A V$

/S

Acousto-Optic Modulator

Beam Splrttar

Flat Mirror

Beam Slop

Oeteaor

/\

^

\

CO Au - 1 Laser :^

\

Fig. I. Functional diagram for the optical polarization heterodyne spectroscopic experiment in the 5-6

iivn region. The diagram has been stylized to a certain extent in the interest of simplicity.

beam with about 99.5: 1 polarization purity as measured with a Rochon polarizer. The

power transmitted through the beam splitter and polarizer was about 165 mW at the

cell entrance. The saturating beam was chopped and the modulation transferred to the probe beam provided the signal at the detector. The beam reflected from the first surface was used for the probe beam after passing

through a two-stage device (with about 78% throughput) which increased its polarization purity to about 200 000: 1, again with the use of reflective elements. The details of both of these two-stage polarization devices appear elsewhere (10, 15). The power

of the probe beam was about 50 mW at the absorption cell. The reflected beam from the second surface was directed to the CO2 laser frequency

synthesizer through an AOM in order to prevent feedback from the MIM diode to the CO laser. The AOM was coated for 3.3 ^m, and this reduced power in the vicinity

of the MIM to about 25 mW.

Since details of the synthesizer appear in several places (2, 6, 16. 17); we briefly

state that the synthesized frequency v^ is given by

h^ mvi nv„ (1)

where we define /, m, and n to be positive integers. A microwave frequency is rep- resented by Vm, and v\ and V2 are the new frequencies of the CO2 laser frequency

standards. The CO2 lasers are now stabilized ( 1 - /detection) by means of 4.3-|um

fluorescence in an external absorption cell using the latest recommendations of Freed

and co-workers ( 18). In general, it becomes more difficult ( more stringent requirements on the impedence of the MIM and the sharpness of the antenna point) to synthesize

a useful reference signal in the MIM diode as the mixing order increases. With the above definition of/, m, and «, the mixing order, MO, is defined as MO = [1 + /+ m + n]. (2)

TN-183
78 WELLS ET AL.

After traversing the cell, the probe beam is processed with the aid of a two-element

analyzer, which is also discussed in Ref. {10). We have shown that the relevant part

of the signal through the two-stage analyzer which reaches the detector is proportional

to (^1 EoiEoAnkoD, where 0i is the deviation of the crossing angle of the first analyzer,

Eo represents the field of the probe beam, A/i describes the birefringence and has a

dispersion characteristic, ko = 2ir/\, and L is the estimated overlap length of the

slightly crossed beams within the cell. The signal amplitude is the term in parentheses,

and the term ^i^o is the local oscillator amplitude. The main advantage of this het- erodyne technique is that a weak signal can be enhanced a great deal by heterodyning

it with a much stronger local oscillator. For the P(16) measurement a comparatively

large local oscillator power helped produce the dispersion signal shown in Fig. 2. The

signal-to-noise ratio shown here is about 10 000:1. The OCS pressure in the cell was

1.3 Pa ( 10 mTorr), and the effective beam overlap length in the OCS absorption cell was estimated to be 1 m. This discriminant was used for locking the CO laser for the

P{\6) frequency measurement.

The measurement of the P{48) OCS line at 5.9 fim was considerably more difficult, and the measurement uncertainty was increased. For this experiment, a direct overlap

between CO and OCS did not exist and it was necessary to shift the frequency of the working beam 90.000 MHz below the frequency of the Pi5( 18) transition by first passing it through the AOM (path changed from A-B to C-D in Fig. 1 ). The 3.3-Atm AR coating on the AOM permitted an even smaller portion of the beam power to be

transmitted than was the case at 5.3 ixm. About 30 mW total was available for the

three beams departing from our uncoated, wedged beam splitter. The power levels at the cell were about 1 3 and 4 mW for the saturation and probe beams, respectively,

and 4 mW was available for generating the beatnote with the CO2 synthesizer. As a

result of the lower power and a more than an order of magnitude reduction in detector

sensitivity in going from 5.3 to 5.9 ^m, the dispersion signal was not nearly as good

as that for the P( 1 6 ) transition. A second difficulty was associated with the higher

mixing order (8 in this case). The harmonic numbers were 4, 2, and 1; the need for

+1 -

c3

>>2

B

<

mc

a>

COc

o

to

Q.

- P(16)

1 r

-

-^0 Frequency

Fig. 2. Dispersion signal for the OCS /^ 16) transition of the 02° 1-00^ band. The peak-to-peak linewidth was about 600 kHz, and the width of the scan shown in the figure was estimated to be about 60 MHz.

TN-184
SUB-DOPPLER OCS MEASUREMENTS 79

higher harmonics also contributed to a larger uncertainty than we had for the Pi 16)

measurement. For the Pi 48 ) measurement, the pressure and effective pathlength were

also 1.3 Pa and 1 m.

In both instances, the frequency of the radiation in the cell was locked to a subDoppler feature of the molecular transition of interest, and a signal was generated in the CO2 synthesizer that was close to that transition frequency. A difference frequency

beatnote, p,( ( between the synthesized frequency and the transition frequency ) was

measured on a spectrum analyzer. The OCS transition frequency was then

"DCS = "s ± "if. ( 3 ) Both the Bonn measurement and our measurement of PC 16) used CO2 reference

lasers of similar design which are not as accurate as the CO2 laser system used by

Chardonnet et al. ( 19) for their very accurate measurements. Even though these two

measurements agree to within 20 kHz, that does not mean that the absolute accuracy

is that good. We believe that the uncertainties given here and in Ref. (9) are good

estimates of the true uncertainties, regardless of how close the agreement may be. The

uncertainty in the PC 48) measurement has a larger uncertainty for the reasons already

discussed. The results of P( 16) and Pi4S) measurements are shown in Table I.

ANALYSIS AND RESULTS

The present results were combined with earlier measurements in a least-squares fit. Earlier heterodyne measurements that involved the 21/3 state are given in Refs. ( 20-

22), and those involving the 2i>2 + p^ state are given in Ref i23). In addition, measurements that involve rotational transitions for these vibrational states were given by

Vanek et al. i24).

The fit used the same Hamiltonian as that described by Maki et al. i23). For the 02° 1-00^0 transition the effect of /-type resonance was taken into account, but that resonance was not present for the 00°2-00*'0 transition. The present new measurements are useful for determining much improved absolute

frequencies for the levels of OCS that are near the same 7 values as the measurements.

TABLE I

Measured Transition Frequencies for Carbonyl Sulfide CO

Trans." OCSTrans.

'' Obs. Freq.-^ (MHz) CO2 Laser'' Synthesis Scheme'^

"if (MHz)

^,(6)

Z'l.sdS)

P(16) A

P(48) A

56 533 766.125±0.035

50 627 632.013±0.100

iP,(30) + P,(12)-p,„ 4x/?,(6)-2x/?„(36)-^,

307.596 -449.840

" For the CO laser designation the subscript indicates the lower state vibrational quantum number and J" appears in parentheses.

* We are using the notations m Ret', (2) for these transitions. Thus for the 57 THz

transition, A represents the 02"l-00"0 band. For the 51 THz line, A is the designation

for the 00"2-00"0 band.

' The observed OCS frequency is the sum of the synthesized frequency and the beatnote frequency.

^ For the COj laser, the designation I indicates the 10 ^m band and II indicates the 9 ^m

band.

' For the ^(16) measurement, i',,, was 10 000.000 MHz, for P(48) v„, was

10 007.022 MHz.

TN-185
80 WELLS ET AL.

This can be seen in the uncertainties shown in Table II. The uncertainties become

quite small for the transitions between 7 = 20 and 7 = 65 of 00°2-00°0. For other

values of J the uncertainties approach the values given in Ref. (2) but are always

smaller. Table II gives the calculated wavenumbers determined by the constants given

by a least-squares fit of all the measurements available for the upper and lower states of the 00°2-00°0 transitions. The constants from that fit are almost identical to those

given by Maki and Wells (2), but there are significant changes in the correlation of

the constants and in the variance-covariance matrix elements.

The earlier (9) sub-Doppler measurement of the P( 16) transition oilvi + v-^ has

been confirmed by the present measurement, and the agreement can also be considered

TABLE II Wavenumbers (cm"') Calculated for the 00^2 -OCO Band of '*0'^"S

/*- Branch /{-Branch P- Branch J' /{-Branch

1690.309 118 (05) 45 1726.972 585 (05) 1689.793 863 (051 46 1727.261 570 (05) 1689 276 166 (05) 47 1727 548 Oil 1051 1688 756 026 (05) 48 1727.831 907 (05) 1688 233 443 (05) 49 1728.113 253 (06) 1687.708 414 (05) 50 1728.392 047 (06) 1687 180 940 105) 51 1728.668 285 (07) 1686 651 018 (06) 52 1728.941 964 (08) 1686.118 647 (07) 53 1729.213 080 (08) 1685.583 827 (07) 54 1729.481 630 (09) 1685 046 556 (08) 55 1729.747 611 (10) 1684.506 833 (09) 56 1730.011 019 (11) 1683 964 656 (10) 57 1730.271 850 (13) 1683 420 024 (11) 58 1730.530 102 (14) 1682 872 936 (13) 59 1730.785 770 (15) 1682 323 389 (14) 60 1731.038 850 (16) 1681.771 383 (15) 61 1731 289 340 (18) 1681 216 917 (16) 62 1731.537 235 (19) 1680 659 987 (18) 63 1731.782 532 (20) 1680.100 594 (19) 64 1732.025 227 (22) 1679 538 734 (20) 65 1732.265 316 (23) 1678 974 407 (22) 66 1732.502 795 (24) 1678.407 611 (23) 67 1732.737 660 (25) 1677.838 344 (24) 68 1732.969 908 (27) 1677 266 604 (25) 69 1733.199 534 (28) 1676 692 389 (27) 70 1733.426 534 (29) 1676.115 698 (28) 71 1733.650 905 (30) 1675. 536 528 (29) 72 1733.872 643 (31) 1674.954 878 (30) 73 1734091 742 (31) 1674 370 746 (31) 74 1734.308 200 (32) 1673 784 129 (31) 75 1734 522 Oil (33) 1673.195 026 (32) 76 1734.733 173 (33) 1672 603 435 (33) 77 1734 941 680 (34) 1672.009 353 (33) 78 1735.147 528 (34) 1671 412 778 (34) 79 1735.350 714 (35) 1670 813 709 (34) 80 1735.551 232 (35) 1670.212 143 (35) 81 1735.749 078 (36) 1669 608 078 (36) 82 1735.944 249 (37) 1669 001 512 (37) 83 1736.136 739 (39) 1668.392 441 (38) 84 1736.326 544 (41) 1667 780 865 (40) 85 1736.513 661 (44) 1667 166 781 (42) 86 1736.698 083 (48) 1666 550 186 (45) 87 1736.879 807 (53) 1665.931 078 (49) 88 1737 058 829 (59) 1665.309 454 (54) 89 1737.235 143 (66)

1710.

1710.

1709.

1709.

1708.

1708. 1708

1707. 1707

1706 1706

1705

1705 1705

1704 1704

1703

1703

1702

1702

1701

1701

1701 1700

1700

1699

1699

1698 1698

1697

1697 1696

1696

1695 1695

1694

1694

1693 1693

1692

1692

1691

1691 1690

570 547

162 392

751 796 338 760

923 286

505 373 085 023

662 237 237 015

809 358

.379 267

.946 741

.511 782

.074 391

.634 567

.192 31 1 .747 623

.300 504

.850 954

398 973 944 561

.487 719

.028 446

566 743

.102 609

.636 045

.167 050

695 624

.221 767

.745 479

266 760

.785 608

302 025

.816 009

.327 559 836 677

343 360

.847 608

.349 421

.848 798

.345 739 840 242

.332 307

.821 932

1 (31) 1 1 (31) 2 1 (31) 3 1 (31) 4 1 (31) 5 1 (30) 6 1 (30) 7 1 (30) 8 1 (29) 9 1 (29) 10 1 (28) 11 1 (28) 12 1 (27) 13 1 (27) 14 1 (26) 15 1 (25) 16 1 (24) 17 1 (24) 18 1 (23) 19 1 (22) 20 1 (21) 21 1 (20) 22 1 (20) 23 1 (19) 24 1 (18) 25 1 (17) 26 1 (16) 27 1 (15) 28 1 (15) 29 1 (14) 30 1 (13) 31 1 (12) 32 1 (12) 33 1 (11) 34 1 (10) 35 1 (10) 36 1 (09) 37 1 (08) 38 1 (08) 39 1 (07) 40 1 (07) 41 1 (06) 42 ] (06) 43 1 (06) 44 1

1711 379

1711 780

1712.178

1712.574

1712 968

1713.359 1713.747

1714.133 1714 517

1714.898

1715 277

1715 653 1716027

1716 399

1716.768

1717.134 1717.498

1717 860

1718.219

1718.575 1718 929

1719 281 1719.630

1719.977

1720 321 1720.663

1721.002 1721.339

1721 673

1722 005

1722 334

1722.661 1722 985

1723 307

1723 626

1723.943 1724 257 1724 569

1724 878

1725.185

1725 489

1725 791 1726 090

1726 386

1726 681

530 (31)^ 357 (31) 739 (311. 674 (311 162 (30) 202 (30) 791 (30) 929 (291 614 (29) 845 (28) 620 (28) 938 (27) 797 (27) 195 (26) 132 (25) 604 (24) 610 (24) 149 (23) 219 (22) 817 (21) 942 (20) 591 (20) 764 (191 456 (18) 667 (17) 395 (16) 636 (15) 389 (15) 651 (14) 420 (13) 694 (12) 471 (12) 746 (1 1) 519 (10) 787 (10) 546 (09) 794 (09) 529 (08) 748 (07) 448 (07) 626 (07) 279 (06) 404 (06) 999 (05) 060 (05)

The estimated uncertainty in the last digits (twice the standard deviation) is given in parentheses.

TN-186
SUB-DOPPLER OCS MEASUREMENTS 81

as a confirmation of the accuracy of the other sub-Doppler measurement of this paper

and of Ref ( 10). The present measurements do not make a significant difference to the transition wavenumbers calculated for the 2if2 + fj band given as Table IV in the

paper by George et al. (9).

ACKNOWLEDGMENTS

This work was supported in part by the NASA Office of Upper Atmospheric Research. A. Dax was funded by the Deutsche Forschungsgemeinschaft and the GraduiertenkoUeg "Wechselwirkung in Molekiilen" in Bonn, Germany. We are grateful to the Institut fur Angewandte Fhysik of the University of Bonn for temporary loan of a large quantity of optics for this experiment.

Received: September 6, 1994

REFERENCES

;. J. S. Wells, F. R. Petersen, and A. G. Maki, Appl. Opt. 18, 3567-3573 (1979).

2. A. G. Mak.1 and J. S. Wells, "Wavenumber Calibration Tables from Heterodyne Frequency Measurements," Natl. Inst. Stand. Technol. Special Publication 821, U.S. Government Printing Office, Washington, DC, 1991.

3. G. Guelachvili and K. Naraharj Rao, "Handbook of Infirared Standards," Academic Press, Orlando, FL, 1986.

4. G. Guelachvili and K. Narahari Rao, "Handbook of Infrared Standards II," Academic Press, Boston, 1993.

5. A. G. Maki and J. S. Wells, NIST Standard Reference Data 39. [This may be purchased by contacting Standard Reference Data, NIST, Bldg. 221 /Room A32, Gaithersburg, MD 20899, or telephoning

(301)975-2208]

6. A. G. Maki and J. S. Wells, J. Res. Natl. Inst. Stand. Technol. 97, 409-470 ( 1992).

7. A. Fayt, J. G. LaHaye, J. Lemaire, F. Herlemont, and J. G. Bantegnie, J. Mol. Spectrosc. 140, 252-258(1990).

8. T. George, S. Saupe, M. H. Wappelhorst, and W. Urban, Appl. Phys. B. 59, 159-166 ( 1994).

9. T. George, M. H. Wappelhorst, S. Saupe, M. MOrtz, W. Urban, and A. G. Makj, / Mol.

Spectrosc. 167, 4 1 9-428 ( 1 994).

10. A. Dax, J. S. Wells, L. Hollberg, A. G. Makj, and W. Urban, / Mol. Spectrosc. 168, 416-428

(1994).

11. B. Meyer, S. Saupe, M. H. Wappelhorst, T. George, F. KOhnemaiw, M. Schneider, M. HAVENrrn, W. Urban, and J. Legrand, Appl. Phys. B . submitted for publication.

12. S. Saupe, B. Meyer, M. H. Wappelhorst, W. Urban, and A. G. Maki, in preparation.

13. A. G. Maki, C-C. Chou, K. M. Evenson, L. R. Zink, and J-T. Shy, J. Moi Spectrosc. 167, 211-

224(1994).

14. C. WiEMAN AND T. W. Hansch, Phys. Rev. Lett.. 1 170-1 173 ( 1976).

75. A. Dax, J. S. Wells, L. Hollberg, A. G. Makj, and W. Urban, NIST Tech. Note 1365 ( 1994).

16. A. Hinz, J. S. Wells, and A. G. Makj, Z. Phys. D 5, 351-358 ( 1987).

17. J. S. Wells, M. Schneider, and a. G. Makj, / Mol. Spectrosc 132, 422-428 ( 1988).

18. K. L. SOOHOO, C. Freed, J. E. Thomas, and H. A. Haus, IEEE J. Quantum Electron. QE-21, 1 159-

1171 (1985).

19. Ch. Chardonnet, a. Van Lerberghe, and Ch. J. Bord^, Opt. Commun. 58, 333-337 (1986).

20. i. S. Wells, F. R. Petersen, A. G. Maki, and D. J. Sukle, Appl. Opt. 20, 1676-1684 ( 1981 ); 20, 2874(1981).

21. i. S. Wells, F. R. Petersen, and A. G. Maki, / Moi Spectrosc. 98, 404-412 (1983).

22. i. S. Wells, M. D. Vanek, and A. G. Makj, / Mol. Spectrosc. 135, 84-88 ( 1989).

23. A. G. Maki, Wm. B. Olson, J. S. Wells, and M. D. Vanek, / Mol. Spectrosc. 130, 69-80 ( 1988).

24. M. D. Vanek, D. A. Jennings, J. S. Wells, and A. G. Maki, / Mol. Spectrosc. 138, 79-83 ( 1989).

TN-187
AppL Phys. B 61, 553-558 (1995) Applied

Physics B^dopttc

© Springer-Veriag 1995

Detection of methane in air using diode-laser pumped

difference-frequency generation near 3.2 \im

K. P. Petrov', S. Waltman-, U. Simon^ R. F. Curl', F. K. Tittel', E. J. Dlugokencky^, L. Hollberr

' Dcpanmems of Electrical and Computer Enginecnng, and Chemistry, Rice University, Houston, TX 77251-189Z USA

(Fax: + 1-713/524-5237, E-mail: FKT@rice.edu)

' Time and Frequency Division. National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80303, USA

^ National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, CO 80303, USA

Received: 23 June 1995/Acccpted: 1 July 1995

Abstract Spectroscopic detection of the methane in natural air using an 800 nm diode laser and a diode-pumped

1064 nm Nd : YAG laser to produce tunable light near

3.2 nm is reported. The lasers were pump sources for ring-cavity-enhanced tunable difference-frequency mixing

in AgGaSj. IR frequency tuning between 3076 and

3183 cm" ' was performed by crystal rotation and tuning

of the extended-cavity diode laser. Feedback stabilization of the IR power reduced intensity noise below the detector noise level. Direct absorption and wavelength-modulation

(2/) spectroscopy of the methane in natural air at 10.7 kPa

(80 torr) were performed in a 1 m single-pass cell with

1 |iW probe power. Methane has also been detected using a 3.2 ^lm confocal build-up cavity in conjunction with an

intracavity absorption cell. The best methane detection

limit observed was 12 ppb m (Hz.)" "^.

PACS: 07.65; 33.00; 42.60; 42.65; 42.80

This work was done to develop a diode-laser-based tech- nique for sensitive detection of environmentally important

atmospheric trace gases such as methane, carbon monoxide, nitrous oxide, and nitric oxide. Several measurements

of optical absorption in methane using tunable near-in- frared lasers have been reported recently. Lucchesini et al. have used diode lasers to access 3v, -i- V3 -i-(v2 or v*) combination-overtone bands of methane near 790 nm, and the 2v, -I- 2vj band near 860 nm [1]. Scott et al. have

investigated the possibility of methane detection with the use of a 1.34 nm Nd:YAG laser which can access the

V, + Ivj combination-overtone band [2]. Uehara and Tai

[3] have been used a diode laser to detect methane in air by monitoring absorption in the 2v3-stretch vibration- overtone band near 1.66 nm, achieving a detection limit of 0.3ppmm with a signal averaging time of 1.3 s. This

corresponds to 680 ppbm(Hz)" "^. Pavone and Inguscio

[4] observed a component of the methane combination

band corresponding to a third overtone at 866 nm.

The fundamental Vj band of methane near 3.2 \ixru however, has transitions that are as much as a factor of

160 stronger than those of the first overtone band and

may be better suited for sensitive detection. The maximum

line intensity and the typical pressure broadening coefficient of methane in this band is 113x10" "cm. and

0.027 MHz Pa"', respectively, which corresponds to

a peak absorption of 0.005 m" ' ppm" ' in air at 1 atm

near 3067 cm"' [5]. Given the typical 1.8 ppm natural

abundance of methane in air the absorption coefficient to be measured is 0.009 m''. The fundamental vj band of

methane is accessible by either conventional spectroscopy

using the carbon monoxide overtone laser [6], the helium- neon laser near 3.39 nm [7], lead-salt diode lasers, colorcenter lasers, or with Ar^-dyc laser difference-frequency

generation [8]. These infrared laser sources are also suit- able for sensitive atmospheric trace gas detection.

McManus et al. [9] demonstrated an atmospheric methane measurement instrument using a Zeeman-split he- lium-neon laser with a sensitivity of 20 ppb with a signal

averaging time of 1 s (40 ppb (Hz)" "^). Simultaneous detection of methane and other gas species in air has been

accomplished with the use of a compact lead-salt diode

laser spectrometer that included a multipass absorption

cell [10]. A detection limit for methane of 4ppbm near

8 nm with a signal averaging time of 3 s was reported

(14 ppb m (Hz)"'").

However, each of the mid-infrared laser sources mentioned above suffers from its own specific practical drawbacks such as large physical size, lack of portability, high

cost, high power consumption, poor tunability. or need

for cryogenic cooling. On the other hand, the use of

commercial single-frequency short wavelength diode

lasers as pump sources offers benefits of small size, reliability, low cost, and low power consumption. These diode

lasers also offer good amplitude and frequency stability

which are important in the design of a compact and

robust gas sensor. Several new interesting diode lasers operating in the 2.7 to 3.9 nm wavelength region have

been developed [11-13] but are not yet commercially

available. These lasers may still require cooling with liquid

nitrogen for normal operation which is sometimes a

TN-188
554

practical drawback. Therefore, CW Difference-Frequency

Generation (DFG) pumped by visible and near-infrared

diode lasers at room temperature remains an attractive technique for generation of tunable mid-infrared light

[14].In this paper, the applicability of CW diode-pumped

DFG to the detection of methane in air is investigated.

The detection limit is based upon the measured perfor- mance charactenstics of the IR probe source and detector. A significant technical difficulty in applying DFG to spec- troscopic detection is its low conversion efficiency when

pumped directly by most single-frequency CW semiconductor lasers. Traveling-wave semiconductor amplifiers

have been successfully applied to boost effective optical

pump power [15]. In earlier work [16] we reported tun- able CW mid-infrared DFG with output power in excess

of 3 |iW pumped by relatively low-power near-infrared

diode lasers. A compact ring enhancement cavity was used

in order to increase effective signal power available for difference-frequency mixing.

In this work, an improved and more robust design of the build-up cavity was implemented. Direct absorption

and wavelength-modulation {If) spectroscopy of methane

in air at 10.7 kPa (80 torr) were performed in a 1 m single- pass cell with 1 ^iW probe power. The detection sensitivity of 12 ppbm(Hzr"^ was Hmited by detector noise. In an

effort to improve detection sensitivity, we tested the effec- tiveness of a confocal 3.2 |im enhancement cavity in combination with an intracavity absorption cell.

1 Diode-pumped cavity-enhanced 3.2 \im DFG

source

A schematic diagram of the experimental setup is shown

in Fig. 1. Two different compact lasers were used for pumping the difference-frequency IR source: a 500 mW

diode-pumped monolithic Nd : YAG ring laser at 1064 nm

(signal), and a 20 mW extended-cavity diode laser (ECDL)

at 800 nm (pump). In later experiments, the ECDL was

replaced with a 100 mW solitary laser diode in order to increase the IR power and allow fast wavelength modulation. The pump and signal laser beams were combined in a polarizing beamsplitter cube after spatial mode matching. They were then focused into a 5.5 mm antirefiection- coated AgGaSi crystal through the input coupler of a bow-tie enhancement cavity. The cavity was designed to build up the 1064 nm light because bulk absorption in the

crystal at that wavelength is lower than at 800 nm and

scanning is simpler. The input coupler was a plano-con- cave fused silica substrate coated for high transmittance near 800 nm and 3.4% input coupling at 1064 nm. The

radius of curvature of the concave side was 100 mm. The

CaF2 output coupler had the same dimensions and was

coated for high reflection at 1064 nm. The transmittance

of the output coupler was measured to be 41% near

3.2 nm using light from a carbon monoxide overtone laser. The long arm of the cavity was not a conventional bow-tie

in that a Littrow prism reflector was used instead of a flat mirror. The function of this element was to eliminate

multiple passes of the 800 nm light in the cavity. Use of a flat mirror resulted in a small portion of the diode laser

^H—

OIOOE-PUMPEO

N<);YAG UTTROW PRISM REFLECTOR

POLARIZING BEAMSPLITTER C.Fz

-^^oy

© 0.^-^

INPUT AgGaSj OUTPUT - COUPLER COUPLER

f ilTER ' ^ CaFj ABSORTDON CELL

TELESCOPE AOM ^^—D-^ 3 \

ANAMORPHIC

PRISM PAIR TELESCOPE

I I PRJSM icuestur-E

C.F,

830 MHz ETALON

Fig. 1. Experimental setup for spectroscopic detection of methane

near 3.2 ^m in air. The AgGaS: crystal was placed into a bow-tic

build-up cavity which was locked to resonance at 1064 nm. The

1064 nm light was supplied by a diode-pumped Nd : YAG laser. The

tunable 800 nm light was supplied by either a grating tuned cx- tended-cavity diode laser or a solitary laser diode. The IR power was

stabilized by adjustmg the diode laser power with an AOM

light circulating in the cavity which produced a systematic

ripple in the IR power when the diode was tuned. The

bow-tie cavity design with the addition of a Littrow prism

reflector provides several advantages: it employs a minimum number of intracavity elements, is easy to align, has

flexible mode diameter control, which is important for reaching optimum DFG conversion efficiency [17], and

eliminates cavity resonance at the pump wavelength.

The Nd:YAG beam was spatially mode-matched to

the cavity and the reflected power was monitored by

a silicon photodetector PD2 (Fig. 1). Optimization of the

cavity mode diameter allowed us to achieve a 90% input

coupling efficiency limited mainly by the impedance mismatch of the input coupler transmittance. However, in normal operation a typical input coupling efficiency of

between 75% and 85% was observed. The intracavity

Nd: YAG power was monitored by a silicon photodetector PDl which detected a 0.011% transmission through

a PZT-driven flat cavity mirror (Fig. 1). The cavity buildup was 16 with the mixing crystal and 144 without. This

corresponds to 6.1% and 0.7% excess cavity loss. Transmission losses in the crystal for the ordinary beam at 1064 nm have increased from 1.5% to 5.4% due to additional surface and bulk losses in the one-year time interval

since the previous work [16]. Present measurements re- vealed 2.5% total reflection loss at 1064 nm compared to an immeasurably small reflection previously. This suggests that the index of refraction at the surface has

changed. The manufacturer suggests that these changes

are induced by exposure to near-UV light.

The 3.2 ^m output beam (idler) was collimated by

a CaFj lens, filtered by a broadband antireflection-coated

germanium filter to remove pump and signal light, and

focused by another CaF2 lens onto a room-temperature

InAs detector. A maximum of 6 nW IR power was measured with 40 mW pump power incident on the crystal, and

TN-189
555

o^ 0.4

0.2

Signal pow«r I2« •»

Oyitai iMtotle J.S «"

Ctvtty (MiiMup: 1* ;

- ,/._

; - - /—— A ^.

-^

3t3S 3140 314S 31SS 31(0 IR frequency, cm'

Fig. 2. Measured DFG power with pump wavelength near 800 nm

for fixed phase matching angle. The full width at half maximum

(FWHM) of the peak is 11 cm"'. The asymmetry is a result of pumpmg with focused Gaussian beams

230 mW signal power in front of the cavity, which corres- ponds to 3.75 W intracavity signal power. Operation with more than 4.2 W intracavity Nd : YAG power was

achieved, accompanied by noticeable thermal lensing in the mixing crystal. Frequency tuning of the idler wave was

performed by tuning of the pump laser and crystal angle.

At a fixed phasematching angle, frequency tuning over

a range of approximately 10cm~' was possible as is apparent from Fig. 2. Therefore, short frequency scans of

10 GHz for spectroscopic measurements did not require

crystal rotation. The observed asymmetry of the phasematching peak is a result of pumping with focused

Gaussian beams [18]. Tuning of the pump laser from

801.3 nm to 795.2 nm and changing the internal

phasematching angle of the crystal from 80° to 90° shifted the peak output IR power from 3076 to 3183 cm" '. Operation at infrared frequencies below 3076 cm" ' was possible with phasematching angles below 80° but at the cost of more than 25% reduction in the output power due to larger beam walkoff, decreasmg effective non-linear coefficient, and increasing Fresnel reflection losses at the AR-coated crystal surfaces which decreased the cavity

build-up.

In the experiments described below the source was

scanned by sweeping the frequency of the ECDL or soli- tary laser diode. In the ECDL. continuous mode-hop-free

frequency tuning of 20 GHz was performed by electronically adjusted synchronous rotation and translation of the PZT-driven tuning mirror. The Littman configuration of

the ECDL allowed tuning without steering of the output

beam. The solitary laser diode was tuned by current and

temperature control. Frequency scans of 10 GHz and

wavelength modulation were performed by modulating

the injection current. Fig. 3 shows a single-sweep 2/ spec- trum near 3086 cm"' of 75.3 ppm methane in air at

13.3 kPa ( 100 torr) in a 59 cm single-pass cell. The spec- trum was acquired by scanning the solitary diode pump

laser. A low-finesse 830 MHz etalon was used for monitoring the scans. The primary objective of the spectroscopic measure- ments was to determine a detection limit for methane in

30es.8323 air'

3085.8606 cm-'

3085.8933 crrr'

(0c

g»

'«>V

*-> JO

03 cc

75.3 ppm

. 3086.0308

. 3086.0720 -25 •20 -IS 10 S s Time, s

10 15 20 25

Fig. 3. Wavelength-modulation (If) single-sweep spectrum of

75.3 ppm methane in 13.3 kPa (100 torr) air in a 39 cm cell. The

spectrum was acquired by tuning of the solitary diode pump laser. Modulation frequency was 2 kHz, lock-in lime constant was 0.1 s. The vertical solid line at ihe center indicates the point of sweep

reversal

«M 10*F

NX

O to*

E

oin

Q.

J2o

z 1

..: ^—rrrn .—-- - : : ; : :

:

? ' '

0.85 pW near 3.2 pm

V._.-:r:-i:;\>d . k-- . 1

\ — v\a — \—- :,;: V ; n -. \; dark : . : '^'rrj^^^^f^'y/f;^^m^

100 Frequency, Hz

Fig. 4. The power spectral density of the noise'from the InSb photodetector/preampjificr measured with a fast Founer transform analyzer. The upper curve was taken when the detector was exposed to 0.85 ^W of IR DFG radiation near 3.2 nm. Note that the buildup

caaiity locking noise dominates at frequenaes below 3 kHz. The

detector/preamplifier responsivity at 3.2 ^m was 1.2 x 10* VW"'

air using light produced by difference-frequency generation pumped by tunable diode lasers and to identify the sources of noise. Figure 4 shows plots of power spectral

density of the amplitude noise in the IR detector signal

acquired with a fast Fourier transform analyzer. In our 2/

spectroscopic measurements, the maximum modulation

frequencyof the ECDL was limited to ~ 100 Hz resulting

in demodulation frequencies below 200 Hz where the cavity locking noise still dominated.

In later experiments, a servo loop was used to reduce

intensity noise in the IR beam. A portion of the IR beam

was focused onto a room-temperature InAs reference detector, and the feedback adjustment of the diode laser power was performed by an acousto-optic modulator.

This allowed the effects of the Nd: YAG build-up cavity

noise, the amplitude modulation of the diode laser resultTN-190
556

ing from frequency tuning, and background fringes to be

cancelled out. In addition to single-pass absorption measurements we tested the effectiveness of a confocal enhancement

cavity to improve the detection sensitivity. The cavity

mirrors were plano-concave quartz substrates with

250 mm radius of curvature coated for high reflection at 3.4 nm. A transmittance of 1% was measured for each

mirror using a probe beam from the DFG source. The

finesse of the empty cavity was measured to be 213 which

suggested a 0.5% additional loss in each mirror. For

spectroscopic measurements an 18 cm long absorption

cell with Brewster windows was placed into the cavity,

reducing the cavity finesse to 182, which corresponds to an additional loss of about 0.25% per round trip. The

cavity was dither-locked to resonance at the idler wavelength by controlling a PZT-driven mirror. In order

to maintain the locking when the idler frequency was

tuned, the diode laser sweep and modulation signals were

supplied to the PZT controller that locked the 3.2 |im

build-up cavity. Only 10% of the IR power from the DFG

source could be coupled into the cavity because of poor

spatial mode matching. Typical idler power delivered to the detector was only about 80 nW. With improved spatial mode matching of the IR beam, it should be possible

to achieve 80% coupling into the cavity and deliver about

0.8 ^W probe power to the detector.

2 Spectroscopic detecrion of methane in air

Direct absorption and wavelength-modulation (2/) spec- troscopy of both pure methane and methane in air was

performed with and without IR cavity enhancement. We

used three calibrated mixtures of methane with natural

air; these had mixing ratios of 75.3, 10.8 and 1.8 ppm. The

last was natural air sampled on a mountain ridge.

Figure 5 shows experimental wavelength-modulation

(2/) spectra of methane in natural air sample at 13.3 kPa

(100 torr) in a 59 cm single-pass cell near 3086 cm" '. This

center frequency was chosen because of the presence of six strong distinct absorption lines of methane. For example,

the transition at 3085.8323 cm"' has a line intensity of

1.70 X 10" '^ cm. It is only 20% weaker than the transition

at 3067.3000 cm~ ' which is the strongest in the band [5]. Tuning of the source to the frequency of this strongest line was possible at the cost of reduction in IR power output.

For each of the spectra, the amplitude of the frequency

modulation was optimized to produce the maximum If

signal size. The spectra were taken without IR power

stabilization. Figure 6 shows direct absorption spectrum of the methane in natural air at 80 torr in a 1 m single-pass cell.

It was acquired using a signal-averaging bandwidth of

1 Hz, and IR power stabilization. Atmospheric pressure- broadened methane in the laboratory air between the power stabilizer beamsplitter and the sample cell is visible

in the baseline trace. The baseline slope is due to interfer- ence from a secondary reflection from the power stabilizer beamsplitter. Based upon the observed signal-to-noise

ratio, a detection limit (signal-to-noise ratio of 1) of

12 ppbm(Hz)~ "^ can be determined; it is in good agree-

« A J

- li,. 1 A^ -An /V . - 75.3 ppm.

10.8 ppm'

(0c

O)

0) X 4

iiir llll

K^^[f\^\ , >

V A/yyijv^A—-

0) -""^lyir fVV maAK''""-

Time

Fig. 5. Wavelength-modulation (2/) spectra of methane in air at 13.3 kPa (100 torr) in a 59 cm cell, obtained with 0.85 nW of IR probe power near 3086 cm"'. Modulation frequency was 100 Hz. Sweep times were 50 s, 50 and 500 s, and lock-in amplifier time

constants were Is, Is, and 3 s, respectively. The build-up cavity

locking noise can be seen in the spectrum of 1.8 ppm methane. The

scan widths were not the same for the 3 traces. The traces have been

offset vertically for clarity

Time

Fig. 6. Direct absorption spectrum of the methane in natural air near 3086 cm"' at 10.7 kPa (80 torr) in a 1 m single-pass cell (A), and the evacuated cell (B). Atmospheric pressure-broadened methane in the laboratory air between the power stabilizer beamsplitter and the sample cell is visible in the baseline trace (B). The traces have

been offset vertically for clarity. Both are 2000 sweep averages

resulting in 1 Hz noise bandwidth for ( A-B). The detection limit of l2ppbm(Hz)""^ can be inferred

ment with the measured InAs detector noise. This corres- ponds to an absorbance root-mean-square noise of

5.1 X 10"^ (Hz)"''^. The detection limit can be improved.

First, more IR probe power can be generated. For

example, a commercial 1 W single-frequency master oscil- lator power amplifier (MOPA) can be used as a pump

source at 800 nm. Also, a somewhat longer mixing crystal can be used. Second, better output coupler transmittance can be obtained. We have measured 60% transmittance at 3.2 nm for the replacement output coupler and 41% for that used in the experiment. Third, an IR detector with

lower noise equivalent power (NEP) can be used. The

room-temperature InAs detectors used in the experiment

had NEPs of 17 pW(Hz)" "^ at 3.2 ^lm, which is a factor

TN-191
557

X 1 75.3 ppm . \\r^,

/-ATr\ f

\ / \ /

\ / CO \J V \J V

c • . O) X 5 10.8 ppm

(A>

4-» ^\'iVy''\f.

n v A^^

X 25 1.8 ppm

V v \j

Time

Fig. 7. Wavelength-modulation (2/) spectra of methane in air at 13.3 k Pa (100 torr) in an 18 cm Brewster window cell inside a confocal enhancement cavity near 3.2 \xm. The frequency of the

transition is 3086.0308 cm"'. The detected IR power was 80 nW,

sweep time was 10 s, lock-in amplifier time constant was 0.3 s. A modulation frequency of 10 Hz was used to mamtain locking of

the IR cavity. The IR frequency sweep range was approximately

3 GHz in order to operate with reliable locking. The traces have

been offset vertically for clarity. The vertical solid lines indicate points of sweep reversal

100

10

E

15c

o>M

CMV

.> 0.1

(0

0) 0^

0.01

--— -f-r^jrri :-__-_::-;:;r;~5=H^lr_

i f ! ! • 'cavity-enhai ;

' !

!

''-"- '^^^^''^^^[^"rnT

:^£:-:t:-ii "r '~t±f.

! 1 I ! ; ; I'

: !>• LI- -p-fT

..^--—^- _i-^,..,.-=rm :_!_:_::

' -1-- l[l

K ' ' ' '

;

j single-pass

- .- - . .:.r^=_^p,prt:i^jv|;.^ „----- — r - -:• —•: — - -: : •

•"""'^ l' :

' '

i 1 ;

1 10

Concentration, ppm

100

Fig. 8. Measured relative 2/ signal amplitude per unit cell length

PifKPofL) in the case of single-pass and cavity-enhanced detection, versus concentration of methane in air at 13.3 kPa (100 torr). The

enhancement factor (max. 1 16) is in good agreement with the measured cavity finesse

of 5 larger than typical NEP of cooled InSb detectors. Fourth, either a multipass absorption cell or a build-up

cavity can be used to increase effective path length.

The confocal enhancement cavity near 3.2 iim de- scribed above was used to increase the relative magnitude

of the absorption signal. The effective number of passes in such cavity is

n

where F is the cavity finesse, and the factor 2 accounts for two passes through an intracavity absorption cell per round trip. Given the previously measured value of cavity

finesse F = 182, the number of passes should be N = 116,

which is in good agreement with the number obtained by

comparing the fractional 2/ signal per centimeter of cell length detected with cavity enhancement (Fig. 7) to that detected in the single-pass configuration (Fig. 5). The ex- perimental enhancement factor for lower intracavity

methane concentrations is in agreement with the experimental value of cavity finesse (Fig. 8). Higher concentrations of methane introduce more absorption per round

trip thus decreasing the cavity finesse and the related

effective number of passes which is the case with the

75.3 ppm sample.

3 Conclusion

In summary, spectroscopic detection of the methane in natural air (1.8 ppmv) using diode-laser pumped cavityenhanced CW tunable difference-frequency generation near 3.2 \im has been performed by four methods: direct absorption spectroscopy, second-harmonic detection

wavelength modulation spectroscopy, cavity-enhanced

second-harmonic detection wavelength modulation spec- troscopy, and direct absorption spectroscopy with power

stabilization. The spectroscopic DFG source was pumped

with an 800 nm diode laser and a diode-pumped 1064 nm

Nd : YAG laser. It delivered a maximum of 6 nW of nar- rowband infrared light with 40 mW pump power and

230 mW signal power and was tunable from 3076 to 3183 cm-\

With no cryogenic components, we observed a noise

equivalent concentration for the detection of methane in airat 80torrof 12ppb(Hz)~"^usinga 1 m cell and direct absorption spectroscopy with power stabilization. This

corresponds to an absorbance root-mean-square noise of

5.1 X 10~* (Hz)""^. We have observed the methane in natural air at atmospheric pressure, as can be seen from

the baseline trace in Fig. 6. The competing effects of in- creased methane density and pressure broadening compared to 80 torr cancel out so the expected detection limit would be the same. By using an output coupler with higher transmittance,

and using thermoelectrically cooled HgCdTe detectors

with 5 times better noise equivalent power, we expect to be

able to observe a noise equivalent column density of

1.6ppbm(Hz)~"^. Proper spatial mode matching into

the 3.2 |im build-up cavity would yield an effective path

length of 15 m and thus a predicted detection limit of

0.1 ppb(Hz)~ "^. Alternatively, a White cell could also be

used. The choice of build-up cavity or multipass cell would be dictated by application-dependent constraints

such as physical size and sample volume. With either the build-up cavity or a multipass cell stray interference

fringes or other baseline effects may limit the actual per- formance before the predicted 0.1 ppb(Hz)"''^ detection

limit is reached.

Acknowledgements. The authors are grateful to Joe Wells for helping with measurements requiring the use of the carbon monoxide

laser and Tamara Zibrova for the special coatings. The work was

supported in pan by the National Science Foundation, and the Robert A. Welch Foundation.

IN- 192
558

References

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TN-193
Appl. Phys. B 64, 567-572 (1997) Applied

r nySICS B and Optics

© Springer-Verlag 1997

Precise measurement of methane in air using diode-pumped

3.4-|im difference-frequency generation in PPLN

K.P. Petrov' , S. Waltman^, E.J. Dlugokencky\ M. Arbore^ M.M. Fejer^ F.K. Tittel', L.W. Hollberg^

' Rice Quantum Institute. Rice University. Houston, TX 77251-1892. USA

(Fax: +1-713/524-5237. E-mail: fkt@rice.edu) -National Institute of Standards and Technology, Boulder. CO 80303. USA

(Fax: +1-303/497-7845)

^National Oceanic and Atmospheric Administration. Climate Monitoring and Diagnostics Laboratory. Boulder, CO 80303, USA

(Fax: +1-303/497-6975) ^Edward L. Ginzton Laboratory. Stanford University, Stanford. CA 94305-4085. USA

(Fax: +1-415/723-2666)

Received: 2 October 1996

Abstract. Fast, accurate measurement of the methane mixing ratio in natural air samples using a compact solid-state 3.4-|im difference-frequency spectrometer is reported. The

spectrometer employed bulk periodically poled lithium nio- bate (PPLN) pumped by a solitary diode laser at 808 nm and

a diode-pumped monolithic ring Nd:YAG laser at 1064 nm.

and a 300 cm-^ volume multi-pass absorption cell with an 18- m path length. The methane mixing ratio was determined by

comparing the direct optical absorption measured in the sample with that measured in a reference gas at 100 torr and room

temperature. Relative accuracy of better than 1 ppb (parts

in 10^, by mole fraction) was achieved in measurements of

natural air that contained 1700- 1900 ppb methane. The typical measurement time for each sample was 60 seconds. The

accuracy was limited by residual interference fringes in the multi-pass cell that resulted from scattering. Without the use of reference samples, the relative accuracy was 20 ppb; it was

limited by the long-term reproducibility of the spectroscopic

baseline, which was affected by drift in the optical alignment

coupled to changes in the ambient temperature. This work

demonstrates the use of diode-pumped difference-frequency

generation (DFG) in PPLN in a high-precision infrared spectrometer. Compact, room-temperature solid-state gas sensors can be built based on this technology, for accurate real-time measurements of trace gases in the 3-5 )im spectroscopic

region.

PACS: 07.65; 33.00; 42.60; 42.65; 42.80

Precise measurements of the global distribution of trace green- house gases such as CH4, CO2, and N2O provide some of the best-known constraints on their global budgets, i.e. sources to, and removal from, the atmosphere. For example, the NOAA

Climate Monitoring and Diagnostics Laboratory (CMDL) operates a globally distributed network of surface air sampling

sites from which more than 7000 air samples are analyzed for CH4 each year [1]. The current measurement technique, gas chromatography (GC), is robust and precise (with a relative precision of ~ 0.1%), but it is slow, requiring approximately

15 minutes for each measurement. Expansion of the sampling

network at the surface into the vertical, a necessary step to better constrain the global CH4 budget [2], would overwhelm

the current analysis capacity. Infrared laser spectroscopy is a uniquely effective method

for the measurement of trace gas concentrations because it combines high precision, remote sensing capabilities, and fast response. These features can benefit applications in which

many gas samples are analyzed or time-dependent changes in gas concentration are monitored. Several instruments have

been developed based on lead-salt diode lasers that offer detection sensitivities down to 0.05 ppb (parts in 10^, by mole fraction) for several trace species in air at atmospheric or reduced pressure [3-5]. However, lead-salt diode

lasers require cooling to liquid nitrogen temperatures, have

problems with mode jumps and multi-mode operation, and

often require a large monochromator for mode selection,

which in many applications are considerable disadvantages.

The need for cryogenic cooling can potentially be elimi- nated in infrared spectrometers based on InAsSb [6] and

InGaAsSb [7] semiconductor lasers, which have recently seen considerable development. They hold the promise of potential single-frequency operation with output powers in excess

of 1 mW at temperatures that can be reached with Peltier coolers. However, single-frequency, single-spatial-mode lasers are not currently available. An attractive alternative to mid-infrared diode lasers is difference-frequency generation

(DFG). Difference-frequency mixing of Ar+ and dye [8], also dye and Ti:Al203 [9] lasers was effectively used for high-resolution infrared spectroscopy of stable molecules and

short-lived free radicals. Several feasibility tests have re- cently indicated that DFG-based spectrometers pumped by

commercial near-infrared diode lasers can cover most of the spectroscopic fingerprint region from 3 to 18)am. In particular, typical linewidths of less than 50 MHz and output powers

from 0.5 to 30 |iW have been reported for diode-pumped DFG

sources operating near 3|um [10], 4|im [I'l], 5 |am [12], and

9 |am [13]. In these experiments, spectroscopic measurements

of methane and carbon monoxide in natural air have indicated

that detector-limited sensitivity can be achieved, corresponding to minimum detectable column densities of less than 10ppbm(Hz)~'''^. Waveguide DFG sources hold promise for

TN-194
568

higher output powers, but no practical spectroscopic system

has yet been reported.

The purpose of this work was to design and test an all-soHdstate room-temperature IR spectrometer for fast measurement

of atmospheric methane with a precision of < 1 ppb, and

to investigate the long-term stability of its calibration. We

report the operation of such a compact spectrometer, based on quasi-phase-matched DFG at 3.4 ^tm in bulk periodically

poled lithium niobate (PPLN) pumped by a solitary diode laser and a diode-pumped Nd:YAG laser. The spectrometer was

used for measurements of the methane mixing ratio in natural

air samples with < 1 ppb relative accuracy with signal aver- aging time of 60 seconds. This is the first reported application

of PPLN in a high-precision infrared spectrometer.

1 Experimental setup

Figure 1 shows a schematic diagram of the DFG spectrometer used for CH4 measurement from natural air samples.

It employed two compact laser sources: a lOOmW solitary

Fabry-Perot diode laser at 808 nm (pump) and a 500 mW

diode-pumped monolithic ring Nd:YAG laser at 1064 nm

(signal). The single-frequency outputs of these two lasers were mode-matched, combined by a dichroic beamsplitter,

and focused into an uncoated PPLN crystal. The 10 mmby-lOmm crystal was cut from a 0.5-mm-thick wafer of

lithium niobate with a 21|im periodic domain grating fab- ricated by electric field poling [14]. The input facets were

cut 13° relative to the grating lines, making it possible to use effective grating periods between 2 1 |im and 24 |im with

external incidence angles below 35°. This configuration al- lows room-temperature generation of 3-5 p.m radiation by

mixing near-infrared diode lasers with a Nd:YAG laser at

1064 nm while using the largest nonlinear coefficient in lithi- um niobate, ^33 = 27pmV"', for mixing three extraordinarily

polarized waves. Quasi-phase-matched generation of 3.35 \xm

radiation (idler) was achieved by using an effective grat- ing period of 22.2 |j.m, with an external incidence angle of

13.2°. The idler was collimated by an uncoated CaFa lens. With

70 mW of diode power at 808 nm and 500 mW Nd:YAG

power at 1064 nm incident on the uncoated mixing crystal, a maximum of 3.4 |iW idler power was measured. Because

the PPLN crystal was oriented such that the incident beams

propagated at an angle with respect to the grating ^-vector, a walkoff between the idler beam and the incident beams

limited the interaction length to approximately 7 mm. This

phase-velocity walkoff [15] effect, analogous to Poynting

vector walkoff in birefringent materials, could be avoided

by using a 22.2-|im grating period at incidence close to normal.

Approximately 40% of the IR output was deflected by

an uncoated ZnSe wedge and measured at a liquid-nitrogencooled InSb detector. The beam transmitted through the wedge

was focused into a multi-pass absorption cell which provided

an 1 8 m optical path length with 90 passes through the sample volume of 300 cm-^. The cell had a tilted BaF2 window

and a measured optical throughput of 4 1 % which corresponds

to a mirror reflectance of 99.1%. The cell was connected to a rotary pump and a manifold that allowed switching between

two high-pressure aluminum cylinders containing natural air that had been previously calibrated for methane at CMDL.

The pressure in the cell was maintained near lOOtorr, as measured by a capacitive manometer with 0.01 torr resolution and 0.2 torr accuracy. The cell temperature was measured

using a mercury thermometer with 0. 1 °C resolution. After

the cell, the DFG beam was collected by an off-axis parabolBeam Stop

InSb Detector (signal)

Parabolic Mirror

Diode-Pumped

1064nmNd:YAG

Pump, Manifold

Isolator Brewster Galvo

Fig. 1. Schematic diagram of

a compact 3.4 \im spectrometer based on bullc PPLN pumped by two solid-state lasers. The spec- trometer was used to measure the methane mixing ratio in natural

air at 100 torr and room temperature relative to a reference gas to better than 1 ppb in 60 seconds

TN-195
569

ic mirror and focused onto a second liquid-nitrogen-cooled

InSb detector with a 1 x 1 mm^ active area. The detector had a noise-equivalent power (NEP) of 1.7pW(Hz)"'/^ at 3.4 |im.

2 Reduction of interference and noise

In addition to the basic elements described above, several other components were required to improve the output stability and

tuning characteristics of the DFG spectrometer. Initial measurements showed that the linearity of the frequency sweep

of the pump laser was degraded by weak optical feedback

from scattering in the optical isolator. This resulted in dis- tortion of the observed spectral lineshapes and an unstable

baseline profile. To reduce the unwanted distortion, a galvodriven Brewster plate [16] was placed in the diode laser beam

100 torr room air, 10 m path H.O

2988.2 2988.4 2988.6 2988.8 2989.0 2989.2 2989.4 Frequency, cm''

Fig. 2. Survey absorption spectrum of room air near 3.35 jim at 100 torr in a 1 0-m multi-pass cell. The observed transitions belong to water (2988.6 cm"'

and lower) and the P(3) group of methane (2988.8 cm"' and higher). The trace shown is a 1024-sweep average with baseline subtracted. The sweep rate was

100 Hz

absorption signal

dark signal

10 Time, ms

Fig. 3. A single period of a typical waveform seen by the signal InSb detector. A direct-absorption spectrum of an isolated methane line was recorded during

the first 10 ms. Over the next 10 ms, the beam was blocked by the chopper and

the dark voltage was recorded. The average of the dark voltage was subtracted from the entire trace

before the isolator. The Brewster plate was rocked at 5 Hz to scramble the phase of the optical feedback. This did not re- move the feedback, but it did ensure a reproducible baseline

for absorption spectra which were averaged over many scans. We observed alignment-dependent optical interference

fringes in the multi-pass absorption cell. They were caused

by scattering from beam spots in close proximity to the output

window at the center of the front mirror. The smallest magnitude of these fringes was approximately 5 x 10^^ absorption

units. To cancel the fringes, a voice coil was attached to the

cell. The coil was driven by a sine-wave generator tuned to an

acoustic resonance in the cell near 800 Hz. Vibration of the

cell mirrors resulted in an excursion of fringes that was larger than their period. This reduced the magnitude of the interfer- ence in the averaged absorption signal by more than a factor of 10. No evidence of drift in the alignment of the cell mirrors was found during 5 weeks of experiment.

The commercial InSb detector that sampled the DFG power before the multi-pass absorption cell was modified to have

a 77 K quartz filter and an aperture. The dc-coupled detector output was subtracted from a precision voltage reference, and

the filtered error signal was used to control an acousto-optic

modulator placed in the Nd:YAG beam. This servo removed

amplitude modulation associated with frequency scans, beam

offset caused by motion of the Brewster plate, acoustic vibration, and alignment drift. However, since the servo-stabilized output of the monitor detector includes dark voltage, the out- put DFG power still changed as the dark voltage changed

with temperature. Temperature stabilization of the entire sys- tem, including the background seen by the monitor detector,

could improve the power stability. After the wedge beamsplitter, the IR beam path to the first detector was nearly equal to the beam path outside the multi-pass cell to the second detector, making it possible to cancel out absorption by methane

in ambient air. Considering that temporal fluctuations of the methane concentration in room air can easily exceed 10%,

improper cancellation of stray absorption would result in sig- nal errors that are unacceptable in this precision application.

Nitrogen-purging of the spectrometer would further reduce

stray absorption caused by spatial fluctuations of methane

concentration.

3 Control and measurement

The temperature of the Fabry-Perot diode laser was stabi- lized for operation with a center wavelength of 808 nm. Fine

wavelength tuning and scans were performed by modulation

of the laser drive current. The maximum available fine-tuning range of 35 GHz without mode-hops was sufficient for simul- taneous observation of several strong molecular transitions of methane and water (Fig. 2). For absorption measurements,

a tuning range of 7 GHz was adequate to capture a single

methane peak. The DFG signal detected after the multi-pass

absorption cell was low-pass filtered below 10 kHz and digitized by a 16-bit analog-to-digital converter. The frequency

sweep was triggered by a 50 Hz chopper, such that the IR beam

was blocked during retrace of the frequency sweep. This ar- rangement permitted sampling of the signal detector's dark

voltage and the absorption trace during each sweep cycle, as seen in Fig. 3. The 50 Hz sweep rate was chosen to combine

TN-196
Fig. 4. A close-up of an absorption peak (thick solid line) similar to that shown in Fig. 3. The thin solid trace in the middle is the difference between

absorption traces acquired 5 minutes apart. Detector noise can be seen in the

flat part of the trace. The anti-symmetric feature is a result of frequency drift

minimal distortion of the signal by the 10 kHz low-pass filter and reasonably short measurement time. Each measurement consisted of a 3000 sweep av- erage acquired over 60 seconds. An example of such

measurement—a trace of detector voltage versus time—is shown in Fig. 4. The thick solid trace was acquired with the use of cancellation of interference fringes in the multi-pass cell. The thin solid line is the difference between two such traces acquired 5 minutes apart. The preamplifier had a single-pole

low-pass filter with a 3 dB corner frequency of 10 kHz. The

equivelant noise bandwidth of the average of 3000 sweeps was 5.2 Hz. Infrared detector noise measured in this bandwidth corresponds to 8 x lO^^rms absorption which can be

easily observed in the thin trace because of the large dynamic range (16+11 bits) available in the averaged signal. The

peak amplitude was extracted from the absorption trace by

using nonlinear least-squares fitting. Prior to fitting, the re- trace average of the dark voltage was subtracted from the entire

trace. The parameters of the fitting included the peak position, pressure- and Doppler-broadened linewidths AVp and Avj, and

a linear fit to the baseline. Voigt line shape was assumed, and

a rational approximation [17] was used to compute the nor- malized absorption profile. Absorption a was determined by

normalizing the peak amplitude to the value of the fitted baseline taken at the center of the peak. Values of the absorption

for the various calibrated air samples used in the experiment

ranged between 3% and 4%. Corrected for total pressure and

temperature, 7, of each sample, the absorption was assumed

to be proportional to the methane mole fraction in that sample [here V{0;AVp/Avj) is the peak value of the normalized

Voigt function]:

C oc -rin(l-«)V(0;^

Such correction was necessary because the cell temperature was observed to change by more than 1 °C during the experiment, and the fill-to-fill variations in sample pressure were as large as 0.5 torr. The constant of proportionality is omitted in the above formula, since it depends on quantities such as the

line intensity and optical path length - each known to ±2%,

at best. The sample pressure and pressure-broadening coefficient, both known to better than ±0.2%, are included in the above formula in the form of AVp, and their combined effect on

the value of the normalized Voigt function is less than 0.04%.

Initially, an attempt was made to determine the constant of

proportionality in the above formula. With the use of a single

air sample with known methane mixing ratio this should be

possible, and the result could be used to measure CH4 from

other samples. We have found, however, that the day-to-day

reproducibility of the spectroscopic baseline, which depended

on alignment and was strongly coupled to changes in ambient temperature, limited the accuracy of such measurement

to about 1%. This demonstrated that measurements with 1%

absolute accuracy would be possible, and in many cases such

accuracy is more than adequate. However, our specific application required precision of better than 0. 1 %. We have therefore

resorted to using a reference sample before (or after) each un- known sample. This is a somewhat less attractive technique

because it requires an additional gas transfer and roughly doubles the measurement time. In some applications, however,

this is acceptable and could be used to verify whether the in- strument is working properly. It is important to point out that

this technique does not solve the problem of baseline drift;

it only makes the drift insignificant on the time scale of an

individual measurement.

4 Performance testing and results

The performance of the DFG spectrometer was tested by using

four high-pressure aluminum cylinders filled with dry air, as supplied by NOAA CMDL. All four cylinders had been

calibrated for methane at CMDL via gas chromatography.

The precision of the measurements was typically better than

1 ppb, and methane mole fractions were assigned relative to the CMDL methane scale [1]. The testing was performed in two parts. In the first part, two cylinders (identification numbers 305 1 6 and 37057 ) were supplied with their methane mole

fractions. The second part was blind; the two authors performing the spectroscopic measurements (KPP and SW) were not

told the methane mole fractions in the two other cylinders

(64040 and 30482).

The methane mole fractions assigned to the cylinders

used in the first test were 1775.3 ±0.1 ppb for cylinder

30516 and 1 896.7 ± 1.3 ppb for cylinder 37057. Air samples from each cylinder were analyzed continuously for 5 minutes, with a 15 minute pause between the samples. The

pause was made to completely evacuate the multi-pass cell and to let the newly injected sample reach thermal equilibrium with the cell. These measurements were performed

without cancellation of fringes in the cell. Figure 5 shows

the measured absorption by methane as a function of time. The sample temperature of 25.0 ±0.1 °C though not actively stabilized, was not observed to change in this test. When

corrected for differences in the sample pressure as explained

above, the ratio of methane mole fractions is found to be

1.0681 ±0.0015, versus 1 .0684 ± 0.0007 as calculated from

the gas chromatograph data. As suspected, the primary source of large deviations among individual measurements is inter- ference fringes in the multi-pass absorption cell. Although

weak, they still produced baseline features clearly distin- guishable from detector noise, and they affected the precision

TN-197
571

with which the fitting parameters were determined. Since no

changes in the ambient temperature were observed during this

test, the measurements were not affected by drift in optical

alignment.

!n the subsequent blind tests, cylinders 30482 and 64040

were analyzed. Cancellation of interference fringes in the multi-pass cell was used this time, as the need for it had

been clearly realized. Measurements of optical absorption

in cylinder 30482 relative to cylinder 30516 (reference)

gave a methane mixing ratio of 1781.1 ±0.8 ppb after cor- rection for pressure and temperature (Fig. 6). The CH4

mixing ratio assigned to that cylinder by CMDL was

178 1.9 ±0.9 ppb. A summary of data obtained for all samples analyzed in the experiment is given in Table 1. Since

Table 1. Summary of methane mixing ratios measured using the 3.4 |im DFG

spectrometer Four samples were available in the experiment, and one of them

(30516) was used as a reference in all measurements. The methane mixing

ratio in this sample was assumed to be known exactly. Standard deviation shown for the DFG data therefore only includes errors of measurement of

absorption, temperature, and pressure. Sample 37057 was measured without

cancellation of interference in the multi-pass cell, hence the large error bar

cylinder CDML CH4 standard 3.4 urn DFG standard

identification assignment deviation measurement deviation number (ppb) (ppb) (ppb) (ppb)

64040 1753.8 0.2 1754.3 0.8 30516 1775.3 0.1 used as areference n/a 30482 1781.9 0.9 1781.1 0.8 37057 1896.7 1.3 1896.2 3.0

3.9

c

.0a.o 3.7

10 <

3.6

1896.7 ppb

- I - T- -i

1775.3 ppb

2 4 6 V ^g 20 22 24 Time, min

Fig. 5. Peak absorption by CH4 versus time, measured for two air samples pre- viously calibrated for methane (indicated on the plot). The measured ratio of mole fractions is 1 .068 1 ± 0.00 1 5, after correction for differences in pressure. This can be compared with the ratio of 1 .0684 ± 0.0007. determined from the CH4 mole fractions assigned to the samples. Cancellation of interference was

not used in this data, hence the large error bar

1

Jj 3.605

XI<

1

" - _.

1775.3 ppb

5 10 15 20 25 30 Time, min

Fig. 6. Peak absorption by CH4 versus time for air from two high-pressure

cylinders. The 10 measurements plotted on the lower left from cylinder 30516

(with a CH4 mole fraction of 1775.3 ppb assigned by CMDL) were used as a reference. The 10 measurements in the upper right were for cylinder 30482

which was analyzed as an unknown. The spectroscopic result for the unknown

was 1781.1 ±0.8 ppb: this compares well with the value of 178 1.9 ±0.9 ppb

assigned by CMDL

cylinder 30516 was used as a reference in all measurements, its methane mixing ratio of 1775.3 ppb was assumed

to be known exactly. Therefore the uncertainty in the mixing ratio determined by CMDL is not included in the

errors given for spectroscopic measurements. The errors quoted in Table 1 represent instead the combined uncertainties in the measured optical absorption, temperature, and

pressure. The data suggest that the combined uncertainty of the spectroscopic measurements over 1 minute is less than

1 ppb for a typical ambient methane mixing ratio of

1700- 1 900 ppb. This is equivalent to about 0.06% rms

relative accuracy. Taking into account the conditions of our experiment (18 m path length, 5.2 Hz bandwidth) we

estimate the noise-equivalent methane column density of

6.3ppbm(Hz)-'/2.

5 Summary

We have demonstrated a precise spectroscopic application of

diode-pumped difference-frequency generation. A compact

3.4-fim spectrometer employed a 1 -cm-long PPLN crystal

with a 2 1 -)im domain grating period, pumped by two compact

solid-state lasers: a 100-mW solitary laser diode at 808 nm

(pump), and a diode-pumped monolithic ring Nd:YAG laser

at 1064.5 nm (signal). With a maximum total output power of

3.4 |iW at 3.4 |im, the DFG source of the spectrometer per- formed continuous frequency scans of more than 35 GHz,

and could be tuned over more than 60 cm"' by scanning

the temperature the pump laser. The use of a galvo-driven Brewster plate allowed compensation of feedback distortion of the frequency sweep. Sampling and servo control of the output power allowed cancellation of the amplitude modulation and noise due to frequency sweep, acoustic noise,

and alignment drift. The spectrometer employed a compact

18 m multi-pass cell which had an optical throughput of

41%.

The measurements were made relative to the CMDL stan- dard methane scale. With a measurement time of 60 seconds,

direct-absorption spectroscopy of methane in natural air samples was performed, and the methane mixing ratios were

determined with a precision of better than I ppb. The pre- cision was limited by residual interference fringes in the multi-pass cell. The peak-to-peak magnitude of the fringes

corresponds to a signal-to-noise ratio of 510 for the measTN-198
572

ured optical absorption of ~ 3.5%. Without a reference

gas, the relative accuracy of 20ppb was limited by the long-term stability and reproducibility of the spectroscopic baseline. The baseline profile depended on the optical

alignment, which drifted following changes in the ambient

temperature.

This precision spectrometer can benefit applications

where many similar gas samples are analyzed. In trace- gas-monitoring applications that require fast measurements

with an accuracy of down to 1%, such a spectrometer can employ room-temperature InAs infrared detectors and operate without reference samples. Diode-pumped DFG in PPLN can effectively replace lead-salt diode lasers and

gas lasers in spectroscopic applications requiring low-noise,

single-frequency sources that are continuously tunable in the 3-5 |im region, and eliminate the need for cryogenic

cooling.

Acknowledgements. The authors are grateful to Charlie Hultgren of New Focus, Inc. and Richard Fox at NIST Boulder for helpful discussions. The work

was supported in part by the NOAA Climate Monitoring and Diagnostics Laboratory, the National Aeronautics and Space Administration, the Advanced

Research Projects Agency through the Center for Nonlinear Optical Materials

at Stanford University, the Joint Services Electronics Program, the National Science Foundation, the Texas Advanced Technology Program, and the Robert A. Welch Foundation.

References

E.J. Dlugokencky, L.P. Steele, P.M. Lang, K.A. Masarie: J. Geophys.

Res. 99, 17021 (1994) L Fung, J. John, J. Lemer, E. Matthews, M. Prather, L.P. Steele,

P.J. Eraser; J. Geophys. Res. 96, 13033 (1991)

J. Reid, M. El-Sherbiny, B.K. Garside. E.A. Balik: Appl. Opt. 19. 3349

(1980) C.R. Webster, R.D. May, C.A. Trimble, R.G. Chave. J. Kendall: Appl.

Opt. 33,454(1994)

M.S. Zahniser, D.D. Nelson, J.B. McManus, PL. Kebabian: Phil. Trans.

R. Soc. Lond. A 351, 371 (1995)

A. Popov, B. Scheumann, R. Miicke, A. Baranov, V. Sherstnev,

Y. Yakovlev, P Werle: Infrared Physics and Technology 37, 1 17 (1996) D.Z. Garbuzov. R.U. Martinelli. R.J. Menna, PK. York, H. Lee, S.Y Narayan, J.C. Connolly: Appl. Phys. Lett. 67, 1346 (1995)

A.S. Pine: J. Opt. Soc. Am. 66, 97 (1976) C.E. Miller, W.C. Eckhoff, R.R Curl: J. Mol. Struct. 352, 435 (1995) K.P Petrov, S. Waltman. U. Simon, R.E Curl, EK. Tittel. E.J. Dlugokencky, L. Hollberg: Appl. Phys. B 61, 553 (1995)

A. Balakrishnan, S. Sanders, S. DeMars, J. Webjom. D.W. Nam,

R.J. Lang, D.G. Mehuys, R.G. Waarts, D.E Welch: Opt. Lett. 21. 952

(1996) K.P Petrov, L. Goldberg, W.K. Bums, R.E Curl, EK. Tittel: Opt. Len. 21,86(1996) K.P Petrov, L.Goldberg, R.E Curl. EK. Tittel: Opt. Lett. 21, 1451 (1996) L.E.Myers, R.C. Eckardt, M.M. Eejer, R.L. Byer, W.S. Bosenberg,

J.W. Pierce: J. Opt. Soc. Am. B 12. 2102 ( 1995) M.M. Eejer, G.A. Magel, D.H. Jundt, R.L. Byer: IEEE J. Quan. Elec. 28,2631 (1992) C.R. Webster: J. Opt. Soc. Am. B 2. 1464 (1985)

J. Humlicek: J. Quant. Spectrosc. Radiat. Transfer 21. 309 (1979)

TN-199
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. D15, PAGES 21,023-21,031, SEPTEMBER 20, 1996

Reactive uptake of NO3 on pure water and ionic solutions

Yinon Rudich, Ranajit K. Talukdarl and A. R. Ravishankaral'2

Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado

R. W. Fox

Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado

Abstract. The reactive uptake coefficients (y) of NO3 onto pure water and dilute solutions of

NaCl, NaBr, and NaNOz were measured using a wetted-wall flow-tube setup combined with a long-path absorption cell for the detection of NO3. The measured y values were in the range

1 .5x10"^ - 6xl0"\ depending on the salt concentration in the water. By measuring y as a function

of sah concentration, HD°^ for NO3 in water was determined to be (1 .9±0.4)xl0"^ M atm"' cm

s"°^ at 273 K, assuming that the rate coefficient for the reaction of NO3 with CI' is 2.76x10* Af

s"' at 273 K. The Henry's law coefficient for NO3 in water is estimated to be 0.6±0.3 M atm"', assuming that the diffusion coefficient of NO3 in water is D, = (1.0+0.5)xlO"^ cm^ s"'. Uptake of

NO3 on pure water is interpreted as due to reaction of N03(aq) with HjOf^) to produce HNO3 and

OH in the liquid phase. Implications of these findings to the chemistry of NO3 in the troposphere

are also discussed.

Introduction

The NO3 radical is a major tropospheric nighttime oxidant and

its gas phase reactions are important loss pathways for many

compounds during the night [Atkinson, 1991; Wayne et al,

1991]. NO3 can also be important in initiating radical reactions within cloud droplets [Chameides, 1986a,b; Lelieveld and

Crutzen, 1991; Mozurkewich, 1986] and in aerosols {Pederson,

1995]. NO3 scavenging by wet aerosols may explain the short

lifetime of NO3 that was observed in the troposphere [Heikes and

Thompson, 1983; Mihelcic et al, 1993; Noxon, 1983], especially

during episodes of high humidity and fog [Piatt et al, 1981,1984].

Odd nitrogen species such as NO and NO2 have limited

solubility in liquid water [DeMore et al, 1994]. Thus the main

removal pathways of NG^ species from the atmosphere are believed to be via the formation of HNO3, which is removed by

both dry and wet deposition. HNO3 is formed in the atmosphere

either by the gas phase reaction of OH with NO2 or heterogeneous hydrolysis of N2O5. Since the NO^ family plays very important roles in various reaction cycles in the atmosphere,

the removal pathways for the members of this family from the atmosphere needs to be well known. The NO3 radical, which is formed by reaction of NO2 and ozone, may also provide a removal pathway of NOx from the atmosphere through its gas phase and heterogeneous loss processes. The uptake of a compound into a liquid is determined by

diffusion, its solubility and its liquid phase reactions [Danckwerts, 1951; Hanson et al, 1994; Schwartz, 1986]. To

model the heterogeneous chemistry of NO3 accurately, properties

'Ako at the Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder.

*Also at the Department of Chemistry and Biochemistry, University of

Colorado, Boulder.

Copyright 1996 by the American Geophysical Union.

Paper number 96JD01844.

1 48-0227/96/96JD-0 1 844$09.00

such as Henry's law coefficient (H) and the reactive uptake

coefficients (y) must be known accurately. In previous studies, H

for NO3 was estimated to be between 3x10" and 2x10' M atm"' [Chameides, \9S6a,h; Jacob, \9S6; Lelieveld and Crutzen, 1991; Mozurkewich, 1986]. To our knowledge, the only experimentally determined value of H, the Henry's law coefficient for NO3, H=

1.8±1.5 Af atm"' is that reported in the thesis of Thomas [1992]. To understand the nighttime processing of NO3 in the troposphere and its impact on cloud and fog chemistry, we have

undertaken the studies of its uptake on pure water and on some

representative ionic solutions relevant to the marine troposphere and to cloud droplets. In this paper we report measurements of

the uptake coefficients of NO3 by water and by aqueous solutions of NaCl, NaBr, and NaN02. From these measurements we also determine HD°^ for NO3 in water and discuss the atmospheric

implications of these results.

Experimental and Data Analysis

Setup

Uptake of NO3 by distilled water (pH~7) and by NaCl (0.01-

0.5 Af), NaN02 (0.0005-0.0038 M), and NaBr (0.001-0.01 M)

solutions was measured. The experimental setup was an

adaptation of the one described by Utter et al [1992], and only

details specific to the current experiment are described here. It consisted of a vertical wetted-wall flow tube, a movable injector

through which NO3 is introduced, a long path absorption cell, and a stabilized diode laser system. A schematic diagram of the apparatus is shown in Figure I. The reactor was 85 cm long with

an internal diameter of 1.9 cm. The first 60-cm section enabled

thermal and water vapor equilibration between the gas flow and

the liquid film. The uptake coefficients were measured in the lowest 25-cm section of the flow tube, where the injector could move up to 18 cm. About 5 L of liquid were stored in a 12-L

bulb above the system and the rate of flow through the reactor was controlled using a Teflon needle valve. The liquid was

continuously pumped back to the reservoir by a Teflon gear pump.
21,024 RUDICH ET AL.; UPTAKE COEFFICIENTS FOR NO,

N^PslMa mlxtur* T-400K N205->N03+N02

Movabia Injector •

cooling jackat -

liquid

White cell: 42 passes, 12.6 meters

optical path

b.

Figure 1. A schematic diagram of the experimental apparatus.

The NO3 radical was generated by thermal dissociation of N2O5 in an oven mounted on top of the injector and maintained

at a constant temperature of 400 K. High purity He was passed

through an N2O5 trap, which was icept at -220 K, to generate a mixture of N2O5 in He. This mixture was flowed to the oven via Teflon tubing. NO3 concentrations of 2x10"" - 1x10'^ cm'^ were used. The concentration of NO3 coming out of the wetted-wall

reactor was determined as a fiinction of exposure time to the Hquid surface by measuring the attenuation of light at 662 nm,

from a diode laser, in a long-path absorption ceil [White, 1942;

1976]. The cell was covered with a glass jacket with an inner diameter of 2.3 cm and a total volume of about 130 cm^ The

dielectric coated mirrors had a reflectance of >99% between 450

and 700 nm. The distance between the mirrors of the cell was 30

cm. The beam was multipassed, 42 times, to get a total path

length of 12.6 m. The temperature and current of the diode laser were adjusted

to give single-mode operation near 662 nm, the peak of the NO3

absorption [Wayne et ai, 1991]. An optical fiber was used to spatially filter and relay the beam to the White cell. To minimize

optical feedback-induced amplitude noise, the fiber ends were

polished at an 8° angle, and an optical isolator was used. Approximately 60% of the laser power (~4 mW total power) was

coupled into the fiber by using a spherical lens, an anamorphic

prism pair, and a telescope (x3), in addition to the collimating and focusing objectives. At the fiber output, approximately 50% of the power was

directed to a photodiode for an amplitude stabilization servo. A

stable offset current was subtracted from the photocurrent to provide an error signal, and then fed back to the laser's injection current with a bandwidth of 100 kHz. The offset current was

derived from a stable, well-filtered voltage reference and a

precision low temperature-coefficient resistor. The remaining

laser power was mode-matched to the waist of the White cell, and the cell output directed to a photodiode.

The fiber caused the beam polarization to vary slightly with

temperature and acoustic noise, which resulted in amplitude

noise on the signal photocurrent due to the polarization

sensitivity of the optics. This noise was minimized by using a

polarizer immediately after the collimated fiber output but before sampling the beam for the servo. The laser's wavelength was tuned to the NO3 absorption line using a diode array spectrometer and a Neon lamp as a wavelength reference. The correction current for the amplitude

stabilization (<0.1 mA) did not significantly change the wavelength. The laser's mode structure and wavelength were

periodically checked with an optical multichannel analyzer.

The output of the detector was averaged for 3 s and read by a

digital voltmeter; the voltmeter signal was monitored by a computer for further analysis. The stability of the detection system was about 8x 1 0"', limited by vibrations of the multipass

cell or optical feedback to the laser. This corresponds to a

sensitivity of ~5xl0' molecules cm^ using ct(662 nm) =2x10"'^ cm^ [Wayne etal., 1991]. Water vapor (~4.5 torr in these experiments) absorbs 662 nm

light. Therefore to obtain /q, the light level in the absence of NO3, NO was added to the gas flow at the entrance to the cell to completely convert NO3 to NO2. Such /q values were measured

for each injector position before and after taking a reading with NO3.

All experiments were performed at 273±1 K and at a total pressure of 9 - 14 torr. Typical liquid flow rates were 2-3 cm-* s'', implying a Reynold's number of -80 and liquid flow velocities of -10-15 cm s''. Typical liquid film thickness was calculated to be

about 0.025 cm. Care was taken to minimize ripples on the water

film by controlling the liquid flow rate, and maintaining constant wetting of the wall. Flow velocities of the gas were typically

-1000 cm s' but were varied from 650 to 1600 cm s''. A flow

velocity of -1000 cm s'' corresponds to a Reynold's number of

-100. The liquid solutions were bubbled with He for at least 15 hours to remove dissolved N2 and O2. Removal of these dissolved gases helped maintain constant unperturbed liquid flow and minimize possible reactive uptake of NO3 by Ol . To

maintain a well-defined temperature in the flowing liquid and to avoid rapid evaporation of the film, we added water vapor from a

saturator to the main He flow. The temperature of the gas, as well of as the liquid film, were measured in several of the runs and foundtobe273±l K. Ozone was prepared by a commercial ozone generator using

high purity (>99.995%) oxygen, which was passed through a molecular sieve trap at 195 K to remove water. N2O5 was

synthesized by the reaction of ozone with NO2. The ozone/02

mixture from the ozone generator was mixed with NO2 which was formed in situ by the reaction of O2 with pure NO. The gases were mixed in a 50 cm long, 3.8 cm inner-diameter reactor at a

pressure of 800 torr and the resulting gas mixture was passed

through a trap at dry ice temperature to collect N2O5. High purity

He (>99.9995%) and chemically pure (ASC reagent grade,

>99%) salts were used throughout the experiments.

Data Analysis

The uptake coefficients of NO3 were calculated from the measured first-order rate coefficients for the loss of NO3 from the gas phase, k^ The loss of NO3 from the gas phase is described by

TN-201
RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO3 21,025

[NO,l^=[NO,l^exp(-k„z/c) (1)

where [NOsJzi and [N03]z2 are the NO3 concentrations at injector

positions Z] and Z2, with z=Z2-Zi and c is the gas flow velocity. A

plot of ln[N03] versus relative injector position (z) yielded a

straight line with a slope of -kjc. Then k^ was corrected for the

radial concentration gradient generated by the uptake of NO3 into the liquid, using the method developed by Brown [Brown, 1978; Hanson etai, 1992]. To determine the true wall loss rate coefficient, kf^'^ , the gas phase diffusion coefficients of NO3 in He and H2O are needed. Since these diffusion coefficients were not measured before, they were calculated [Mason and Monchick, 1962; Monchick and

Mason, 1961] using estimated Lennard-Jones parameters for NO3

((j=3.77 A, e/A:=395 K [Patrick and Golden, 1983]) to be 100 and 370 torr cm^ s'', respectively. Variation of zlK, the well

depth, by a factor of 2 changed the diffusion coefficients by only

10%. The calculated diffusion coefficient of NO3 was between

13 and 17 cm^ s"' under our experimental conditions (4.5 torr H2O, 5-10 torr He). In addition to calculating them, we measured

the pressure-independent diffusion coefficients of NO3 in He and

water vapor under our experimental conditions (K Rudich et al.. Uptake of NO3 on KI Solutions: Rate Coefficient for the NO3 +

I" Reaction and Gas-Phase Diffusion Coefficients for NO3,

Submitted to Chemical Physics Letters, 1996). The calculated values agreed very well with the measurements. The reactive uptake coefficient y was calculated from the corrected first-order rate coefficient, kF%^ , using the relation for a cylindrical reactor [Howard, 1979]

Y = 2 r k^"^"- /(o (2)

where co is the average molecular speed of NO3 and r is the flow

tube radius. Here, A:„ was measured 10-25 times for each salt concentration, while varying pressure and liquid flow velocities. Such measurements were repeated at various salt concentrations. The relationship between y and reactive loss in the aqueous phase

is given by (e.g., Hanson et al. 1992)

1 1 0) Y a 4RTH^y[i^

(3)

where a is the mass accommodation coefficient, H is Henry's law

coefficient (M atm"'), T is the temperature (K), R is the gas

constant (L atm mol"' K''), and k^ is the first-order loss rate coefficient of NO3 due to reaction in the aqueous phase {£), that

is, k^ = l^^x [salt]x/ (yt^' is the second-order rate coefficient for reaction of NO3 with the salt in the aqueous phase, and / is the

activity coefficient of the reactive ion in the sah solution). D( is the diffusion coefficient of NO3 in liquid water (cm^ s''). In cases where multiple reactions can simultaneously take place in the aqueous phase, equation (3) should be modified to include all reactive channels: 1=1

y « 4RmVa^ (4)

In equation (4) kf/ is the first-order loss rate coefficient for reaction of NO3 with species Ri in the aqueous phase {£), i.e., k,j=kj^\Ri]xfi (A:," is the second-order rate coefficient for reaction of NO3 with species i in the aqueous phase). The

summation is over all the reactants. In cases where the uptake is not limited by mass accommodation, i.e., y«a, equation (4) reduces to

(5)

When NO3 was lost by more than one reaction, y was

measured as a function of the concentration of one reactant /, while the concentrations of the other j reactants were held

constant. Under these conditions,

n2 r'=H'D,

ART

ILKj+H'D,

ART

(6)

a plot of measured y2 versus [(4^7') /«] kft=\{ART) I aXk" [X,]

yields \^^Df as the slope and H^/)J(4^r)/«] Y,^fj as the

j intercept. For this analysis, k" must be known.

Results and Discussion

First-order decay plots of NO3 for a few NaCl concentrations and pure water are shown in Figure 2. From such plots, y for that

set of conditions was calculated. The measured uptake

coefficients of NO3 on water and NaCl, NaBr, and NaN02

solutions are given in Table 1 . The error bars in Figure 2 are the standard deviation of the mean of 10 - 25 measurements of y for each salt concentration.

Determination of HZ>, and Measurements of Liquid Phase

Rate Coefficients To extract HD^^ for NO3 in water from reactive uptake

coefficients measurements, at least one aqueous phase rate constant (A:") has to be known. The reaction of NO3 with CI"

(Rl) N03(aq) + Cl-(aq)

-^

N03-(aq) + Cl(aq)

has been previously studied by Exner et al. [1992] as a function of temperature and by Neta and Huie [1986] and Kim and Hamill

[1976] at 298 K. The values of*, at 298 K reported by Neta and Huie and by Kim and Hamill are 7-10 times higher than the value reported by Exner et al. This difference was attributed to the effect of high ionic strength of the NaN03 solutions used in the pulsed radiolysis studies [Exner et al., 1992]. Therefore, we

used the rate coefficient, k^{T) = (1.9+0.2)xl0" exp[-

(4300±500)/7] M"' s"', measured by Exner et al. at low ionic strength for the analysis of our results. A loss of NO3 on water was observed even in the absence of NaCl. This observation points to a possibility that NO3 is lost due

to reaction with the water. To account for this additional loss, we

used equation (6) to extract HD/^

•e

(0

10 15 Injector position (cm)

20

Figure 2. Plots of NO3 concentrations as a fiinction of exposure

to pure water and solutions of NaCl: squares, pure water;

triangles, 0.1 A/NaCl; circles, 0.5 MNaCl.

TN-202
21,026 RUDICH ET AL.; UPTAKE COEFFICIENTS FOR NO,

Table 1. Measured Values of y Over Various Ionic Solutions Along With Experimental Parameters

[salt] Activity* Total pressure. Flow Velocities, 7x10^ " M (Atsalt]) torr cms"'

H20 0.000 0.0000 10.0-16.2 580-1000 0.20 ±0.10

NaCl 0.0087 0.0079 11.8-14.0 640-1020 0,78 + 0.12 0.0096 0.0087 12.0-14.75 700-960 0.85 ±0.12

0.0101 0.0091 11.5-14.5 620-860 1.14±0.12

0.0123 0.0111 10.2-14.7 730-1500 0.67 ±0.20

0.0150 0.0136 8.1-10.3 860-1500 1.39 ±0.25

0.0506 0.0458 10.4-14.6 650-1000 1.98 ±0.28

0.0790 0.0717 12.2-13.0 920-1100 0.21 ±0.06

0.100 0.0904 7.2-12.8 500-1380 2.73 ± 0.40 0.2090 0.1890 11.6-13.3 920-1180 3.01 ±0.53

0.2620 0.2370 9.2-13.8 730-1300 4.21 ±0.53

0.5000 0.4520 6.6-9.1 830-1870 4.70 ± 0.65 0.5000 0.4520 11.5-13.0 910-1050 6.00 ±1.50

NaNOa 0.0005 0.0005 10.5-14.5

• 620-1000 1.74 ±0.20

0.0010 0.0010 11.3-13.5 660-950 2.75 ±0.53

0.0010.0010 11.0-13.5 690-960 2.61 ±0.52

0.0038 0.0037 10.1-12.5 730-1050 4.6 ±1.2

NaBr 0.0010 0.0010 10.6-13.8 520-800 1.56 ±0.26

0.0040 0.0037 11.1-13.6 700-800 3.22 ±0.22

0.0083 0.0076 10.7-12.6 790-1330 5.32 ±0.58

0.0100 0.0090 11.7-13.1 660-780 5.5 ±1.3

"Here / is the activity coefficient of ions in the solution. "The quoted errors are 2a in the standard deviation of the mean

of many measurements and do not include any systematic error. Precision of each measurement is much smaller.

r' = ART

\^D\kf,{H,0\ + kANaCl\^f\ (7)

where ^4[H20] is the first-order loss rate coefficient of NO3 in the liquid phase due to its reaction with water. Figure 3 shows a

plot of f versus [{4,RT)l(iifH^Df[k^[H20]+k^[NaCl\^J], where

*,=2.76x 10* A^'s-' at 273 K [Exner et ai, 1992]. By fitting these data to a straight line, we obtain HZ>»,°^ =(1.9±0.4)xl0-' M atm' cm s'*'^ for NO3 in water. Taking the value of D, for NO3 in water to be D/ = (1.0±0.5)xlO-' cm^ s"', we obtain H=0.6±0.3 M

atm'. Using our measured value of H£>,° ', we can extract the rate coefficients of other aqueous phase reactions, such as the

reactions of NO3 with NO2' and Br' by measuring y as a function of their concentration in water. The rate coefficients for the

reactions (R2) N03(a^ + Bt\^ -^^ NO3

and

J-i(»ad +Br(^

4.0x1&<

2.0x10-5-

(R3) N03(.^ + N02-(.^-^ NO3-(«0 + N02(.q)

(4RT/co)2kii[satt]

Figures. A plot of y^ versus (4/Jr/aj)^(t^[saItlx/) for water,

NaCl, NaBr, and NaN02. The solid line is a weighted fit of the NaCl data, and from the slope we calculate HD°^ =

(1.9±0.4)xl0-^ A/ atm' cm s^^^

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RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO, 21,027

have not been measured under experimental conditions that are applicable to ours [Daniels, 1969; Neta and Huie, 1986]. The

measured y of NO3 on Br' and N02' solutions were fitted to equation (6) using the HD°^ value obtained above to extract ki and kj. The derived values for ^2 and ^3 are used in Figure 3, where -f values for NaBr and NaN02 solutions are plotted

against [4^7yco]^k^i (where i can be either 2 or 3). Since we have measured ^2 and k^ relative to ^i, the ratios ^2/^1 and k^/k^ are more accurate than the absolute values. We report k2/k]=31±4 and kilk]=()l±l, for dilute NaBr and NaN02 solutions, at /7H~6

and 273±1 K. The majority of the experiments discussed here were obtained by using solutions which were bubbled with He to remove

dissolved oxygen. To simulate conditions relevant to the atmosphere, some experiments were carried out with water

saturated with O2. No differences in the measured uptake

coefficients were observed in these experiments. The effect of

ionic strength and dissolved oxygen on these measurements will be discussed in a separate publication (T. Imamura et al., manuscript in preparation, 1996).

Uptake of NO3 on Pure Water

A value of y = (l.Otd? 0)xlO"^ was measured for the uptake of NO3 by pure water. The first-order decays for NO3 on pure water were exponential (see Figure 2) and did not show effects of

saturation. Using HZ?^"^ that was obtained from the measured

uptake coefficients, saturation is expected to occur within [Hanson et al, 1992] less than 100 ps, given by

AHRT D,<\QOps (8)

(assuming a=l). This time is much smaller than the contact time between NO3 and the water-film in our experiments (18-26 ms). Hence the observed uptake of NO3 on pure water implies that a

reactive loss is taking place. The reaction of NO3 with OH'

(Jt(273 K) = 4x10^ Af's'' [Exner et al., 1992]) cannot account for the observed uptake of NO3 in pure water at pH of ~7. Further, the measured uptake coefficient onto water did not change when

the pW was ~6 or even ~5. In addition, we have used ion- chromatography to analyze the water sample for possible presence of other reactive ions prior to the uptake measurements. The analysis revealed that none of the ions present in the water were in concentrations that could lead to the measured loss rate of NO3. After exposure to NO3, N03' ions were detected in the

water. However, since N2O5 is also present in our gas flow and is efficiently taken up by water, we cannot attribute the presence of

the nitrate ion as solely due to uptake of NO3.

The gas phase loss of NO3 due to the reaction NO3 + NO2 + M ^'"^

) N2O5 + M ,

followed by rapid uptake of N2O5 into the liquid can potentially contribute to the measured loss rate coefficient of NO3 in the absence of reactants in the water. We measured Arec under our

experimental conditions by adding known amounts of NO2

([N02]=2. 5-27x10'^ cm"^) to the gas flow and by measuring the enhancement in the rate constant for the loss of NO3 (see Figure

4). The slope of a plot of the measured loss rate constant as a

function of [NO2] resulted in k^^ = (3.0±0.2)xl0-'^ cm^

molecule'' s"' (where the error is Ict due to precision of the measurements), corresponding to a loss rate constant of less than

0.5 s'' under most of our experimental conditions. The loss of NO3 due to recombination with NO2 is negligible compared to the measured loss of NO3. The intercept of the plot did not

tn_ n ' j^ c /^ii ^

TO Jo 8-

-TIL/^» /T^ -' - ^ T 1

0) Ty^

\ re tb/^' ' Linin 4-

(U 0Cl

(/) u. L. 0- 1 1 '

• I '

1 1X1013 2x1013 3x1013 [NO2] (cm-3)

Figure 4. First-order rate coefficients of NO3 in the presence of

excess NO2.. The initial concentration of NO3 in this experiment were 1.3x10'^ cm'^ while [NO2] ranged between 4.6x10'^ and

2.6x10'^ cm'^. The slope of this line is the second-order rate coefficient for the recombination of NO3 with NO2,

Arec=(3.0+0.2)xl0"'' cm"^ molecule'' s'', where the error bars denote only precision. The intercept corresponds to uptake of NO3 on pure water, 7=1.2x10"^. This intercept did not change upon changing [NO3] by a factor of 2.

change when the gas phase concentration of NO3 was 2 times

higher. This further indicates that there were no major loss processes other than the reactive loss on the water film and that NO2 concentrations in the gas flow were comparable to that of

NO3. Finally, a plot of the measured loss rate constants versus [NO3] resulted in a similar values of k^^. Therefore we suggest that the observed value of y measured

with pure water is caused by reactive uptake of NO3 due to the

reaction of N03(aq) with water:

(R4) N03(a<,) + H20(A # HN03(a<,) + 0H(.q) k

Based on kinetic and thermodynamic properties of the forward and reverse reactions (see the appendix), we estimate the rate coefficient kf^ to be about 6 Af's'' at 298 K and 1.5 Af's'' at 273

K. In principle, it should be possible to extract ^4 from the

intercept of Figure 3. However, since ^4[H20] is very small compared to the uncertainties in some of the measured y values, there is a very large error associated with the value of the

intercept. For that reason, we use the values actually measured

for y to extract ^4 . The measured value of y in our experiments

corresponds to ^4 » 23!|3 Af' s"' and is different from the value

calculated from thermodynamic properties. This discrepancy may

result either from errors associated with the thermodynamic

parameters that we used or by another, unknown, loss process

that occurs either in the gas phase or in the liquid. It should be

noted that a change of «750 cal/mol in AG° for reaction (R4) can

account for the observed difference. Our interpretation that the y measured on pure water is due to reaction (R4), critically depends on the rate coefficient for the

reaction of NO3 with liquid water. Jiang et al. [1992] reported

the rate coefficients of ^4 and A^4 to be 5.3x10' and 5.3x10^ Af'

s'', respectively, while our measured y values on liquid H2O

suggest ^4 to be ^4 « 23!^° Af' s'' at 273 K. It appears that the value of kf^ quoted by Jiang et al. is too high. Katsamura et al. [1991] measured A:;.4=<1.4±0.1)xl0* Af' s''. Using this value of

krA and the AG° for reaction (R4) calculated in the appendix, we

TN-204
21,028 RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO3

obtain a value of *^ of 6 A/' s' at 298 K. The redox potential for NO3 calculated using our estimated AG/ for NOj(,q) and AG/ for N03"(aq) 'S 2.38 V, which is in excellent agreement with the value calculated by Berdnikov and Bazhin [1970] of 2.3±0.1 V. This value is lower than the value of 2.67 V, which was

calculated by Jiang et al. [1992], based on what we believe is an erroneous value for k^. Finally, the value of ^4=(1.4±0.1)xl0*

Af ' s' reported by Katsamura et al. [1991] and used by us is consistent with the rate coefficient for the high pressure hmit of

the OH + HNO3 reaction in the gas phase [DeMore et al., 1994].

Possible Sources of Error The major sources of uncertainty in these experiments are the fluctuations in the water vapor pressure in the flow tube and

ripples on the liquid film. The water vapor pressure in the flow

tube influences the NO3 gas phase diffusion coefficient and the gas flow velocity [Hanson et al., 1992; Utter et al., 1992]. Ripples on the water film may also introduce an error in the measured y due to enhanced transport of NO3 caused by. eddies near the wall. The effect of ripples is discussed by Hanson et al. [1992]. To minimize these uncertainties, slow liquid flows

(Reynold's number of -80) and almost laminar gas flows

(Reynold's number ~100) were employed. We estimate that these phenomena can contribute 1 0% error to our measurements. To minimize fluctuations in the water vapor pressure, we added He saturated with water vapor to the flow tube. This procedure

suppressed evaporation and cooling of the liquid film. In addition, we allowed a long time for the gas flow to equilibrate with the water film. Also, the experiments were carried out with slower liquid flows and at the highest possible pressures, so that fluctuations in water pressure had minimal effect. High uptake

coefficients measured at high pressures are uncertain because Ic^

is close to the diffusion controlled loss rate coefficient, k^iff [Hanson et al., 1992]. Under those conditions, the uncertainties

in k^iff contribute to the error in the diffusion correction due to radial concentration gradient [Srown, 1978].

Finally, NO2, which is also present in the NO3 source, can

enter the liquid water and form N02'(aq)- Then N02' can react with NO3 and slightly enhance its uptake. Using the known low

solubility constant of NO2 [Lee and Schwartz, 1981; Schwartz and White, 1983], we calculate a y<lxlO"' for this process.

Atmospheric Implications

Three results and conclusions from this study that are relevant

to the atmosphere are (1) NO3 is taken up by liquid water via a

reactive process that produces OH radicals in solution, (2) the physicochemical parameters, such as H£>/^ and i", which are necessary for deriving the reactive uptake of NO3 into water

containing various reactants are determined and (3) the solubility of NO3 in water is small and the previous controversy about the magnitude of this quantity is settled. Of these, the production of OH oxidant from NO3 uptake is probably the most important

conclusion. Here, we discuss the implications of these findings

to the chemistry of the lower atmosphere, including those of the marine boundary layer and polar troposphere.

The solubility of NO3 in water has been a disputed issue, with

the assumed values ranging from 3x10'^ to 2x10^ M atm"' [Chameides, I986a,b; Jacob, 1986; Lelieveld and Crutzen, 1991; Mozurkewich, 1986]. Our value of H=0.6±0.3 M atm' is much

lower than what has been assumed in many atmospheric

calculations. This number is uncertain by ~50%, mostly because

of the uncertainties in the rate coefficient for the reaction of NO3

with CI" and the value of the diffusion coefficient of NO3 in liquid water. Once these quantities are determined by some

independent method, our measurement can be used to derive a more accurate value of H. To our knowledge, only Thomas

[1992] has previously reported a value of H. Thomas could not derive a precise value of H because of experimental difficulties. However, her results greatly constrained the value of H and is in agreement with ours. Our measured value of H places a limit on

the heterogeneous uptake coefficients that are possible.

We have measured HZ)/^ , the quantity that is most important

for calculating the uptake of NO3 by water. If HD°^ is known,

the uptake coefficient can be calculated using equation (4) for a known composition of solution. We can calculate the rate of removal of NO3 from the gas phase and the rate of product

formation in the liquid phase using the HD,"^ value determined

here, if the concentrations of dissolved species in the liquid

droplets and the rate coefficients for their reactions with NO3 are known. Even in the absence of additional reactive species in the

liquid water droplets, there will be loss of NO3 due to its reaction with water. This loss alone leads to an uptake coefficient, y, of

-2x10"^. The presence of other reactive species in the water

droplet will increase y. If the surface area of the water droplets in air is known, the

loss rate of NO3 can be calculated. For example, we calculate the NO3 lifetime due to heterogeneous loss to be of the order of 5 min in clouds by assuming a surface area of -3x10'^ cm^ per cm-' of air (e.g., 40 particles cm"* with 50 |im diameter [Graedel and

Crutzen, 1993]). In fog, where the drop size is smaller than in a

cloud, the diffiiso-reactive length is close to the drop radius [Hanson et al., 1994; Ravishankara and Hanson, 1994] and

leads to effective uptake coefficients that are a factor of 2 - 3 smaller than in large droplets. The lifetime calculated here is in reasonable agreement with the short lifetime observed for NO3 in the troposphere [Mihelcic et al., 1993; Piatt et al., 1981]. Under

certain conditions, NO3 will be in equilibrium with N2O5. Then, removal of N2O5 by heterogeneous hydrolysis will affect gas phase NO3 concentrations. As temperature increases to make

[N03]/[N205]>1, the effect of heterogeneous N2O5 uptake on the NO3 concentration becomes smaller. Such conditions are reached when 7>285 K and for low NO2 mixing ratios (<20 pptv). In the marine boundary layer (MBL), sea-salt aerosols will be

the medium for heterogeneous reactions. For sea-salt aerosols with [Cr] = 1 A/ and [Br] = SxlO"^ M, the uptake coefficient will be y ~ 1x10'^. Under these conditions, the uptake will be

restricted by interfacial mass transport for particles of size up to about 15 |im [Schwartz, 1986]. For particles above this size, gas phase diffusion will be the rate limiting step. In the presence of

sea-salt aerosols, the major loss process for NO3 will be removal by the these particles. Its rapid heterogeneous removal in MBL

may be responsible for the low concentrations of NO3 in this region. Low concentrations of NO3 in the MBL may also help

explain the observed diurnal variation in the abundance of

dimethyl sulfide (DMS) in spite of the large rate coefficient for the reaction of NO3 with DMS [Saltzman and Cooper, 1988]. If the sea-salt aerosols are indeed suppressing NO3 abundance in the MBL, NO3 may not be a major oxidizer of DMS.

Outside of the MBL, based on the measured values of the rate constants and estimated concentrations of reactive species in tropospheric liquid droplets, loss of NO3 via its direct reaction with water may be an important loss mechanism for NO3. Liquid

phase reactions of NO3 with reactants other than water can also lead to the formation of very reactive oxidants within the TN-205
RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO, 21,029

droplets. These oxidants can be CI (reaction (Rl)), Br (reaction (R2)), or OH (due to reaction (R4)). The radical products can

initiate reactions of various organic and inorganic species dissolved in rain and fog drops or in sea-salt aerosols. Here we

very briefly and qualitatively explore the consequences of such

oxidant production.

Piatt et al. [1984] hypothesized that there should be a mechanism for converting NO3 to HNO3 in the liquid phase. Our

work very strongly suggests that the direct reaction of NO3 with water is responsible for what was observed by Piatt et al. The

importance of this finding is that not only there is a reaction between liquid H2O and NO3, but also the product of this reaction is an oxidant in the liquid phase. This is in contrast to NO3 removal via formation of N2O5 and its subsequent

hydrolysis, which results in only formation of HNO3.

Chameides [1986a,b] has shown that NO3 can initiate an

oxidation chain within cloud droplets that can convert S(IV) to S(VI) . However, Henry's law coefficient, H=12 A/atm"', used in these calculations was larger than the one measured here and

reaction (4) was not considered. Therefore the role of NO3 in rain chemistry, sulfur chemistry, and chemical processes within seasalt aerosols must be reevaluated using the lower solubility

measured here and the reaction of NO3 with liquid water to produce OH. Reevaporation of NO3 from the droplets that was

suggested by Mozurkewich [1986] will not be significant because

the uptake of NO3 even in pure water is reactive, i.e., not determined by physical solubility. Uptake of NO3 into sea-salt aerosols and cloud droplets can

directly oxidize S02(aq), HSO3", and S03^" dissolved in them and

also indirectly via reactions of CI2", Br2", and OH that are produced by the NO3 reactions in the solution. These reactions produce SO3", which is capable of further initiating catalytic oxidation reactions of S(IV). Production of SO3", Cl2', OH, and

Br2' in the sea-salt aerosols can initiate a mechanism similar to that proposed by Mozurkewich [1995] for release of halogens

(chlorine, bromine, and possibly iodine) by oxidation of halide ions via involvement of Caro's acid in the liquid phase. It will be

interesting to investigate the role of such a mechanism in the Arctic springtime troposphere. Mozurkewich's mechanism is based on daytime radicals such as OH and HO2 as initiators. However, NO3 can be important during the dark. The above discussion is very qualitative and highlights the many possible consequences of our laboratory findings. A

quantitative assessment of the impact of the reaction of NO3 with

liquid water (oxidant production), the refined values of H, and

the derived values of HD,"^ require more sophisticated

atmospheric modeling calculations.

Appendix: Estimation of Henry's Law Coefficient for NO, in Water, kf^ and y Due to Reaction of NO, with H2O

In our experiments, we measured HD°^ for NO3 in aqueous

solutions. To estimate Henry's law coefficient for NO3 in water from this value, the diffusion coefficient of NO3 in water must be known or estimated. Crudely, the diffusion coefficient in the aqueous phase can be estimated by the equation [Atkins, 1990]

kT A =

67n]R (Al)

Where 77 is the viscosity of the liquid (t](273 K) = 1.787 cP), T

is the temperature, k is Boltzmann constant and R* is the effective radius of the solvated molecule. Since the exact value of R* is unknown, we assume it to be 1.2±0.6 A and obtain D,(N03(aq)) =

(1.0±0.5)xlO'' cm^ s"'. Such a diffusion coefficient yields H=

0.6±0.3 Matm'. A better knowledge of the diffusion coefficient of NO3 in water will allow a better calculation of H and to reduce

the uncertainties in the value determined here. The reaction of N03(aq) with H2O can be considered to be a two-step process:

1. Solvation of NO3 in water H

NO3(g):^NO3(a<0

2. Reaction of aqueous NOs^aq) with H2O

hi (R4)

/C/4 N03(aq) + H20(a<,) 1^ HN03(aq) + OH(aq)

Calculating the standard fi-ee energy change, AG", of step (R4)

would allow us to evaluate kf^. The AG" value for reaction (R4)

can be estimated from the free energy change in the formation of

individual species. The standard free energy change, AG*^ of compounds in the liquid phase are calculated by AG'/=AG / +

AG^soi, where AG''soi is the AG due to solvation, which is calculated using Henry's law coefficient and AG y is the standard energy of formation in the gas phase. Although the standard state for solutions is molality, we will use molarity throughout this calculation, since for dilute aqueous solutions, these quantities are essentially the same. For NO3, AG*soi= -RT ln(H) = 0.27;S^/o kcal mol"' using H =

0.610.3 Matm-'. AG°/of N03(g) is 27.75 kcal mol"' [Chase et al., 1985]. HenceAGVofN03(aq)=27.75+0.27=28.0;Sfo kcal mol"'. For HN03(aq) the physical Henry's law coefficient is needed. There are three equilibria processes that must be taken into account, i.e., Henry's law partition of the nonionized acid H^noj

HNO3 (g) . HNO3(aq)

followed by the ionization equilibrium, .^eq

HN03(aq):;^ HVq)+N03-(aq)

These can be combined to give the overall equilibrium for nitric acid A^H HN03(g):^ H\aq) + N03-(aq)

Several calculated values for A^h (^ atm'') at 298 K exist:

3. 26x10'^ [Schwartz and fVhite, 1981], 2A5x\0^ [Brimblecombe

and Clegg, 1988], and 2.66x10* [Tang et al, 1988]. For this calculation, we will use the most recent value of AfH=2.45xl0*.

A^eq has been measured to be 20 M [Redlich et al., 1968]. Henry's law constant for HNO3 can be calculated by [Schwartz and

White, 1981] to be

Hhno3 = ^h / -^eq = 1 22x 1 0^ a/ atm-' Knowing H^q^ and AG'/ of HN03(g) = -17.72 kcal mol', we

calculate AG*/ of HN03(aq)= -17.72 - /?71n( Hh^oj ) = "24.66 kcal

mol"'. (Note that the AG/ for HN03(aq) in the CRC Handbook is actually that for N03-(aq)). Using known AG*/ for OH(aq), and H20(aq) (6.2 and -56.5 kcal mor', respectively [Golden et al., 1990]), AG° for reaction (R4)

is calculated to be AG° = 10.0±0.3 kcal mol"'. This standard free energy change yields an equilibrium constant K2 = kf^lKA -

expi-AG/RT) =4.3x10"* at 298 K. Assuming yk,4= (1.4±0.1)xl0* Af' s"' [Katsamura et al, 1991], kf^= e!^^ AT's"' is obtained at 298 K. With AG°= 10.0+0.3 kcal mol"', kf^ at 273 K is calculated

to be kfn = 1.3 Af' s"' , corresponding to y=5xlO"^

Acknowledgments. We thank David R. Hanson and Edward R. Lovejoy for their valuable help throughout this work and Paul Wine for valuable discussions. The authors also acknowledge

TN-206
21,030 RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO3

the help of Richard B. Norton for the ion chromatographic

analysis of the liquid samples. This work was performed while Yinon Rudich held a National Research Council-NOAA

Postdoctoral Research Associateship. This work is funded in part by NOAA's Climate and Global Change program

References

Atkins, P.W., Physical Chemistry, Oxford University Press, New

York, 1990. Atkinson, R., Kinetics and mechanisms of the gas-phase

reactions of the NO3 radical with organic compounds, J. Phys. Chem. Ref. Data, 20, 459-507, 1991. Berdnikov, V.M., and N.M. Bazhin, Oxidation-reduction

potentials of certain inorganic radicals in aqueous solutions, Russ. J. Phys. Chem. Engl. Transi, 44, 395-398, 1970. Brimblecombe, P., and S. Clegg, The solubility and behavior of

acid gases in the marine aerosol, J. Atmos. Chem., 7, 1-18, 1988. Brown, R.L., Tubular flow reactors with first-order kinetics, J. Res. Natl. Bur. Stand U.S., 83, 1-8, 1978. Chameides, W.L., Possible role of NO3 in the nighttime

chemistry of a cloud, J. Geophys. Res., 91, 5331-5337,

1986a. Chameides, W.L., Reply to comment on "Possible role of NO3

in the nighttime chemistry of a cloud", J. Geophys. Res., 91, 14,571-14,572, 1986b. Chase, M.W., Jr. , C.A. Davis, J.R. Downey, Jr., D.J. Frurip, R.A. McDonald, and A.N. Syverud, JANAF thermochemical

tables, J. Phys. Chem. Ref. Data, 14, Suppl. 1, 1985. Danckwerts, P.V., Absorption by simultaneous diffusion and

chemical reaction into particles of various shapes and into falling drops. Trans. Faraday Soc, 47, 1014, 1951.

Daniels, M., Radiation chemistry of the aqueous nitrate system,

III, Pulse electron radiolysis of concentrated sodium nitrate solutions, y. Phys. Chem., 73, 3710-3717, 1969. DeMore, W.B., S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara, C.E. Kolb, and

M.J. Molina, Chemical kinetics and photochemical data for use in stratospheric modeling. Evaluation 11, JPL publ. 94-

26, 1994. Exner, M., H. Herrmann, and R. Zellner, Laser-based studies of

reactions of the nitrate radical in aqueous solution, Ber. Bunsenges. Phys. Chem., 96, 470-477, 1992. Golden, D.M., V.M. Bierbaum, and C.H. Howard, Comments on

"Reevaluation of the bond-dissociation energies for H-OH,

H-OOH, H-00-, H-0, H-00- and H-00", J. Phys. Chem.,

9^5413-5415, 1990.

Graedel, T.E., and P.J. Crutzen, Atmospheric Change - An Earth System Perspective, W.H. Freeman, New York, 1993. Hanson, D.R., J.B. Burkholder, C.J. Howard, and A.R.

Ravishankara, Measurement of OH and HO2 radical uptake

coefficients on water and sulfuric acid Surfaces, J. Phys.

Chem., 96, 4979-4985, 1992. Hanson, D.R., A.R. Ravishankara, and S. Solomon,

Heterogeneous reactions in sulfiiric acid aerosols: A

framework for model calculations, J. Geophys. Res., 99, 3615-3629, 1994.

Heikes, B.G., and A.M. Thompson, Effects of heterogeneous

processes on NO3, HONO and HNO3 chemistry in the troposphere, y. Geophys. Res., 88, 10,883-10,895, 1983.

Howard, C.J., Kinetic measurements using flow Tubes, J. Phys.

Chem., 83, 3-9, 1979.

Jacob, D.J., Chemistry of OH in remote clouds and its role in the production of formic acid and peroxymonosuifate, J. Geophys. Res., 91, 9807-9826, 1986.

Jiang, P.Y., Y. Katsamura, K. Ishigure, and Y. Yoshida,

Reduction potential of the nitrate radical in aqueous solution, Inorg Chem., 31, 5135-5136, 1992. Katsamura, K., P.Y. Jiang, R. Nagaishi, T. Oishi, K. Ishigure, and Y. Yoshida, Pulse radiolysis study of aqueous nitric acid

solutions: Formation mechanism, yield, and reactivity of NO3, J. Phys. Chem., 95, 4435-4439, 1991. Kim, K.J., and W.H. Hamill, Direct and indirect effects in pulse

irradiated concentrated aqueous solutions of chloride and

sulfate ions,y. Phys. Chem., 80, 2320-2325, 1976. Lee, Y.N., and S.E. Schwartz, Reaction Wnetics of nitrogen dioxide with liquid water at low partial pressure, J. Phys.

CAe/w., 55, 840-848, 1981.

Lelieveld, J., and P.J. Crutzen, The role of clouds in tropospheric

chemistry, J. Atmos. Chem., 12, 229-267, >.;yi. Mason, E.A., and L. Monchick, Transport properties of polar-gas

mixtures, J. Chem. Phys., 36, 2746-2757, 1962. Mihelcic, D., D. Klemp, P. Musgen, A.W. Patz, and A. Voltz- Thomas, Simultaneous measurements of peroxy and nitrate radicals at Schauinsland, J. Atmos. Chem., 16, 313-335,

1993. Monchick, L., and E.A. Mason, Transport properties of polar

gases, y. Chem. Phys., 35, 1676-1697, 1961. Mozurkewich, M., Comment on "Possible role of NO3 in the nighttime chemistry of a cloud", J. Geophys. Res., 91, 14,569-14,570, 1986. Mozurkewich, M., Mechanisms for the release of halogens from

sea-salt particles by free radical reactions, J. Geophys. Res., 100, 14,199-14,207, 1995. Neta, P., and R.E. Huie, Rate constants for reactions of NO3

radicals in aqueous solutions, J. Phys. Chem., 90, 4644-4648,

1986. Noxon, J.F., NO3 and NO2 in the mid-pacific troposphere, J. Geophys. Res., 88, 11,017-11,021, 1983.

Patrick, R., and D.M. Golden, Third-order rate constants of

atmospheric importance. Int. J. Chem. Kinet., 15, 1 189-1227,

1983. Pederson, T., Nighttime hydrogen peroxide production on

sulfuric-acid aerosols involving nitrate and sulfate radicals, Geophys. Res. Lett, 22, 1497-1499, 1995.

Piatt, U., D. Pemer, J. Schroder, C. Kessler, and A. Toenissen,

The diurnal variation of NO3, J. Geophys. Res. ,86, 11 ,965-

11,970, 1981.

Piatt, U.F., A.W. Winer, H.W. Bierman, R. Atkinson, and J.N.

Pitts Jr., Measurement of nitrate radical concentrations in continental air. Environ. Sci. TechnoL, 18, 365-369, 1984. Ravishankara, A.R., and DR. Hanson, Chemistry in sulfate aerosols, in Low Temperature Chemistry of the Atmosphere,

NATO ASI Ser, edited by G.K. Moortgart, et al., SpringerVeriag, Berlin, 1994.

Redlich, O., R.W. Duerst, and A. Merbach, Ionization of strong

electrolytes, XI, The molecular states of nitric acid and

perchloric acid, J. Chem. Phys., 49, 2986-2994, 1968. Saltzman, E.S., and D.J. Cooper, Shipboard measuremnts of

atmospheric dimethylsulfide and hydrogen sulfide in the Caribbean and gulf of mexico, J. Atmos. Chem., 7, 191-209,

1988.

TN-207
RUDICH ET AL.: UPTAKE COEFFICIENTS FOR NO3 21,031

Schwartz, S.E., Mass-transport considerations pertinent to aqueous phase reactions of gases in liquid-water clouds, in NATO ASI Ser., edited by W. Jaeschke, pp. 415-471,

Springer-Verlag, New York, 1986. Schwartz, S.E., and W.H. White, Solubility equilibria of the nitrogen oxides and oxyacids in dilute aqueous solution, in Advances is Environmental Science and Technology, edited by J.R. Pfafflin and E.N. Ziegler, pp. 1-45, Gordon and

Breach, New York, 1981. Schwartz, S.E., and W.H. White, Kinetics of reactive dissolution of nitrogen oxides into aqueous solution. Adv. Environ. Sci. TechnoL,12, 1-116, 1983. Tang, I.N., H.R. Munkelwitz, and J.H. Lee, Vapor-liquid

equilibrium measurements for dilute nitric acid solutions, Atmos. Environ., 22, 2579-2585, 1988. Thomas, K., Ph.D. Thesis, Univ. of Wuppertal, Germany, 1992.

Utter, R.G., J.B. Burkholder, C.J. Howard, and A.R.

Ravishankara, Measurement of the mass accommodation

coefficient of ozone on aqueous surfaces, J. Phys. Chem., 96, 4973-4979, 1992. Wayne, R.P., et ai. The nitrate radical: physics, chemistry and

the atmosphere, .4/7no5. Environ., 25A, 1-203, 1991. White, J.U., Long optical paths of large aperture, J. Opt. Soc. Am., 32, 285-288, 1942. White, J.U., Very long optical paths in air, J. Opt. Soc. Am., 66, 411-416,1976.

AR. Ravishankara, Y. Rudich and R.K Talukdar, Aeronomy Laboratory, NOAA R/E/AL2, 325 Broadway, Boulder CO 80303. (e-maU:

ravi@al.noaa.gov, yrudich@al.noaa.gov, talukdar@al.noaa.gov) R.W. Fox, Time and Frequency Division, NIST, 325 Broadway, Boulder CO 80303. (e-mail: rich@nistgov)

(Received November 15, 1995; revised May 18, 1996;

accepted May 28, 1996.)

TN-208
An All-Diode-Laser Optical Frequency Reference

Using Laser-Trapped Calcium

C. W. Gates, M. Stephens, and L. Hollberg

Time and Frequency Division

National Institute of Standards and Technology

325 Broadway

Boulder, CO 80303

Abstract

The 657 nm calcium intercombination line is an

attractive optical frequency/length reference due to its high

line Q (10") and insensitivity to external perturbations. In

this paper we describe progress towards an aU-diode-laserbased rcf(Mence using laser-trapped Ca To genoate 35 mW

of 423 nm trap light, we double the frequency of a 150 mW,

846 nm diode laser with a nonlinear crystal (KNbO,) inside a resonant build-up cavity. We use this light to trap 2x10^

atoms in a compact, oiagneto-optic trap. Spectroscopy of

the narrow 657 nm transition is performed with a frequencystabilized diode laser system. With the tr^>ped atoms we

have measured optical Ramsey fringes with a lisewidth of 6

kHz. We discuss future improvements as well as potential

performance which could achieve a fractional frequency

instability of <3x 10".

Introduction

Due to their narrow linewidth and insensitivity to extenud perturbations, the intercombination lines in alkaline earth atoms are attractive optical frequency/length

references.[l,2] From preliminary work on the lowest lying

'So - 'Pi lines in Ba, Ca, and Mg, potential uncertainties in the determination of the line centers were estimated to be < 1 Hz in the best cases.[3,4,5] This predicted performance

is particularly attractive wlien compared with that of two

well-known systems, the iodine-stabilized HeNe laser at 633

nm, and the two-photon system in Rb at 778 mn, which have

uncertainties > 1 kHz.[6,7] Thus, there is a strong impetus

for fiirth^ investigations and development of these alkaline earth-based references.

In particular, the 657 nm intercombination line 'Sg (m=0) -> 'P, (m=0) in atomic calcium is an excellent candidate due to its high line Q (10*^ and convenient

wavelength. Ca also has a strong 'Sq -> 'Pi transition at 423

nm which is well suited for laser cooling and trapping.

Contribotion of U.S. Govemmmt; not subject to copyri^t

The use of laser-cooled samples offers two benefits for a Ca

frequency reference: (i) the extended interaction time needed

to resolve the 400 Hz (FWHM) natural linewidth of the 657 nm transition, and (ii) greatly reduced systematic errors. Another attractive feature of Ca is that the 657 nm and 423

imi transitions are accessible with semiconductor laser systenos, enabling a compact, reliable, and low power

frequency/length reference. These factors led the BIPM in 1994 to recommend that this be one of those transitions used

for the realization of die meter. [6] The first high resolution Ramsey spectroscopy on

the narrow 657 nm transition was performed in 1979 where

a frequency-stabilized dye laser was used to achieve

linewidths as narrow as 6 kHz.[l] Since then there have

been numerous measurements using thermal atoms, laser- cooled atoms, and even laser-trapped atoms, with resolutions

just now approaching the natural linewidth.[3,8] Recently

PTB has used an optical frequency synthesis system to measure the absolute frequency of this transition with an

uncertainty of less than 450 Hz,[9] making it the most

precisely known optical reference. There are presently several groups around the world developing optical

fi^uency/length references based on this transition. At MIST our work has focused on the development

of a such a refCTence based on semiconductor laser systems

(most previous work used dye lasers at 423 nm and 657 nm).

This required construction of a diode laser system at 657 nm

with high frequency stability and high power, and another at 423 nm which can generate sufficient blue light for use in a Ca magneto-optic trap (MOT)[10]. Additionally, we have

designed a simple, compact MOT which stores samples of

-2x10' atoms suitable for high-resolution spectroscopy at 657 nm.

This paper will first describe our {Hesent ^paratus,

beginning with the diode laser systems. We will then

present some preliminary specfroscopic results which

indicate that, when optimized, our frequency ref^ence could

attain a fractional frequency instability of <3xl0''^ in 1 sec. Finally, we wiU outline some modifications to this initial experimental setup which promise much improved

performance in die near fiiture.

1997 IEEE INTERNATIONAL FREQUENCY CONTROL SYMPOSIUM

TN-209
Trapping Ca with Diode Lasers

There were two important technical challenges in the construction of a compact, diode-laser-based Ca trap. TTie first was to generate blue light with sufficient power,

tunability, and frequency stability to trap Ca. Since there are no suitable semiconductor laser sources at 423 nm, we

instead double the frequency of a high-power diode at 846

nm. Figure 1 shows the apparatus used to generate the blue

IighL[ll] A 150 mW beam from a soUtary diode is sent through beam-shaping optics and an optical isolator to a

resonant cavity containing a KNbO, nonlinear crystal cooled

to -10°C. With 105 mW incident on the build-up cavity

(x20) the crystal produces 30 mW of light at 423 nm. We

control the frequency of the high-power diode by injectionlocking it with a lower power (20 mW) extended-cavity

diode las^ (ECDL). Long-term drifts of the laser frequency

are suppressed by locking the master ECDL to an absorption

signal derived from our Ca beam apparatus.

Trapping Bea

620" c Ca Oven

KI3

B-grad=12mT/ciri

V

35 m¥

423 nm

AOU

Figure 2. Design of a compact Ca MOT. A retroreflected

vertical beam is omitted for clarity.

846 om Diode Laser

BuDd-up Civitj

Figiire 1 . Schematic of the frequency-doubling apparatus

which generates >30 mW of 423 nm light

The second important challenge was to find a compact design for our Ca MOT. Simple vapor cell MOT

designs which are conmionly used for Cs and Rb are

difficult for Ca, since Ca must be heated to over 400°C to generate adequate \apoT pressure for trap loading. Previous

Ca MOT designs[3,12] relied instead on loading from laser- slowed atomic beams. They achieved efficient loading via

the technique of Zeeman slowing, which keeps the atoms

resonant with the slowing laser beams as their velocities are reduced. The Zeeman slowing technique, however, requires

large magnetic field coils. We chose instead to modify a

design first demonstrated at Stanf(Hxl[13] using Li atoms and more recently at PTB using Ca[7], which traps slow atoms

directly from an atomic beam without using a Zeeman

slower. Such a trap compensates the reduced range of

trapped atomic velocities by placing the trap much closer to

the atomic source, thus increasing die flux of atoms throu^

the trap region.

In our design (shown in Figure 2) the trap is located 13 cm from the oven nozzle, which operates at 620''C. We use 8 mW of 423 nm light in a single horizontal beam (1 cm diameter) which is recirculated and

retroreflected to generate the two popendicular horizontal trapping beams, set at 45 ° relative to the atomic beam axis. The retroreflected vertical trapping beam contains 2 mW of

blue power. We generate the large magn^c field gradient

(12mT/cm) required by our trap by sending 150 an^res of

current through a wat^-cooled pair of anti-Helmholtz coils. Under these conditions our MOT fills with noorc than lO' Ca

atoms with a loading time constant of 20 ms, apparently

limited by optical pumping to the 'D; state which lies below

the 'P, state. We observe the hi^iest level of blue fluorescence from the trapped atoms with the blue light

detuned -30 MHz below the 423 nm resonance.

In previous versions of this type of MOTl7,12] one

or more frequency sidebands were added to the trapping

light in order to extend the capture velocity, thus increasing

the loading rate. We instead implemented a slowing beam

counter-propagating to the atomic beam, which slows atoms

(without benefit of Zeeman slowing coils) before they reach

the tr£q>ping region. We could not however, simply send

this light through a window downstream fit>m the oven. A

window in this position quickly becomes coated with Ca

from the atomic beam and no longer transmits the blue slowing beam. To avoid this problem we send the slowing

li^t through a window on the side (see Hgure 2) and reflect

it off a mirror located inside the vacuum system downstream

from the oven. It turns out that layers of deposited Ca make

a fairly decent mirror (-70% reflectivity) at 423 nm, so the mirror continues to reflect the slowing beam even after becoming coated with Ca. Tuning the frequency of this beam 1 10 MHz to the red of the cooling transition gives a

TN-210
tenfold increase in the loading rate, producing laser-cooled samples of -2x10^ atoms in -20 ms. We used the narrow 657 nm transition to measure

the temperature of the cold atom cloud via the first-order Doppler effect. Typical temperatures of the trapped atoms

range from 2-3 mK, depending on trap laser intensity and

detuning. These temperatures are higher than those

routinely achieved in alkali traps due to the absence of

Zeenian structure (and hence polarization gradient cooling)

in the Ca ground-state. Without such structure, the minimum achievable temperature is set by the Doppler

cooling limit.[14] For Ca this limit is 0.8 mK, which

corresponds to a root-mean-square velocity of 40 cm/s (see

ref. [3] for further discussion).

High-Power. Frequency-Stabilized 657 nm

Diode Laser System

The requirements for the red diode system are (i)

its frequency be sufficiendy stable to resolve the 400 Hz

natural linewidth of the intercombination line and (ii) its power be greater than 10 mW to excite this weak transition by the Ramsey method.

To achieve sufficient frequency stability we started with an extended-cavity diode laser at 657 nm, which

yielded 3 mW output power (see Figure 3). To reduce the

Extended- Cavity

Diode Laser

l.SmW

Isolator fv

Loop Filter — Detector

B Ih—J^

Fabry- Perot Cavity

ZOUf—

\

Tapered

Amplifier

^

200 mW

AOy

Optical

Fiber

Synthesizer |h| aOM X

o

Ca atoms

Figure 3. Block diagram of the frequency-stabilized laser system at 657 nm used for high resolution spectroscopy.

1(X) kHz linewidth of this laser, we lock its frequency to a

resonance of a high-finesse, Fabry-Perot cavity (3 GHz FSR

and 50 kHz fringe FWHM) . We send 100 ^W of the laser output to this cavity and use the Pound-Drever-Hall

technique[14] to derive a high signal-to-noise error signal

using a modulation frequency of 13.3 MHz. We then filter this signal to correct laser frequency fluctuations via the

laser current (fast corrections) and a PZT-driven mirror on

the laser cavity (slow corrections). A servo bandwidth of over 3 MHz yields fast laser linewidths of < 100 Hz, as inferred from the error signal relative to the cavity. To

rediice long-term frequency fluctuations due to drifts of the reference cavity, we constructed the cavity spacer out of

ultra-low expansion (ULE) material and placed it inside a vacuum chamber. This chamber was then placed inside a

thermally-stabilized, vibrationaliy-isolated environment. To

enable precise tuning of the laser frequency relative to the cavity resonance, we use a double-passed, acousto-optic

modulator (AOM) before the cavity.

We increased the 657 nm laser power available for Ca spectroscopy by using 2 mW of light from the stabilized ECDL to injection-lock a semiconductor tapered

amplifierfTA). The stabilized ECDL serves as the master

laser and the tapered amplifier as the power amplifier in a

master-oscillator power-amplifier (MOPA) configuration.

With 1 .9 amperes of current in the TA, the MOPA produces

a remarkable 240 mW of light without adding significant

phase noise to the frequency-stabilized light After spatially

filtering the output with an optical fiber, however, we have

typically only 10-20 mW of usable light, a level adequate

though somewhat low for the Ramsey spectroscopy. The

MOPA system also allows us to stabilize the intensity level of the light after the fiber by feeding back to the TA current As a first test of this system we performed

spectroscopy on a thermal beam of calcium. To achieve

high resolution while maintaining good signal-to-noise ratio, we used the optical Ramsey fringe technique.[16] This

technique is analagous to the microwave Ramsey technique

but uses four (rather than two) spatially-separated interaction regions in order to cancel the first-order Doppler effect The

distance between the four traveling waves (along with the most probable velocity of the atomic beam) then sets the

spectral resolution for a given measurement We generated

Ramsey lineshapes by measuring the induced atomic beam

fluorescence downstream from the interaction region.

Figure 4 shows an example of a Ramsey fringe taken at a probe power level of 8 mW (40 scans averaged -

total data accumulation time of 1 minute). Here the spacing

between each pair of beams was 15 mm, which yields a Ramsey resolution of 11.5 kHz for our most probable

velocity of 100 m/s. Actually seen here are the two recoil components for this transition, which are separated by 23.1 kHz. Our Ramsey resolution of 1 1 .5 kHz was chosen so the fringe patterns of the two components would interfere constructively in order to give the best contrast, which was

about 25%.

Note that such a signal can be used as an optical

frequency reference simply by locking a laser to one of the two recoil components, one of which can be suppressed, if so desired.[17] If limited only by the signal-to-noise ratio demonstrated in Figure 4, one should attain a fractional frequency uncertainty of 5x1 0"'^ in 1 sec. Workers at PTB

TN-211
20 40 60 80 100 120 140 160 180

Relative 6S7 lun tuning (kHz)

Figure 4. Optical Ramsey fringes in a Ca atomic beam.

are presently constructing a compact version of this type of

device to use as a transportable fi^uency reference.[8]

They have determined, however, that a laser locked to a Ramsey fringe derived from an atomic beam is susceptible

to drifts as large as 1 kHz, which seriously compromises its long-term performance.[8]

High'Resolution SpectroscopY with Laser-Cooled

Ca Atoms

Presently we perform spectroscopy on the narrow

red transition using laser-cooled and tr^ped atoms. Optical

Ramsey ^)ectroscq)y with tr^ped san^iles differs from that in a beam in that one must separate the four interaction zones temporally rather than spatially.[3,4] Thus this second spectroscopic investigation uses four pulsed

traveling waves (two in one direction followed by two in the opposite) to excite the narrow transition. In this case, the

time, T, between the pulses of each pulse pair determines the Ramsey fringe resolution, Av=l/(4T). An added

complication is that we must turn off the blue trap light

during this excitation time so that the relevant atomic levels are unperturbed.

A typical measurement cycle conmiences with 5-10 ms for trapping, after which we shut off the trap light and

magnetic field gradient. Next we illuminate the atoms with

four pulses (controlled by two AOM's) from our frequencystabilized 6S7 nm laser system. The cycle ends with a 300

|xs detection p^od, during which we collect red

fluorescence with a photomultiplier tube. We typically

repeat this cycle 200 times for each frequency data point

Hgure 5 shows a preliminary scan taken (without

chopping the magnetic field gradient) with a total pulse

separation of 80 fis, which yields a Ramsey resolution of 6

kHz. One immediately notices that many more fringes are present than we saw in the case of atomic beam Ramsey

spectroscopy. In a thermal beam the effective pulse

separation time as seen by an atom depends on its velocity.

Due to the wide range of velocities in an atomic beam, the resultant lineshape was in fact the superposition of fringe

patterns with different resolutions, which washed out all but

the central fringe. For samples of trapped atoms, however,

all atoms see the same time separation between pulses, so

the individual contributions add coherently, leading to a lineshape such as that seen in Figure 5.

iJ5r

1.25 10 20 M 40 SO 60 70 80 90 100 Relative 657 nm Laser Tuning (kHz)

Figure 5. Optical Ramsey fringes at 657 nm using laser- trapped Ca atoms.

The actual situation is even more comphcated due

to the fact that we again have the two recoil con^nents,

thus producing two fiill fringe patterns (separated by 23.1 kHz). To have good fringe contrast, the Ramsey fringe

period needs to be chosen to be an integral fraction of the

recoil splitting (or one of the recoil components must be

suppressed). In either case, one can then determine the central fringe (i.e. the line center) for each component by

taking spectra at several different resolutions. The signal-to-noise ratio in this preliminary scan was far from shot-noise limited and should be greatly

improved in the near future. For our current apparatus, a

shot-noise limited lineshape should yield a fractional uncertainty of SxlO"'^ in 1 sec, a level comparable to one

demonstrated in a similar setup at PTB using dye lasers.[8] A laser locked to such a fringe could then provide an

excellent length reference. For use as a frequency reference, however, the frequency stability of the locked laser would

first have to be transferred to the microwave domain using

presently unavailable optical frequency-syndiesis

techniques.

TN-212
Future Work and Prospects

While our present apparatus provides good

performance, there are several aspects which can be readily

improved. We presently collect less than 2% of the total fluorescence, so improved collection optics could increase our signal by at least an order of magnitude. To increase the signal further we are presently implementing a different excitation strategy which first uses a resonant blue pulse to measure the number of atoms in the sample before the four red pulses. [4] Immediately following the last red pulse, a second blue pulse can read out the fraction of atoms still in the ground state after the Ramsey interaction. Since we can

scatter hundreds of blue photons per atom per blue pulse, we

can have a much larger signal. Moreover, this signal is normalized to the number of atoms in the sample, reducing

noise induced by shot-to-shot, trap-number fluctuations. These improvements can, in principle, reduce the uncertainty of our optical frequency reference by one or more orders of magnitude. What will be the ultimate performance of such a system? This remains an open

question as there have yet to be detailed studies of

systematic effects associated with an optical reference based on trapped atoms. Independent estimates[4,8] predict that known systematic effects should contribute < 1 Hz (or a

fractional frequency uncertainty of 2.5x10"), but several

effects such as those due to cold-atom collisions[18] have

not yet been investigated. Such studies will require

comparisons between independent systems. The first Ca

intercomparison, between a portable thermal beam apparatus

constructed by PTB and our apparatus here, is scheduled for

later this year.

Acknowledgements

We thank our colleagues in the group of J. Helmcke and F. Riehle at PTB, R.W. Fox and J.C. Bergquist

at NIST, and J.L. Hall at JILA for useful discussions and

suggestions. We also gratefully acknowledge the financial support of AFOSR.

References

[1] R.L. Barger, J.C. Bergquist, T.C. English, and D.J. Glaze, "Resolution of photon-recoil structure of the 6573-A

calcium line in an atomic beam with optical Ramsey

fringes," Appl. Phvs. Lett., vol. 34, pp. 12-14, June 1979.

[2] J.L. Hall, M. 2hu, and P. Buch, "Prospects for using

laser-prepared atomic fountains for optical frequency

standards applications," J. Opt. Soc. Amer.. vol. 6, pp. 2194-2205, Nov. 1994.

[3] Th. Kisters, K. Zeiske, F. Riehle, and J. Helmcke,

"High-resolution spectroscopy with laser-cooled and tr^ped

calcium atoms," Appl. Phvs. B. vol. 59, pp. 89-98, Aug.

1994.

[4] K. Sengstock, U. Sterr, J. H. MuUer, V. Rieger, D.

Bettermann. and W. Ertmer, "Optical Ramsey spectroscopy on laser-trapped and thermal Mg atoms," Appl. Phvs. B. vol. 59, pp. 99-115, Aug. 1994.

[5] A.M. Akulshin, A.A. Celikov, and V.L. Velichansky,

"Nonlinear Doppler-free spectroscopy of the 6'S,-6^P,

intercombination line in barium," Opt. Comm.. vol. 93, pp. 54-58, Sept 1992.

[6] T. Quinn, "Mise en Pratique of the Definition of the Metre (1992)," Metroloeia. vol. 30, pp. 523-541, Jan. 1994.

[7] D. Touahri, O. Acef, A. Qairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez,

"Frequency measurement of the 55,^j (F=3) - 5Dj„ (F=5)

two-photon transition in rubidium," Opt. Comm.. vol. 133,

pp. 471-478, Jan. 1997.

[8] F. Riehle, H. Schnatz, B. Lipphardt, P. Kersten, T.

Trebst, G. Zinner, and J. Helmcke, "Optical Calcium

Frequency-Standard: Status and Prospects," in PTB-Bericht

Opt-51. Proceedings of 'TreQuencv Standards Based on

Laser-Manipulated Atoms and Ions." Schierke, Germany,

Feb. 12-14, 1996, pp. 11-20.

[9] H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G.

Zinner, 'Tirst phase-coherent frequency measurement of

coherent visible radiation," Phvs. Rev. Lett., vol. 76, pp. 18- 21, Jan. 1996.

[10] E.L. Raab, M. Prentiss, A. Cable, S. Chu, and D.E.

Pritchard, 'Trapping of neutral sodium atoms with radiation pressure," Phvs. Rev. Lett, vol. 59, pp. 2631-2634, Dec.

1987.

[11] R.W. Fox, L. HoUberg, and A.S. Zibrov,

"Semiconductor Diode Lasers," in Experimental Methods in the Phvsical Sciences, vol. 29C, (F.B. Dunning, and R.G.

Hulet, ed.) New York:Academic Press, 1997, ch. 4, pp. 77-

100. Leo Hollberg, V. L. Velichansky, C.S. Weimer, and

R. W. Fox, "High-Accuracy Spectroscopy with

Semiconductor Lasers: Application to Laser-frequency

Stabilization," in Frequency Control of Semiconductor

Lasers. (Motoichi Ohtsu, ed.). New York:John Wiley &

Sons, Inc, 1996, ch 3, pp. 73-93.

[12] Takayuki Kurosu and Fujio Shimizu, "Laser cooling

and trapping of calcium and strontium," Japanese J. Of

Applied Phvs.. vol. 29, pp. L2127-2129, Nov. 1990.

TN-213
[13] Brian P. Anderson and Mark A. Kasevich, "Enhanced

loading of a magneto-optic trap from an atomic beam,"

Phvs. Rev. A. vol. 50, pp R3581-R3584, Nov. 1994.

[14]. T. W. Hansch and A.L. Schawiow, "Cooling of gases by laser radiation," Opt. Comm. . vol. 13, pp. 68-69, Jan. 1975. D.J. Wineland and Wayne M. Itano, "Laser cooling

ofatoms." Phvs.Rev.A. vol. 20, pp. 1521-1540, Oct. 1979.

[15] R.W.P. Drever. J. L. Hall, F.V. Kowalski, J.Hough,

G.M. Ford, A.J. Munley, and H. Ward, "Laser Phase and

Frequency Stabilization Using an Optical Resonator," Appl.

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[16] Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev,

"Non-bnear Ramsey resonance in the optical region," Appl.

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J.C. Bergquist, S.A. Lee, and J.L. Hall, "Saturated

absorption with spatially separated laser fields: observation

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[17] F. Riehle, J. Ishikawa, and J. Helmcke, "Suppression of

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Sterr, K. Sengstock, J.H. Muller, D. Betterman, W. Ertmer,

"The magnesium Ramsey interferometer: applications and

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1774, March 1993.

TN-214
Part IV

Optical Synthesis and Extended

Wave Length Coverage

Precise optical frequency references and difference frequencymeasurements with diode lasers^

S. Waltman, A. Romanovsky, J. Wells,

R.W. Fox, and L. Hollberg

National Institute of Standards and Technology

Boulder, CO 80303

M.P. Sassi

Instituto di Metrologia

Torino, Italy

H.G. Robinson

Duke University, Department of Physics

Durham, NC

ABSTRACT

Heterodyne methods have been used in conjunction with molecular

calculations to accurately determine the wavelengths of more than 35,000

infrared transitions. We have used high speed whisker contact Schottky

diodes to extend this technology to the 0.8 |im spectral region. Using

microwave harmonic mixing we demonstrate that it is possible to detect

beat notes between diode lasers to frequencies as high as 400 GHz.

1 . INTRODUCTION

Optical heterodyne techniques can play a fundamental role in

precision spectroscopy and laser frequency control. Increasing demand

for precise frequency measurements in the visible and near-infrared

regions of the spectrum have resulted in a number of ideas for optical

frequency synthesis . ^''' These proposals often require several tunable

narrow-linewidth laser sources. For purely practical reasons these

sources might best be supplied by diode lasers. Achieving optical

frequency synthesis and measurement will require high-accuracy optical

frequency references, very narrow linewidth, well-controlled lasers, and

the ability to make frequency difference measurements over extremely

large frequency intervals. We have explored and continue to explore

some of the promising optical frequency references that are compatible

with diode lasers. Of particular interest in this area are the narrow

intercombination transitions in the group-II atoms such as calcium, ^'^ barium,' and strontium.® Our effort at NIST on diode-laser compatible

frequency/wavelength references has focused primarily on the calcium

transition at 657 nm and on laser-cooled cesium. ^'^°

'Work of United States Government. Not subject to copyright.

386/SPIEVol. 1837(1992) 0-81 94-1038-1 /93/$4.0(

TN-215
An effort in measuring the frequencies of molecular transitions

in the infrared has just been completed at NIST by J. Wells and A.

Maki."'^^ They determined the absolute frequencies of more than 35,000

molecular transitions in the wavelength range between 486 and 4352 cm"^.

in their measurement system tuneable lead-salt diode lasers were used to

probe the molecular transitions, and heterodyne techniques were used to

measure the frequency of the diode laser relative to known stabilized

gas laser frequencies. These newly tabulated frequencies now provide a

precise calibration atlas for wavelengths in the infrared. This work

demonstrates the utility of using heterodyne methods for precision

spectroscopy.

We have been exploring the potential for extending these heterodyne

techniques using diode lasers to larger frequency intervals and up into

the visible and near-visible spectral regions. Some time ago H. U.

Daniel, J. Bergquist, and collaborators^^- ^^ demonstrated that very small

Schottky diodes could be used to measure difference frequencies of

visible lasers to hundreds of gigahertz. Their devices were similar to

ours which were actually designed as millimeter -wave detectors for

applications such as radio astronomy. Following their lead we have been

using these high-speed, whisker-contact Schottky diodes simultaneously

as photodetectors and microwave harmonic mixers. These detectors consist

of small, recessed Pt-Au islands on a GaAs epilayer grown on a GaAs

substrate. The area of the gold islands is about 1.5 [im^ which gives a

capacitance of about 2.6 fF and a 3 dB corner frequency for millimeterwaves of about 3.7 THz. The useful optical detection bandwidth has not

yet been fully determined.

2. EXPERIMENTAL DETAILS

The experimental apparatus is diagrammed in Fig. 1. It consists of

two 830 nm, AlGaAs lasers that are optically locked^^ to different modes

of a single confocal Fabry-Perot cavity. The lasers' outputs are

combined and focused on the Schottky diode along with the output from

the microwave source. The Schottky diode generates the laser beat

frequency as well as the harmonics of the microwave source. The laser

beat note is detected directly or is mixed down by heterodyning with the

microwave frequency or one of its harmonics. The microwaves are supplied

by a klystron (at about 47 GHz) or by a synthesizer.

A picture of the beatnote between two diode lasers and the eighth

harmonic of a 47 GHz klystron is shown in Fig. 2. With an optical

frequency difference of 382 GHz, this beatnote demonstrates the good

signal-to-noise ratio that can be achieved with this detection system

even though the Schottky diode is not at all designed for optical

detection. The typical experimental parameters were ~5 mW in each of

the two lasers beams, =2 00 mW of klystron power, and a spectrum analyzer

resolution bandwidth of 10 kHz. The detector can be biased to enhance

the mixing and/or harmonic generation efficiency. However, we have

found that when the microwave power on the detector is high the bias has

very little effect on the detected signal-to-noise ratio. A large

experimental uncertainty in the actual microwave power that is coupled

onto the detector remains, but we typically operate the detector so that

SPIEVol. 1837 (1992)/ 387

TN-216
/- Y

^

L02

V

Fr«q««acy

Laeh

S;

^

^ 'Klytlrea

<> /(^

-^

oa i lor Co* i ly

^

ujJ Moich i aq P^ Nalaork'*

Schei liijr Died*

Fig. 1. Optical -microwave mixing experimental diagram,

the rectified current from the microwaves is about 1.5 mA. The direct

optical detection efficiency of the laser light, as measured from the

DC photocurrent, is about 2 (lA/mW. Even though this value is quite low

compared to silicon photodiodes (=450 }J.A/mW at these wavelengths) we

measure good signal-to-noise ratios on the beatnotes. With the lasers

off, the dominant noise from the detector is shot noise in the rectified

microwave current.

The good signal-to-noise ratio

spectral width of the opticallylocked diode lasers, which allows us

to use a 10 kHz bandwidth. We

measured short-term laser linewidths

between 1 and 10 kHz.^° The laser

beatnote was about 70 dB above the

background noise in a 10 kHz

bandwidth when both lasers are

optically locked. This background

noise is from residual high frequency

noise on the lasers. By locking both

lasers to the same optical cavity we

remove most of the problems of cavity

vibration and drift. Even so, the

lasers still have substantial low

frequency jitter (approximately 100

kHz) and drift, which are mainly due

to the low finesse of the optical

locking cavity and mechanical

instabilities in the feedback phases.

The present optical locking cavity

is partly the result of the narrow

-65

-70

E -75 OQ3 .80 w

1 -85

-90

1

t . 1 . 1

If 'In.

i .8 729 730 731 732 733 734

Frequency (MHz)

Fig. 2. Beatnote at 382 GHz

between two diode lasers detected

relative to the eighth harmonic

of a 47 GHz klystron. Spectrum

analyzer resolution bandwidth was

10 kHz.

38a/SPIEVol. 1837(1992)

TN-217
has a free spectral range of 300 MHz

and a finesse of about 30.

3. RESULTS

By mixing the laser-laser beat

note with increasingly higher

harmonics of the klystron, we have

observed the beat note between the

two diode lasers out to almost 400

GHz. A plot of the signal-to-noise

ratio (SNR) as a

function of the difference frequency

between the lasers is shown in Fig.

3.

70

60

OQ3

50

Z

00

40

100 200 300

Frequency (GHz)

400

Fig. 3. Beatnote SNR as a

function of frequency. Lowest

The data points in Fig. 3 f^^equency data point is the

correspond to the harmonics of the 47 direct laser-laser beatnote.

GHz klystron. The signal-to-noise ^^her data points correspond to

ratio in the baseband response of the i^i^mg the laser-laser beatnote

detector in direct measurements of ^^^^ ^7 ^"^ radiation and its

the laser-laser beatnote is harmonics,

essentially flat out to about 27 GHz.

The actual electrical bandwidth of the present Schottky diode mount is

flat to about 8 GHz. This is presently limited by the imperfect

matching of the whisker and diode mount to the 50 Q transmission line.

Better matching would be helpful, but is not necessary because the

signal-to-noise ratio is limited by noise, not by signal, out to 27 GHz.

This 27 GHz spans more than half of the 47 GHz local oscillator

frequency. Thus we have, at least in principle, complete coverage with

this detector for any laser beat note between dc and 400 Ghz . In

practice, for IF frequencies above about 12 GHz an additional mixing

stage with a standard microwave mixer can be helpful.

We do not know whether the rolloff we see at higher frequencies in

Fig. 3 is due to some optical

detection bandwidth, or whether it is

due to the harmonic generation

efficiency. Most probably it is the

result of both. Evidence for this is

seen in Fig. 4 which shows the

signal-to-noise ratio as a function

of harmonic number for two different

LO frequencies (10 GHz and 47 GHz) . Plotted in this manner, the 47 GHz

data fall off faster than the 10 GHz

data. In contrast, if these data are

plotted as a function of the laser

beat frequency, the signal-to-noise

ratio of the 10 GHz data falls off

70

,^,^^ ^

10 GHz

DQ3

60

50

x. -^». — 47 GHz

^s^^ • \

z

oo

40 - X

30

20 '•

1 2 3456789 10 Hamionic Number

Fig. 4. Beatnote signal-to-noise

ratio as a function of microwave

^ , r- , harmonic for two different

^^^^i^^^ ^^.^^^ l^^^;^^^^^y ^PP^^^^^^^ microwave frequencies, 10 and 47

100 GHz, while the 47 GHz data fall ^u^ GHz

SPIEVol. 1837(1992)/ 389

TN-218
more slowly and extend out to about

400 GHz.

In order to better understand

the general applicability of this

technique we have looked at the

wavelength dependence of the dc

optical detection efficiency for our

diodes. These results are shown in

Fig. 5 and indicate that the optical

detection efficiency is relatively

flat between 600 and 850 nm.

4. CONCLUSION

60 [-

/-*\ e« •| 50 . ^ 40

ka

4-> 1 3» i. S«^ \

0) \ 1 20 o / \ . / \ (X \

ti 10 k oc 500 600 700 800 900

Wavelength (nm)

Fig

the

5. Wavelength dependence of

Schottky diode optical Our results demonstrate that we . . can now directly measure the detection efficiency,

frequency difference between tunable

diode lasers out to at least 400 GHz with a signal-to-noise ratio

greater than 20 dB in a 10 kHz bandwidth. Although we have a long way

to go in direct measurement of optical frequencies, 382 GHz corresponds

to 0.1 % of the optical laser frequency and is significantly higher than

has been measured with other kinds of optical detectors. We are hopeful

that by using higher LO frequencies we can push the useful beatnote

detection bandwidth well beyond our present 400 GHz.^*

5. ACKNOWLEDGMENTS

We gratefully acknowledge the many helpful discussions with J.

Bergquist, K. Evenson, and J.L. Hall. This work was supported in part

by NASA and AFOSR.

6. REFERENCES

1. D.A. Jennings, C.R. Pollock, F.R. Petersen, R.E. Drullinger, K.M.

Evenson, J.S. Wells, J.L. Hall, H.P. Layer, "Direct frequency

measurement of the I2-stabilized He-Ne 473-THz (633-nm) laser," Optics

Lett., Vol. 8, pp. 136-138, 1983.

2. D.J. Wineland, "Laser- to-microwave frequency division using

synchrotron radiation," J. Appl . Phys, Vol. 50, pp. 2528-2532, 1979.

3. H, Telle, D. Meschede, T. Hansch, "Realization of a new concept for

visible frequency division: phase locking of harmonic and sum

frequencies," Optics Lett., Vol. 15, pp. 532-534, 1990.

4. N.C. Wong, "Optical frequency division using an optical parametric

oscillator," Optics Lett., Vol. 15, pp. 1129-1131, 1990.

5. J. C. Bergquist, R.L.Barger D.J. Glaze, Laser Spectroscopy IV , H.

Walther and K.W. Rothe eds . , Springer-Verlag, 120, 1979.

6. J. Helmcke, A. Morinaga, J. Ishikawa and F. Riehle, "Optical

frequency standards," IEEE Trans. Inst. Meas . , Vol. 38, pp. 524-532,

1989.

7. A.M. Akulshin, A. A. Celikov and V.L. Velichansky, "Nonlinear Dopplerf ree spectroscopy of the 6^So-6-'Pi intercombination transition in barium, " Optics Comm., Vol. 93, pp. 54-58, 1992.

i90/SPIEVol. 1837 (1992)

TN-219
8. G.M. Tino, M, Barsanti, M. de Angelis, L. Gianfrani and M. Ingusicio,

"Spectroscopy of the 689nm intercombination line of strontium using and

extended-cavity InGaP/InGaAlP diode laser," Appl Phys . B, pp. 397-400,

1992.

9. L. Hollberg, R. Fox, N. Mackie, A.S. Zibrov, V.L. Velichansky, R,

Ellingsen, and H.G. Robinson, "Diode Lasers and Spectroscopic

Applications, " Tenth International conference on Laser Spectroscopy . M.

Ducloy, E. Giacobino and G. Carry, pp. 347-352, World Scientific, 1992.

10. R.W. Fox et . al . in these proceedings.

11. A. Dax, M. Murtz, J. S. Wells, M. Schneider, E. Bachem, W. Urban

and A. G. Maki, "Extension of Heterodyne Frequency Measurements on OCS

to 87 THz (2900 crn'M , " J. Mol . Spectroc. (accepted).

12. Arthur G. Maki and Joseph S. Wells, Frequency Calibration Tables

From Heterodyne Frequency Measurements , NIST Special Publication 821,

654 pages, 1991. (printed March 1992).

13. Arthur G. Maki and Joseph S. Wells, "New Frequency Calibration

Tables from Heterodyne Frequency Measurements," J. Res. NIST, Vol. 97,

pp. 409-470, 1992; & NIST Standard Reference Database #39, Wavelength

Calibration Tables (1992) . (The NIST SDR 3 9 four floppy disk companion

set of tables of reference data is available upon request from NIST)

.

14. H.-U. Daniel, B. Maurer and M. Steiner, "A broadband Schottky Point

contact mixer for visible laser light and microwave harmonics," Appl.

Phys. B, Vol. 30, pp. 189-193, 1983.

15. J.C. Bergquist, H.-U. Daniel, "A wideband frequency-offset-locked

dye laser spectrometer using a Schottky barrier mixer," Opts. Comm.

,

Vol. 48, pp. 327-333, 1984.

16. B.Dahmani, L. Hollberg, R.Drullinger, "Frequency stabilization of

semiconductor lasers by resonant optical feedback," Opt. Lett., Vol. 12,

p. 876, 1987.

SPIEVol. 1837(1992)/ 391

TN-220
1586 a reprint from Optics Letters

Proposed sum-and-difference method for

optical-frequency measurement in the near infrared

D. A. Van Baak* and L. Hollberg

National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303

Received March 4, 1994 We propose a method for the determination of optical frequencies in the near infrared that is based on the nonhnear

generation of the optical sum and difference frequencies of two near-infrared lasers followed by the comparison of the sum and difference frequencies with standards in the visible and in the far infrared, respectively. We also address questions of practicability and discuss some examples open to the method.

The impressive stability exhibited by lasers locked

to atomic and molecular standards has created a

set of frequency fixed points, and some of these

frequencies have been tied to the Cs-based def- inition of the second through the use of intri- cate frequency-transfer chains. Because of the

complexity of such measurements, there is ample

motivation both to exploit the standard frequencies already established by them and to find simpler frequency-measurement techniques applicable

to general frequency targets. Here we highlight a method especially suitable for measuring optical fre- quencies in the near infrared. The basic idea is that, given two lasers of stable but unknown fre- quency, knowledge of the sum and the difference

of their frequencies suffices to determine both un- known frequencies. For laser frequencies in the near infrared it is often possible to arrange for both

the sum frequency to lie sufficiently near a stan- dard in the visible and the difference frequency to

lie sufficiently near a standard in the far infrared

for such a measurement to be performed. Furthermore, the required nonlinear processes of sum- and

difference-frequency generation can be accomplished

with adequate efficiency. We conclude with examples of possible frequency measurements near laser

wavelengths of 1.338, 1.153, and 1.126 fim.

The method proposed here is an extension of the

bisection method proposed by Telle et al. ^ and demonstrated by Wynands et al} and obeys the same

algebra as the optical parametric oscillator technique

proposed and demonstrated by Wong^ and by Lee and

Wong,* respectively. A special case of the method

has already been demonstrated by Kourogi et al}

We start by assuming that vi and V2 are the frequencies of two stable lasers in the near infrared; of these, we treat one as the target frequency to be measured

and the other as a free variable. If milliwatt beams

from these two lasers are available, then the use

of two separate nonlinear processes will permit the

simultaneous creation of nanowatt beams of the optical sum {v^ = vi + V2) and difference (v^ = vi - V2) frequencies. The idea is to choose the free-variable

near-infrared frequency such that both the sum and

the difference frequencies fall at (or sufficiently near)

0146-9592/94/191586-03$6.00/0

standard optical frequencies previously measured

with respect to the Cs-based standard. In general,

the variation of only one free parameter would not

allow two such matching conditions to be met, but

here we take advantage of three levels of frequency

flexibility. On the first level there is a growing list of well-known frequencies in the visible,^ with fre- quency spacings of the order of 20 THz, which can be

compared with the sum frequency. On the second

level there is a large list of lines of CO2 lasers^ in the

25-33-THz range, with typical frequency spacing of

the order of 20 GHz, which can be compared with the

difference frequency. On the third level there is the

ability to measure a heterodyne beat note of more

than 400 GHz in the visible,^ and more than 30 GHz

near CO2 wavelengths,^ between a nonlinearly derived sum or difference frequency and a visible or C02-based standard. The result is that significant

fractions of the near infrared are accessible to the

proposed technique.

The easiest way to visualize the possibilities open

to the method is to draw the two-dimensional t'iJ'2 plane, in which (through the convention ^2 < ^"1) the arena of interest is the lower 45° wedge of the first quadrant. In the plane, lines of slope - 1 represent

the loci of constant sum frequency; lines of slope -l-l, the loci of constant difference frequency. Figure 1 shows such a plane, with some of the useful stan- dards in the visible shown as candidate sum frequencies and with the C02-laser lines shown as a band of

candidate difference frequencies. Each intersection

of a visible line with the CO2 band defines projections onto the vi and the V2 axes, giving two regions (each

approximately 4 THz wide) accessible to the method;

each new visible standard developed will add another

two such regions. The present state of visible stan- dards, with spacings greater than 20 THz, combined

with a range of only approximately 8 THz of available CO2 lines, implies that certain frequencies vi or

V2 are not yet measurable by the method.

Apart from the need for visible and far-infrared

standards for comparison, this method requires ways

to generate adequate power levels at the sum and

the difference frequencies to be heterodyned against

those standards. The nonlinear processes used will

1994 Optical Society of America

TN-221
October 1, 1994 / Vol. 19, No. 19 / OPTICS LETTERS 1587

300

320

Frequency v (THz)

Fig. 1. A portion of the i^i i'2-frequency sum-anddifFerence plane, which shows loci of constant sum

frequency for some interesting visible-laser frequencies,

and the band of constant difference frequencies available

from CO2 lasers.

thus need to be phase matched, either by angle or by temperature tuning. For generating the sum

frequency one solution is temperature-tuned noncritically phase-matched sum-frequency generation in

lithium niobate (LiNbOs). The dispersion curves for the pure materiaP° give phase-matching loci (for the

o + o—^ e process, where o and e denote ordinary and

extraordinary axes) shown in the vi V2 plane in Fig. 2; the temperatures required are feasible (and will dif- fer somewhat if congruently melting, or MgO-doped,

material is used). For generating the difference fre- quency the nonlinear material must be transparent

beyond 10 /u,m; one attractive possibility is silver

selenogallate^^ (AgGaSe2). Its dispersion curves^^

give the room-temperature phase-matching locus

for noncritically phase-matched difference-frequency

generation (for the e - o—* o process) shown in Fig. 2. The extent to which AgGaSe2 can be temperature

tuned is not yet known; angle tuning of the material

{9 < 90°) maikes accessible the region above and to the left of the locus shown. For regions inaccessible

to AgGaSe2 a useful material (although of smaller

nonlinear coefficient) is proustite^^ (AgsAsSa), which

at room temperature will give angle-tuned e - o—>

difference-frequency generation in the required re- gion for angles = 16-20°."

One more choice can be exercised in the measurement of the difference frequency p^ = vi — i'2- The most obvious method is to illuminate the nonlinear material with input beams at frequencies vi and 1^2 and to extract the output beam at p^- This

beam, and one from a CO2 laser, can then illuminate a far-infrared photodetector to generate the beat

signal. An alternative method is to use the nonlin- ear material as an upconverter, illuminating it with

frequency P2 and a beam from the CO2 laser, to pro- duce an output t^up = J'2 + ^"002; this output can be

combined with the beam of frequency vi to form a

beat note on a photodetector sensitive in the near

infrared (where detectors of greater sensitivity and

bandwidth are available). The phase-matching conditions and the polarization requirements on the nonlinear material are the same for the two alternatives.

One of the attractions of the proposed method is that the only use made of the sum and the difference

frequencies is to compare them by direct heterodyning with reference lasers in the visible and the far

infrared. Given the power available from visible and

CO2 standards serving as local oscillators, the generation of very modest powers at the sum and the dif- ference frequencies will suffice to give adequate beat

signals at the detectors. For example, sumfrequency generation^^ in a 5-cm crystal of LiNbOa

with two 10-mW input beams will give an output

power of the order of 10 nW; when combined on

a photodetector with a visible-standard beam of

power 100 /xW, this output will generate a beat

note with a signal-to-noise ratio^^ of approximately

48 dB in a bandwidth of 100 kHz. Similarly, even

angle-tuned upconversion in a 0.5-cm-long sample of

proustite^^ is efficient enough that a 10-mW beam

at V2, combined wdth a CO2 beam of 100 mW/mm^,

will give an upconverted output of the order of

10 nW; when combined on a photodetector with a 10-mW beam at frequency Pi, this output suffices

to give a signal-to-noise ratio of 52 dB in the same

bandwidth. Such beat-note signal strengths are

sufficient to permit tight phase locking of the lasers

at frequencies vi and P2 to the visible and CO2

standards, if desired. Thus there is no need to create new transfer-standard oscillators at the sum

and the difference frequencies.

The first application of this sum-and-difference

method was demonstrated by Kourogi et al.,^ who

locked a solid-state laser at 1.06 /xm and a diode laser

30a

280-

260-

240-

260 280

Frequency v (THz)

Fig. 2. Phase-matching loci in the i'ii'2-frequency plane.

The family of curves gives the phase-matching loci for temperature-tuned type-I sum-frequency generation in pure LiNbOs, calculated with the data of Ref. 10. The

dashed curve gives the phase-matching locus for type-I

difference-frequency generation in AgGaSe2 at room temperature, calculated with the data of Ref. 12. TN-222
1588 OPTICS LETTERS / Vol. 19, No. 19 / October 1, 1994

at 1.55 fxm by beating their sum frequency against an l2-stabilized 633-nm He-Ne laser and their dif- ference frequency against a CH4-stabilized 3.39-/im

He-Ne laser. With v^ and i^d thus fixed there is no

slack in the system, and it is indeed fortunate that

the required vi falls within the range of Nd-based

solid-state lasers and that the resulting v^ is of such

interest to the optical-fiber communication band.

As another possible application of the method, we mention the availability of diode-pumped monolithic Nd:YAG lasers^^ at wavelengths of 1.064, 1.319,

and 1.338 /xm; the first two of these have had their

doubled frequencies stabilized to absorption lines

in iodine cells, ^^ and because of their compact size

and their excellent passive stability all three are at- tractive candidates for absolute-frequency measurements. The three frequencies available are near

281.63, 227.26, and 224.06 THz, respectively. With

the available CO2 lines the last of these is directly ac- cessible to the sum-and-difference technique: if we

choose the 1.338-/u.m laser to give 1^2 = 224.06 THz

and build a 1.201-yitm laser (using available diode

lasers or the Cr-doped forsterite^° laser system) to provide vi = 249.55 THz, then the sum frequency

lies at the 473.61-THz 633-nm He-Ne standard, and

the difference lies at 25.49-THz, near enough to the

25.475-THz P(38) line of the ^^COz hot band.

Another example is a remeasurement of the

1.153-/Am He-Ne laser frequency (whose second

harmonic, stabilized by absorption in iodine, has

already provided a 520-THz standard in the visible).

The direct remeasurement of the frequency vi =

260.103 THz at 1.153 yu.m is possible, given a commercially available diode-laser source at 1.305 /xm

to provide 1^2 = 229.77 THz, because the sum fre- quency of 489.880 THz matches the l2-stabilized

612-nm He-Ne visible standard, and the difference

frequency of 30.326 THz can be compared with the

i^C02 P(8) line at 30.315 THz. This remeasurement

could provide a very tight consistency check on fre- quencies already measured by means of more complicated frequency chains.

A final example is a measurement of the

266.188-THz frequency of the 1.126-/Am Nd:FAP

laser, whose fourth harmonic matches the clock

transition of the mercury ion-trap standard.^^ The

use of a commercially available 1.446-^im, 207.394-

THz diode-laser system would yield a sum frequency

within 30 GHz of the 633-nm Ij-stabilized He-Ne

standard and a difference frequency of 58.794 THz

at the P5(13) line of the ^^Ci^O laser.^^ This carbon

monoxide frequency could in turn be stabilized with

a metal-insulator-metal diode to double and to mix with the 29.407-THz R(28) line of the i^QieOa

laser. The necessary sum- and difference-frequency

generation can be phase matched by temperature

tuning in LiNbOa and by angle tuning in AgGaS2,

respectively.

We thank U. Simon and J. L. Hall for stimulating

discussions and NASA and the U.S. Air Force Office

of Scientific Research for supporting this research.

^Permanent address. Department of Physics,

Calvin College, Grand Rapids, Michigan 49546.

References

1. H. R. Telle, D. Meschede, and T. W. Hansch, Opt. Lett. 15, 532 (1990).

2. R. Wynands, T. Mukai, and T. W. Hansch, Opt. Lett. 17, 1749 (1992).

3. N. C. Wong, Opt. Lett. 15, 1129 (1990).

4. D. Lee and N. C. Wong, Opt. Lett. 17, 13 (1992).

5. M. Kourogi, K. Nakagawa, and M. Ohtsu, IEEE J. Quantum Electron. 29, 2693 (1993).

6. Examples include the l2-stabilized 473-THz (633-nm),

490-THz (612-nm), and 520-THz (doubled 1.15- fj-m)

He-Ne lasers ["Documents concerning the new defi- nition of the metre," Metrologia 19, 163 (1984)] and

the Rb-stabilized 385-THz (778-nm) standard [F. Nez,

F. Biraben, R. Felder, and Y. Millerioux, Opt. Commun. 102, 432 (1993)]. Standards of accurately measured wavelengths include the 456-THz (657-nm)

Ca-stabilized and the 582-THz (514-nm) l2-stabilized Ar^ systems. A standard likely to be measured soon

is the 563-THz (532-nm) Iz-stabilized doubled NdYAG

system.

7. More than 400 CO2 lines are listed in A. G. Maki and

J. S. Wells, Natl. Inst. Stand. Technol. Spec. Publ. 821,

9 (1991).

8. S. Waltman, A. Romanovsky, J. Wells, R. W. Fox,

L. Hollberg, M. P. Sassi, and H. G. Robinson, Proc.

Soc. Photo-Opt. Instrum. Eng. 1837, 386 (1992); Waltman has now extended heterod5me techniques beyond

600 GHz.

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J. Appl. Phys. 75, 4243 (1994).

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(1966).

11. R. S. Feigelson and R. K. Route, Opt. Eng. 26,

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R. K. Route, R. S. Feigelson, and J. van der Laan,

Appl. Phys. Lett. 47, 786 (1985).

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(1973).

13. K. F. Hulme, O. Jones, P. H. Davies, and M. V. Hobden, Appl. Phys. Lett. 10, 133 (1967).

14. M. V. Hobden, Opto-electronics 1, 159 (1969).

15. T. H. Jeys, A. A. Brailove, and A. Mooradian, Appl.

Opt. 28, 2588 (1989).

16. K. Nakagawa, M. Kourogi, and M. Ohtsu, Appl. Phys.

B 57, 425 (1993).

17. J. Warner, Appl. Phys. Lett. 12, 222 (1968).

18. T. J. Kane and R. L. Byer, Opt. Lett. 10, 65 (1985);

W. R. Trutna, Jr., D. K. Donald, and M. Nazarathy,

Opt. Lett. 12, 248 (1987); A. B. Neilson, W. A. Clarkson, and D. C. Hanna, Opt. Lett. 18, 1426 (1993).

19. A. Arie, S. Schiller, E. K. Gustafson, and R. L. Byer,

Opt. Lett. 17, 1204 (1992); A. Arie, M. L. Bortz,

M. M. Fejer, and R. L. Byer, Opt. Lett. 18, 1757

(1993); J. L. Hall, in Proceedings of the Eleventh In- ternational Conference on Laser Spectroscopy, L. A. Bloomfield, T. F. Gallagher, and D. J. Larson, eds. (American Institute of Physics, New York, 1994).

20. V. Petricevic, S. K. Gayen and R. R. Alfano, Appl. Opt.

28, 1609 (1989); Opt. Lett. 14, 612 (1989).

21. J. C. Bergquist, F. Diedrich, W. M. Itano, and

D. J. Wineland, in Frequency Standards and Metrology, A. De Marchi, ed. (Springer-Verlag, Berlin, 1989).

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432 (1990).

TN-223
Reprinted from Journal of the Optical Society of America B 323

External-cavity difference-frequency source near 3.2 /xTa^

based on combining a tunable diode laser

with a diode-pumped Nd:YAG laser in AgGaSz

U. Simon

Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251-1892

S. Waltman

Time and Frequency Division, National Institute of Standards and Technology, 235 Broadway, Boulder, Colorado 80303

I. Loa and F. K. Tittel

Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251-1892

L. Hollberg

Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303

Received April 29, 1994; revised manuscript received August 26, 1994 AgGaS2 has been used to generate more than 2 /tW of cw mid-infrared radiation near 3.2 ^m by difference- frequency mixing of the outputs of an extended-cavity diode laser near 795 nm (pump wave) an a compact

diode-pumped Nd:YAG laser at 1064 nm (signal wave). An external ring enhancement cavity was used to build up the signal power inside the nonlinear crystal by as much as 14.5 times. The novel mid-infrared source incorporating a single diode laser could be angle-tuined from 3.155 to 3.423 /^m (from 3170 to 2921 cm"'). This system was used to detect the Doppler-broadened fundamental t-a -asymmetric stretch vibration of methane

(CH4) by both direct and wavelength-modulation absorption spectroscopy.

1. iisrrRODUcnoN

Difference-frequency generation (DFG) of continuous- wave (cw) tunable infrared single-frequency radiation

has proved to be a useful technique for high-resolution

infrared spectroscopy but was limited until recently to wavelengths shorter than 5 fj-m by the infrared trans- mission characteristics of the available nonlinear optical

materials (LiNbOa and LilOs).^ Recent advances in the

grov^rth and the fabrication of nonlinear optical materials,

such as AgGaS2 and AgGaSe2, now offer a convenient means for extending the wavelength coverage of DFG

sources to a wider wavelength range (3-18 fj.m).^-^ Semiconductor diode lasers are particularly attractive as pump sources in the nonlinear DFG process, as their compact size and ease of operation will per- mit the construction of portable and robust mid-infrared

laser sources that are especially suitable for environmental remote sensing, pollution monitoring, chemical

analysis, and medical research. Until now the nonlinear frequency conversion efficiency of all-diode-laser DFG sources has been limited by the relatively low out- put power of commercially available single-mode III-V

diode lasers. We reported several nanowatts of cw midinfrared radiation"* near 5 fim, obtained by difference- frequency mixing of two visible -near-infrared diode

lasers (2 and 10 mW) in AgGaS2. Using KTP as the

nonlinear optical material, Wang and Ohtsu^ generated

0740-3224/95/020323-05$06.00 ©1995 Optical Society of America

as much as 300 nW of near-infrared radiation ( ~ 1.6 ^m)

from two diode lasers (50 mW each). One way to in- crease the infrared DFG output power is to use opti- cal semiconductor amplifiers to boost tae power of the

single-mode diode lasers to the watt level. Recently we demonstrated difference-frequency mixing of a high- power, GaAlAs, tapered, traveling-wave, semiconductor

amplifier^ with a cw Ti:Al203 laser in a 45-mm-long

AgGaS2 crystal cut for type-I noncritical phase matching

at room temperature. The diode amplifier was injection

seeded by a low-power, single-mode, index-guided diode

laser and provided 1.5 W of 860-nm radiation for the

DFG mixing experiment. As much as 47 /xW of cw in- frared radiation and 89 /u.W of pulsed infrared radiation,

tunable near 4.3 /j.m, was generated. Alternatively, the

infrared DFG output power can be increased by use of the high circulating fields inside optical resonators with

the nonlinear crystal placed either in an external (passive) enhancement cavity or in one of the pump-laser

cavities. The latter approach was investigated by Dixon

and co-workers^ with a nonlinear KTP or AgGaS2 crystal

introduced into a Nd:YAG laser cavity. In this paper we describe a DFG source that uses a

tunable extended-cavity diode laser (ECDL) near 795 nm

(500-kHz linevsridth), a diode-pumped monolithic Nd:YAG

laser at 1064 nm (5-kHz linewidth), and an external

ring enhancement cavity around a AgGaS2 crystal. The

enhancement cavity resonates the signal wavelength

TN-224
324 J. Opt. Soc. Am. B/Vol. 12, No. 2/February 1995 Simon et al.

anamorphic

prism pair

extended cavity

diode laser 795 nm

chopper

cavity feedback

signal

prism separates

diode and Nd:YAG

laser beams

InSb

detector

sample cell #o

Ge

filter cavity feedback ^ * signal

cavity t I 1 reflection signal Fig. 1. Experimental setup used to mix the outputs of an ECDL near 795 nm and a diode-laser-pumped Nd:YAG laser at 1064 nm

in AgGaS2 cut for 90° type-I phase matching. The Nd:YAG laser radiation inside the mixing crystal is resonantly enhanced by

a three-mirror ring buildup cavity.

(Nd:YAG laser), thereby increasing the signal power

present inside the mixing crystal. The infrared power

scales as the product of the signal and the pump powers, and hence its enhancement depends linearly on the

buildup factor.

2. EXPERIMENTAL SETUP

The experimental diagram in Fig. 1 shows the ring

buildup cavity, the ECDL, and the diode-pumped Nd:YAG

laser. The ECDL® uses an index-guided, quantum-well

laser,^ a 0.60 N.A. collimating objective, and a reflection grating (2400 lines/mm) used in the Littman configuration. To improve the tuning characteristics of the

ECDL, the output facet of the laser chip was antireflec- tion (AR) coated with AI2O3 and Hf02. Most high-power

diode lasers are supplied from the manufacturer with

reduced-reflectance coatings on the front facet and highreflectance coatings on the back facet. These standard

high-power lasers will work well in an ECDL configuration, but further reduction of the front facet reflectance permits a broader timing range. An anamorphic prism

pair (6x) and a telescope were used to match the spatial

mode of the ECDL approximately to the Nd:YAG laser mode in the ring buildup resonator. The signal wave was provided by a cw diode-pumped

monolithic Nd:YAG ring laser^° at 1064 nm. Pump- and

signal-wave polarizations were perpendicular for type-I

phase matching in AgGaS2. Both beams were spatially

overlapped with a polarizing beam splitter. Telescopes were used in both beam paths to match the beam waists at the center of the crystal. The beam waists (half-width at

1/e^ of maximum) were set to ~20 yum in both vertical and

horizontal planes, which is close to optimum focusing.^

To minimize thermal effects on the nonlinear con- version efficiency, the signal wave at 1064 nm rather

than the pump wave at 795 nm was resonated in the

buildup cavity. Owing to poor thermal conductivity

(~0.115 W cm"^ K"^), AgGaS2 suffers from thermal lens- ing problems, especially if high-power pump sources at wavelengths close to the absorption-band edge of the material (~500 nm) are used.^^ Both to avoid degradation

of the wave fronts by thermal lensing effects and to have

a broad angle tuning range, we chose a short AgGaS2

mixing crystal (5 mm long) in this experiment. Aft;er AR coatings were applied to the crystal facets, the total linear absorption loss of the AgGaS2 crystal at 1064 nm

was measured to be —1.5%.

The ring buildup cavity consisted of three flat mirrors

(M1-M3) and two intracavity lenses (Li, fi-^ = 50 mm;

L2, fii = 25 mm) together with a 5-mm-long AgGaS2

crystal cut for type-I 90° phase matching. With a crystal aperture of 5 mm this configuration gave us access

to phase-matching angles between 90° and 67°. The to- tal length of the ring cavity was ~28 cm, and the fiill angle on mirror Mi was —3°. The facets of the nonlin- ear mixing crystal were coated with a single-layer AI2O3

AR coating for low loss at 1064 nm (i? == 4 x 10'^). In

spite of the quality of the coatings, passive losses from

the lenses {R < 0.25% per surface, nominally) reduced

the cavity buildup. However, the cavity setup shown in

Fig. 1 could be realized almost exclusively with standard

Nd^YAG laser optics. Mirrors M2 and M3 were highreflectance coated (nominally R ~ 98.5% and R ~ 99.7%,

respectively) for s-polarized light at 1064 nm. The in- frared radiation generated inside the crystal was coupled

out through mirror M2, which was an AI2O3 substrate

high-reflectance coated for 1064 nm with transmission

T = 78% for the generated difference-frequency radiation near 3 fim. Mirror Mi was used as the input coupler,

with T == 4% (nominally) at 1064 nm chosen to impedance

match^^ the buildup cavity to the signal-wave losses. Approximately 85% of the diode laser power at 795 nm inci- dent u{K)n the cavity could be coupled through Mi.

TN-225
Simon et al. Vol. 12, No. 2/February 1995/J. Opt. Soc. Am. B 325

3. RESULTS AND DISCUSSION

With no mixing crystal inside the buildup cavity, ap- proximately 75% of the incident Nd:YAG laser power was

coupled into the cavity and enhanced by a factor of —24.5,

corresponding to a total cavity round-trip loss of —4.1%.

After the crystal was introduced into the cavity, the cou- pling increased to —83%, indicating a better match of the

input coupler transmission to the total cavity round-trip

loss. However, owing to the additional absorption of the

mixing crystal, the buildup factor decreased to —14.5, cor- responding to a total cavity round-trip loss of —6.9%.

The coupling efficiency of the Nd:YAG laser power into the buildup cavity was determined from the power re- flected off the input coupler Mi while the buildup cavity was tuned over the resonance with the piezoelectrictransducer- (PZT-) driven mirror Mi. The circulat- ing power inside the cavity could be inferred from the

Nd:YAG laser power that leaked through mirror M3. After traversing a 60° prism that separated the Nd:YAG

laser beam from the diode laser beam, the transmitted

signal was also used to lock the cavity resonance to the

Nd:YAG laser frequency with a standard modulationcontrol scheme.

The difference-frequency radiation generated in the AgGaS2 crystal was collimated outside the

buildup cavity with a CaF2 lens (5-cm focal length)

and then detected by a liquid-N2 -cooled photovoltaic

detector (InSb with a 1-mm-diameter area and a fac- tory calibrated responsivity of — 1.248 A/W at 3 /xm).

A broadband AR-coated germanium filter blocked

pump and signal waves while transmitting the 3-^m

difference-frequency radiation. Using 1064.504 nm as the signal wave, we found type-I

90° phase matching at a diode laser wavelength of 795.5 nm, corresponding to a difference-frequency wavelength of -3.148 fim (3176.7 cm~M. The laser wavelengths were determined with a spectral resolution of —30 MHz and an absolute accuracy of —500 MHz with

the radiation coupled via a single-mode probe fiber into a lambdameter.^^ The DFG phase-matching bandwidth at a phase-matching angle of 90° is shown in

Fig. 2. This was recorded by tuning the wavelength

of the ECDL. The large phase-matching bandwidth

of —8.8 cm"^ (FWHM) is in good agreement with the

theoretically calculated value of 8.1 cm~^, which results mainly from the short length (5 mm) of the nonlinear

optical mixing crystal.

Figure 3 depicts the mid-infrared DFG power at 90°

phase matching for a fixed diode-laser power of 12.1 mW

(measured after the input coupler of the buildup cavity) as a function of the Nd:YAG laser power incident upon

the enhancement cavity. The NdTAG laser power was

varied by the relative angle between a polarization rota- tor and an analyzer. Values shown are corrected for the

3-yLtm transmission loss of the optical components exter- nal to the cavity (T == 89%), but not for the transmission loss of the infrared light in the output coupler of the

buildup cavity {T == 78%). The plot shows the expected

linear dependence of the generated infrared power on the

signal power. However, the experimentally determined

slope efficiency of -4.1 nW/mW at 12.1 mW of diode laser power is approximately four times less than the value

that was predicted based on the theoretical model (given

in Refs. 2 and 3) assuming ideal Gaussian beams and

an effective nonlinear coefficient of 12 x 10"^^ m/V for type-I 90° phase matching in AgGaS2. This deviation

between experiment and theory was also found in pre- vious AgGaS2 DFG experiments.^ A maximum cw DFG

power of —1.7 /iW was obtained after the external cavity with —13.6 mW of diode laser power and 360 mW of Nd:YAG laser power. Taking into account the buildup

cavity output coupler transmission at 3 jj.m, this cor- responds to —2.1 /iW of DFG power after the mixing

crystal. Even at the high-signal-power levels circulating

inside the buildup cavity, the infrared DFG power was

the same for both cw and pulsed modes of operation. For cw operation the buildup cavity resonance was locked to

Diode Laser Wavelength (nm) 796.5 796 795.5 795

m - io

a.Oa.O

£ -

. . I -L-l. _I_L

90» type I PM. AgGaSj

Nd:YAG laser 1064.504 nm

_ FWHM = 8.78 cm

'I I n II I I I |1 I I I

I

I I I I

I

I I I I

I I I I I p ri I 3155 3160 3165 3170 3175 3180 3185 3190

Infrared DFG Frequency (cm')

Fig. 2. Phase-matching bandwidth of the DFG mixing process

at a phase-matching angle of 90°, recorded with the diode laser wavelength tuned. The large bandwidth of >8 cm~^ (FWHM)

is due to the 5-mm length of the crystal used in the nonlinear

optical mixing.

•a

1.2

1 -

0.8-

0.6-

0.4-

0.2-

I ' I' I ''''' I' 'I ' J—L

diode laser at 79S.S nm

with 12.1 mW of cw power

slope: 4.1 nW/mW

I I I I

I

I I I I

I

I I I I II I I I II I I I 50 100 150 200 250

Incident Nd:YAG Power (mW)

Fig. 3. Grenerated infrared DFG power as a function of the Nd:YAG laser power incident upon the enhancement cavity. For this measurement the diode laser power was fixed at

12. 1 mW (measured after the input coupler of the buildup cavity). Values shown are corrected for transmission losses of the optical

components external to the buildup cavity at a wavelength of 3 ^im. TN-226
326 J. Opt. Soc. Am. B/Vol. 12, No. 2/February 1995 Simon et al.

Infrared DFG Frequency (cm'')

3150 3100 3050 3000 2950

I I I ' I I I ' ' '

I ' ' ' 'I '

I I I

I

I I I I 800 805 810 815

Diode Laser Wavelength (nm)

Fig. 4. Tuning range and power output of the infi-ared DFG

radiation. Infrared tuning was accomplished by variation of the wavelength of the diode laser for a given orientation of the mixing

crystal.

the Nd:YAG laser while pulsed operation was obtained

by sweeping the cavity over its resonance in —0.4 ms and

detecting the transmitted infrared signal. This indicates

that, even at circulating power levels of >3.5 W inside

the cavity, no degradation of the nonlinear conversion ef- ficiency by thermal lensing effects was observed.

With the wavelength of the ECDL tuned from 795 to 812 nm (over ~17 nm) and the phase-matching angle

of the mixing crystal adjusted (over —15°), the infrared

wavelength could be tuned from 3.155 to 3.423 /im

(3170-2921 cm"^). Figure 4 shows the relative infrared

DFG power as a function of the diode laser and infrared

wavelengths over the entire tuning range of the diode

laser. We recorded the tuning curve by setting the

phase-matching angle to a given value and tuning the

diode laser over the DFG phase-matching bandwidth.

The DFG power levels shown here are normalized to the incident diode-laser power, which varied from 10 to 15 mW over this tuning range. We achieved continuous

infrared tuning ranges of >40 GHz without mode hopping

by scanning the piezoelectric transducer on the ECDL.

Figure 4 indicates that for phase-matching angles above

80° the effective phase-matching length^"* is actually

larger than the physical length of the mixing crystal,

which results in a nearly constant infrared DFG power

between 90° and 80°. For phase-matching angles smaller

than 80° the effective phase-matching length drops

below the physical length of the crystal because of walk-off

effects, resulting in an equivalent drop of the generated

infrared power. Figure 5 shows the experimentally measured phase-matching points compared with the values

theoretically calculated from the Sellmeier coefficients given in Ref. 15. Rotating the nonlinear crystal in the

buildup cavity introduced a shift of the laser beams.

Therefore at each crystal angle a realignment of the

cavity was required. This can be avoided, however, by

use of two crystals in a walk-off compensated cavity configuration as demonstrated by Bosenberg et al.

^^

To demonstrate the applicability of this compact all- solid-state DFG source, we recorded a portion of the

absorption spectrum of the fundamental I's -asymmetric

stretch vibration of methane (CH4) around 3.2 /xm (see

Fig. 6). The phase-matching angle was set to 90° and the

ECDL wavelength was tuned over an —30-GHz portion

of the DFG phase-matching bandwidth. Only 100 mW

of incident Nd:YAG laser power was used to record this spectrum, which corresponds to an infrared power level of —0.45 //W. The methane pressure in the 50-cm-long

absorption cell was set to the vapor pressure of methane

at 77 K (1333 Pa, 10 Torr) with a liquid-Nz -cooled reservoir. Figure 6 depicts a portion of the recorded methane

absorption spectrum and demonstrates the high signal- to-noise ratios that could readily be obtained. Trace 1 of Fig. 6 shows a (single-sweep) background-free absorption spectrum recorded by wavelength modulation of the diode laser (cavity length), with the 2/"-absorption signal

detected by lock-in techniques. Trace 2 of Fig. 6 shows

825 Nd:YAG laser at 1064.50 nm

70 75 80 85

Internal Phasematching Angle (deg)

Fig. 5. Comparison of the experimentally determined (data

points, circles; fit, top solid curve) and theoretically calculated (bottom curve) phase-matching angles. The calculated values

are based on the Sellmeier equations given in Ref 15.

trace 1

trace 2

3174.2 3174.4 3174.6 3174.8 3175.0 3175.2 3175.4

Infrared DFG Wavelength (cm"'')

Fig. 6. Methane absorption spectrum near 3.2 ^m (fundamental »'3 -asymmetric stretching motion), obtained with a 50-cm-long

absorption cell and a methane pressure of —10 Torr. Trace

1, 2/"-absorption signal (single sweep) recorded with a lock-in amplifier. The spectnun was recorded at a phase-matching

angle of 90° with the diode laser wavelength tuned over a 30-GHz portion of the phase-matching bandwidth; trace 2, a

direct absorption signal obtained by the averaging of 10 sweeps.

TN-227
Simon et al. Vol. 12, No. 2/February 1995/J. Opt. Sec. Am. B 327

the direct absorption spectrum of the same Unes recorded

with a digital oscilloscope averaging 10 sweeps. The

buildup cavity was resonant only at 1064 nm, with no measurable buildup at the diode laser wavelength. Thus

no channeling on the baseline of the methane spectrum was observed when the diode laser wavelength was tuned.

4. CONCLUSION

In conclusion, more than 2 /iW of cw tunable infrared ra- diation near 3.2 fim have been generated by difference- frequency mixing an ECDL (pump source) near 795 nm

and a diode-pumped Nd:YAG laser (signal source) in AgGaS2. The signal source was resonated in a ring en- hancement cavity, resulting in buildup factors for the

signal power of as much as 14.5. The compact infrared

DFG source (footprint of 0.5 m^) could be tuned from 3.155

to 3.423 fim (3170 to 2921 cm~^), which coincides with the

fundamental CH stretch vibrations of the vast majority

of molecular organic compounds. The DFG source was

used to detect the fundamental t-a-asjanmetric stretching

motion of methane by direct and modulation spectroscopy.

Methane was chosen in this feasibility study because of

its convenience and its environmental significance (it is an important greenhouse gas that supports ozone for- mation in polluted air). With the Nd:YAG laser line at

1.32 fim as the signal wave and a tunable high-power

ECDL near 855 nm as the pump wave, angle-tunable midinfrared radiation from 2.42 to 2.57 yu.m (phase-matching

angles 90-75°) could be generated. The cavity-enhanced

DFG source demonstrated here is a useful system whenever low power consumption, relatively low cost, and

no-water cooling are important and for wavelength re- gions in which high-power semiconductor GaAlAs optical

amplifiers^ are not available. This makes it an attractive tool for wide range of applications in the mid-infrared

wavelength range. ACKNOWLEDGMENTS

This work has been supported in part by the Robert A. Welch Foundation, the National Science Foundation, the

U.S. Air Force Office of Scientific Research, and NASA.

The authors thank J. L. Hall for significant contributions and Lightwave Electronics, Inc., for providing the

diode-pumped Nd'YAG laser^" used in this work. U. Simon gratefully acknowledges the support of the A. v. Humboldt-Foundation by a F. L3Tien Fellowship.

REFERENCES AND NOTES

1. A. S. Pine, "Doppler-limited molecular spectroscopy by

difference-frequency mixing," J. Opt. Soc. Am. 64, 1683

(1974); M. G. Bawendi, B. D. Rehfuss, and T. Oka, "Laboratory observation of hot bsinds of H3*," J. Chem. Phys.

93, 6200 (1990).

2. P. Canarelli, Z. Benko, R. F. Curl, and F. K. Tittel, "A continuous-wave infrared laser spectrometer based on difference-frequency generation in AgGaS2 for highresolution spectroscopy," J. Opt. Soc. Am. B 9, 197 (1992).

3. A. H. Hielscher, C. E. Miller, D. C. Bayard, U. Simon,

K. P. Smolka, R. F. Curl, and F. K. Tittel, "Optimization

of a midinfrared high-resolution difference-frequency laser spectrometer," J. Opt. Soc. Am. B 9, 1962 (1992).

4. U. Simon, C. E. Miller, C. C. Bradley, R. G. Hulet, R. F. Curl, and F. K. Tittel, "Difference-frequency generation in AgGaS2

by use of single-mode diode-laser pump sources," Opt. Lett. 18, 1062 (1993).

5. W. Wang and M. Ohtsu, "Frequency-tunable sum- and

difference-frequency generation by using two diode lasers in a KTP crystal," Opt. Commun. 102, 304 (1993).

6. U. Simon, F. K. Tittel, and L. Goldberg, "Difference- frequency mixing in AgGaSa by use of a high-power GaALAs

tapered semiconductor amplifier at 860 nm," Opt. Lett. 18,

(1993).

7. F. J. Effenberger eind G. J. Dixon, "2.95 fim intracavity

difference-frequency laser," in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America,

Washington, D.C., 1992), p. 59; "Intracavity difference fre- quency generation," in Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 380.

8. C. E. Wieman and L. HoUberg, "Using diode lasers in atomic

physics," Rev. Sci. Instrum. 62, 1 (1991).

9. SDL, Inc., Model SDL5410C (mentioned to help to specify

experimental parameters; other sovu-ces may be suitable). Lightwave Electronics, Inc., Model 122-1064-500-F, 500 mW

(mentioned to help to specify experimental parameters;

other sources may be suitable). C. E. Miller, W. C. Eckhoff, U. Simon, F. K Tittel, and

R. F. Curl, "Difference-frequency laser spectrometer us- ing AgGaSa: problems encountered in power scaling," in Nonlinear Optics for High-Speed Electronics and Optical

Frequency Conversion, N. Peyghambarian, H. Everitt, and

R. C. Eckardt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.

2145, 282 (1994).

12. W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, "Efficient second harmonic generation of a diode-pumped cw Nd:YAG

laser using monolithic MgOXiNbOs external resonant cavities," J. Quantum Electron. 24, 913 (1988).

13. J. L. Hall and S. A. Lee, "Interferometric real-time display of cw dye laser wavelength with sub-Doppler accuracy," Appl.

Phys. Lett. 29, 367 (1976).

14. R. L. Byer and R. L. Herbst, "Parametric oscillation and

mixing," in Nonlinear Infrared Generation, V. R. Shen, ed. (Springer-Verlag, New York, 1977), pp. 81-137.

15. Y. X. Fan, R. C. Eckardt, R. L. Byer, R. K Route, and

R. S. Feigelson, "AgGaS2 infrared parametric oscillator," Appl. Phys. Lett. 45, 313 (1984).

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y8-BaB204 optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).

10.

11.

TN-228
September 1, 1996 / Vol. 21, No. 17 / OPTICS LETTERS 1387

Division by 3 of optical frequencies by

use of difference-frequency generation in noncritically

phase-matched RbTiOAs04

Olivier Pfister

fILA, National Institute of Standards and Technology and University of Colorado. Boulder. Colorado 80309-0440

Manfred Miirtz

Institute fiir Angewandte Physik der Universitdt Bonn. D-53115 Bonn. Germany

Joseph S. Wells and Leo Hollberg

National Institute of Standards and Technology. Boulder, Colorado 80303

James T. Murray

Optical Sciences Center, University of Arizona, Tucson, Arizona 85721-0001

Received March 7, 1996 A new scheme for coherently connecting optical frequencies in a 3:1 ratio has been demonstrated. To phase

lock a Nd:YAG laser at 1064 nm with a CO overtone laser at 3192 nm, we generated their difference frequency

in RbTiOAs04 (RTA) and beat it against the second harmonic of 3192 nm that was generated in AgGaSe2-

The ability to measure optical frequencies is a critical technology for tests of QED, as demonstrated in the

beautiful experiments of Hansch and co-workers^ and

Biraben and co-workers.'' A number of promising new optical frequency references have been pro- posed in recent years, including trapped ions^* and

cooled Ca atoms. ^ One expects higher precision

and accuracy with standards at optical frequencies

rather than the Cs primary frequency standard

at 9.2 GHz. The ultimate linewidth of the Hg+ -based

system, for example, is 1 Hz at 10^^ Hz, with a

projected stability of 10~^^ r""^^^ (t is the averaging

time). A serious limitation to the feasibility of optical

references is that it is difficult to measure optical

frequencies and to transfer the stability to lower fre- quencies, where it is compatible with electronics. This

is also what makes the connection of these potential new references to each other and to the microwave

standards an interesting if formidable task. A few modern ideas for optical frequency synthesis are now being developed, including the optical

cyclotron,^ the bisection method of Telle et al.J

four-wave mixing techniques,* and optical comb generators.® These ideas often feature an attractive way to address the problem, which is the use of nonlinear mixing crystals together with solid-state and diode lasers. Divide-by-3 schemes are of particular interest for many reasons. First, as Wong discussed,'*' building

a frequency chain that could go from the Cs clock up

to visible frequencies might require only a few lasers

if 2:1 and 3:1 optical parametric oscillation (OPO) fre- quency dividers were combined. Also, a 3:1 frequency

connection is a convenient way to jump from tunable

visible lasers (diodes, Ti:sapphire) to the gas lasers

that are established IR frequency standards (He-Ne

laser locked on CH4 at 3.39 /unn, CO2 laser locked on

OSO4 at 10 yu,m). Finally, we could combine a 3:1 divider with the twice-frequency-doubled Nd:FAP

laser (1126 nm), which will be used at the National

Institute of Standards and Technology to excite the

282-nm Hg^ transition." Such a combination would

produce a wavelength of 3378 nm, which is close to the methane reference. If this divide-by-3 system were implemented with the 1126-nm wavelength (one

fourth of the Hg^ "clock" transition), we could readily

generate an array of reference lines across the visible and the near IR. Adjacent elements of this array

would be spaced by one twelfth of the Hg^ transition

frequency. In this case the wavelengths would be ap- proximately 3378, 1689, 1126, 844, 676, 563, 483, 422,

375, 338, 307, and 282 nm. For the present study,

with a Nd:YAG laser instead of a Nd:FAP laser, the

wavelengths would be 3192, 1596, 1064, 798, 638, 532,

456, 399, 355, 319, 290, and 266 nm. In part to test the feasibility of these schemes, we have already used

difference frequency generation (DFG) to generate

wavelengths close to some of those listed above: For

example, a diode laser at 657 or 800 nm and a Nd:YAG

laser at 1064 nm have been mixed to produce 1700

or 3200 nm,^^ respectively. Recent high-precision

measurements'^ of an I2 electronic transition near 532 nm do make the Nd:YAG laser an interesting star- ting point.

A 3:1 connection (through second-order frequency

mixing) is achievable with two input waves, such

as sum-frequency generation (/ + 2f ^^ 2>f) or DFG

{Sf - f ^ 2f,3f - 2/ ^ /), or with a single input

wave, that is, OPO {3f ^ f + 2f). An exact con- nection requires another mixing stage to lock the 3:1 ratio (the phase-matching requirements of the crystal are not precise enough). We need two different

mixings of {f,2f,3f) to guarantee a division by 3.

TN-229
1388 OPTICS LETTERS / Vol. 21, No. 17 / September 1, 1996

For example, we can use OPO (3/" >-*/' + 2/') and

second-harmonic generation (SHG, f

^^ 2f), or we can

use DFG {3f - f ^ 2f) and SHG (/" ^ 2f), to obtain a beat note at 2f, which can then be used to phase lock the OPO resonator to the 3/" pump or

to lock the two DFG input lasers together, respectively.

The OPO beat note is actually much less sensitive to pump frequency noise than is the DFG beat note, for which the fluctuations of two independent lasers do

not cancel each other. However, because of the additional problems related to OPO threshold, and because

two good laser sources are available, we chose to build a DFG-SHG setup first. The frequencies involved are

/(1064 nm) - /(3192 nm) ^ /"(ISge nm) (1) The input wavelengths were provided by a diodepumped Nd:YAG monolithic ring laser (output power

530 mW) and by a CO overtone laser. ^'* CO over- tone lasers are not common but are nonetheless re- markable mid-IR sources. They were first developed

in W. Urban's group in Bonn, Germany. They pro- vide laser oscillation on 400 rotational lines, spread

over 28 vibrational Ay = 2 transitions between 2.6 and

4.1 /Am, with an output power as high as 200 mW in our

case. Fortuitously, three times the frequency of the

3193.5-nm P2i(14) line is only 4 GHz away from the

center of the Nd:YAG gain curve. This falls well

within the 30-GHz temperature-tuning range of the

Nd:YAG monolithic oscillator. Of the many crystals that permit phase matching

for interaction (1) with reasonable nonlinear coeffi- cients and low absorption (LiNbOs, KNbOs, AgGaS2,

proustite), none gives noncritical phase matching at a

convenient temperature, which is a prerequisite if one hopes eventually to build a cw OPO system. Alkali

metal-titanyl arsenate crystals (KTA, RTA, CTA) are

of prime interest here: While they retain all the

properties of their better-known parent KTP (reasonable nonlinearity, reduced walk-off in the X-Y plane,

high optical damage threshold, very high ferroelectric

Curie temperature), they lack the phosphate-ion vi- brational resonances that lead to significant absorption at 3.5 /xm.'^ Also, RTA^^ gives noncritical phase

matching at room temperature for^^

/'(1064 nm) - /"(SIS? nm) ^ /"(leiO nm)

.

(2) We observed that interaction (1) is phase matched

in RTA at 335 °C. We predicted this temperature by

measuring the phase-matching bandwidth at 3 /xm by

tuning the CO overtone laser through its i; = 23 —> 21

emission band. A least-squares fit with a sinc^

function gave us a 552 ± 25 GHz FWHM bandwidth,

which, when divided by a temperature bandwidth

of 100 °C (obtained from KTP's temperature dependence'*), yields an approximate temperature-tuning

coefficient of -5.52 GHz/ °C. Thus, to displace the

phase-matching central wavelength from 3137 nm

[interaction (2)] at room temperature to 3193.5 nm

(-1691 GHz), one should increase the temperature

by 306 °C. This is in fair agreement with the ex- perimental determination and indicates that KTP's

temperature dependence is a good first guess for

arsenates as well. This large temperature acceptance

gives sluggish temperature tuning, but, on the other

hand, the sensitivity of the DFG interaction to temperature fluctuations is very low. We calculated the

second-derivative FWHM angular bandwidth to be

8.9 °. Our attempt to measure it was not successful

because of the inhomogeneity of our crystal.

The propagation in the biaxial crystal was along

the X axis. Since the interaction is of type II ioee) in the X -Y plane, the polarizations were along the

Z axis for the 3192-nm ordinary beam and along the

Y axis for the 1064- and 1596-nm extraordinary

beams. The 7.25 mm x 5 mm x 5 mm RTA sample

that we used was cut at 30° from the Z axis, so we had

to use it sideways (normal axis at 30° from the X axis)

with an —65° incidence angle (Fig. 1). This alignment

is close to Brewster incidence for the p-polarized light at 3192 nm, but it gives Fresnel losses of —33% on

the uncoated faces for the two other, s-polarized,

beams. It also results in significant astigmatism,

since the light was focused in the crystal. (Calculated

waist sizes were 23 /zm for the Nd:YAG beam and

40 /xm for the CO beam.) The experimental setup is diagrammed in Fig. 2: The two pump beams were combined by means of a dichroic mirror (DM) and a 35-^tm-diameter pinhole placed at the common waist

position. A removable mirror mount of kinematic

design allowed us to send the two beams into the

RTA crystal, which was enclosed in a Au-plated

Cu oven and heated to 330-340 °C. Two fusedsilica mirrors, with transmittances of — lO"'* at 1064 nm and 90% at 1.6 ytxm, were used between

the crystal and the detector to block the powerful

Nd:YAG radiation and also to absorb the less- intense 3.2 /im light. Part of the CO beam was

simultaneously frequency doubled in a AgGaSe2 crystal. This produced a second 1.6-/xm beam, which was overlapped on a fast photodetector with the DFG

signal. The {R — 1/3) beam splitter on the CO laser beam path was chosen to maximize the power on the

beat detector:

Pbeat ^ [(TPi)2i?PiP3]"' ^ R^'^H - R) (3)

1 596 nm "e" DFG-beam

(92 = 64.20)

3192nm

"o" beam

(6, = 66.2°)

1 064 nm "e" beam

(93 = 64.8°) ^/^

Fig. 1. RTA crystal: beam alignments and polarizations,

optical axes (o.a.), and principal axes {X,Y,Z).

TN-230
September 1, 1996 / Vol. 21, No. 17 / OPTICS LETTERS 1389

CO OVERTONE UVSER

(X=2.6 to 4.0/i,m. 400 lines)

» Pin L2 ^^ Hole

I V I

I Power

^ TT—I Meter

PD (InGaAs)

Fig. 2. Experimental setup: L1-L6, lenses; BS, beam

splitter; PD, photodiode.

1

1

1

i'lUfP'IWf ""11" 1^ Tt

Fig. 3. Spectrum of the beat note between DFG and SHG

1596-nm waves. Vertical scale, 10 dB/division; horizontal

scale, 500 kHz/division; resolution bandwidth 30 kHz; center frequency 6 MHz.

The powers at 1596 nm at the photodetector were

25 nW for the DFG beam and 1 /mW for the SHG beam.

A 60-/u,m-diameter InGaAs photodiode (bandwidth

5 GHz) was used to detect the beat note, which was

amplified (40 dB gain, 60 MHz bandwidth) and sent

to a spectrum analyzer (Fig. 3). The 40-dB signalto-noise ratio should be adequate to phase lock the

two lasers together. Fast frequency control of the

CO laser is now being developed for this purpose. A

frequency lock between the lasers has been established and gives a beat note with a 150-kHz linewidth

(owing to the jittering of a narrower peak under

acoustical and discharge noise in the CO laser) and a 1-kHz center frequency stability.

We have demonstrated a coherent frequency connection in an exact 3:1 ratio between 1064 and 3192 nm. The fact that RTA noncritically phase matches this

process is encouraging for the extension of this re- search to an OPO system. We also look forward to realizing the 1126-3378-nm link on the way to con- necting the Hg+ 282-nm transition to the primary Cs

standard.

We thank G. M. Loiacono (Crystal Associates, Inc.) for growing the RTA crystal, R. A. Stolzenberger (Crystal Associates, Inc.) for information about RTA, and

S. Waltman and J. L. Hall for significant contributions

to this research. This research is supported in part

by the U.S. Air Force Office of Scientific Research.

M. Mtirtz acknowledges support from the German

Science Foundation; O. Pfister acknowledges a

Lavoisier grant from the Ministere des Affaires

Etrangeres of France.

References

1. T. Andreae, W. Konig, R. Wynands, F. Schmidt-Kaler,

C. Zimmermann, D. Meschede, and T. W. Hansch,

Phys. Rev. Lett. 69, 1923 (1992).

2. F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien,

F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent,

A. Clairon, M. Abed, Y. Millerioux, and P. Juncar,

Phys. Rev. Lett. 69, 2326 (1992).

3. D. J. Wineland, J. C. Bergquist, W. M. Itano,

F. Diedrich, and C. S. Weimer, in The Hydrogen Atom,

G. F. Bassani, M. Inguscio, and T. W. Hansch, eds. (Springer-Verlag, Berlin, 1989), p. 123.

4. E. Peik, G. Hollemann, and H. Walther, Phys. Rev. A

49, 402 (1994); H. Lehmitz, J. Hattendorf-Ledwoch,

R. Blatt, and H. Harde, Phys. Rev. Lett. 62, 2108

(1989); G. P. Barwood, C. S. Edwards, P. Gill, G. Huang, H. A. Klein, and W. R. C. Rowley, IEEE

Trans. Instrum. Meas. 44, 117 (1995); B. G. Whitford,

K. J. Siemsen, A. A. Madej, and J. D. Sankey, Opt.

Lett. 19,356(1994).

5. H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and

G. Zinner, Phys. Rev. Lett. 76, 18 (1996).

6. J. C. Bergquist and D. J. Wineland, in Proceedings

of the Thirty-Third Annual Symposium on Frequency

Control (Electronic Industries Association, Washington,

D.C., 1979), p. 494.

7. H. R. Telle, D. Meschede, and T. W. Hansch, Opt. Lett. 15,532(1990).

8. H. R. Telle, in Proceedings of the Twelfth International Conference on Laser Spectroscopy, M. Inguscio,

M. Allegrini, and A. Sasso, eds. (World Scientific, Sin- gapore, 1996), p. 230.

9. M. Kourogi, K. Nakagawa, and M. Ohtsu, IEEE J. Quantum Electron. 29, 2693 (1993).

10. N. C. Wong, Appl. Phys. B 61, 143 (1995); Opt. Lett. 17,

1155(1992).

11. F. C. Cruz, M. Rauner, J. H. Marquardt, L. HoUberg,

and J. C. Bergquist, in Proceedings of the Fifth

Symposium on Frequency Standards Metrology, J. C. Bergquist, ed. (World Scientific, Singapore, 1996),

p. 511.

12. U. Simon, S. Waltman, I. Loa, F. K. Tittel, and

L. HoUberg, J. Opt. Soc. Am. B 12, 323 (1995).

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and S. Waltman, IEEE Trans. Instrum. Meas. 44, 151

(1995).

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W. Urban, J. Mol. Spectrosc. 168, 416 (1994); E. Bachem, A. Dax, T. Fink, A. Weidenfeller,

M. Schneider, and W. Urban, Appl. Phys. B 57, 185

(1993).

15. J. C. Jacco and G. M. Loiacono, Appl. Phys. Lett. 58,

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16. L. T. Cheng, L. K. Cheng, and J. D. Bierlein, in Growth,

Characterization, and Applications of Laser Host and

Nonlinear Crystals H, B. H. Chai, ed., Proc. SPIE 1863,

43(1993).

17. RTA Sellmeier coefficients published in Ref. 16 are not accurate at 3 ^im. Interaction (2) was measured by

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TN-231
Demonstration of a phase-lockable microwave to submillimeter-wave sweeper

S. B. Waltman, L. W. Hollberg

National Institute of Standards and Technology

Boulder. Colorado 80303-3328

K. A. Mcintosh

Lincoln Laboratory

Massachusetts Institute of Technology

Lexington, Massachusetts 02173-9108

E. R. Brown

Defense Advanced Research Projects Agency

Arlington, Virginia 22203-1714

ABSTRACT

The develc^jment of low-tempcrature-grown GaAs photomixers enables the construction of a microwave to submillimeter-wave source cj^able of large frequency sweeps. By utilizing semiconductor diode lasers to drive the photomixer, this source is all solid-state and compact, and has small power consumption. Frequency stabilization of the semiconductor diode lasers allows this source to be phase-locked to an external microwave reference. Two 805 nm

extended-cavity-diodc lasers are mixed in a low-temperature-grown GaAs photoconductive photomixer. The difference- frequency mixing product is radiated by a planar spiral antenna and collimated by a Si lens. This output is phase-locked to a microwave reference by downconverting it in a whisker-contacted Schottky-banier diode harmonic mixer and using the output to offset-phase-lock one laser to the other. The photomixer output power is 300 nW at 200 GHz and 10 nW at 1 .6 THz, as measured by a 4 K InSb bolometer calibrated with a methanol laser and a power meter at 526 and 812 GHz.

1. INTRODUCTION

The earliest and possibly the most important application of submillimeter-wave radiation was spectroscopy.' As

submillimeter-wave sources have become more compact and robust, spectroscopic applications outside the laboratory, such

as remote sensing for atmospheric science and astrophysics, have become practical. The most serviceable present

submillimeter-wave source is a 50-100 GHz Gunn diode oscillator harmonically multiplied with a whisker-contacted

Schottky-diode varactor. However, this source is not yet electrically tunable over even a 10% bandwidth with high power.^

Optical heterodyne conversion, or photomixing, was proposed as a method for producing coherent microwave and

millimeter-wave radiation over three decades ago.^ But application of this method was delayed until the development of

suitable photomixers. Such photomixers have recently become possible with the advent of low-temperature-grown (LTG)

GaAs with photoconductive response, sub-picosecond electron-hole recombination time, and >10' V»cm' dc breakdown

field properties.* Photomixers made from this material have produced as much as about 3 |iW of output power with a 3 dB

bandwidth of 650 GHz.^*

One advantage of photomixing over other ways of generating millimeter and submillimeter-wave radiation is the ease of tuning the output frequency by tuning one of the pump lasers. Diode lasers with a single-mode frequency sweep

range of 1 .4 THz at 100 Hz sweep rate have been demonstrated. Since the photomixer conversion efficiency is approximately constant below its comer frequency, multi-octave frequency sweeps with minimal amplitude variation are

possible.

A nice demonstration of the spectroscopic capabilities of these photonuxers has been made by A. Pine.^ A

spectrometer based on LTG GaAs photomixers was used to study SO2 self broadening coefficients in the 0.1- 1. THz

SPIE Vol. 2842 • 0-8 194-2230-4/96/56. 00 55 TN-232
frequency range. In this instrument, the photomixer was driven by two single-mode

dye lasers which were pumped by an argon

ion laser. Subsequent work demonstrated

operation of LTG GaAs photomixers

pumped by semiconductor diode lasers.* Semiconductor diode lasers are ideal for driving photomixers because they are compact, efficient, tunable, and relatively

inexpensive. They also have sufficient output power and can be spectrally narrow. The extended-cavity tunable diode lasers used in this work occupy 780 cm^, consume less than 1 W of electrical power, and can be mechanically tuned over at least 14 THz.

to lasar dlagnoistlct

ptwtealur off-axia

I tl^ hyTMrOMlapiMr* parabola

Figure 1. Experimental setup. The extended-cavity diode lasers use conunerdal 100 mW, 805 nm devices.

The Unewidth and stability of the radiation produced by the photomixer is determined by the lasers used to drive it. The lasers in this work have linewidths of approximately 100 kHz and low-frequency jitter of a few megahertz. By

coherently detecting the radiation, we can phase-lock the offset between the two lasers to a harmonic of a microwave source. The Unewidth, stability, and accuracy of the millimeter and submillimcter radiation are then determined by the phase noise,

stability, and accuracy of the microwave source.

2. EXPERIMENT DESCRIPTION

The photomixers used in this work consist of interdigitated electrodes on an epitaxial layer of LTG GaAs. The

electrodes are 0.2 pjn wide, separated by 1.8 ^m wide gaps, and cover a total area of 8x8 \im. The electrodes drive a three- turn self-complementary spiral antenna. The output radiation propagates through the GaAs substrate and is coupled out of

the substrate and partially collimated by a hyperhemispberical Si lens mounted in contact with the back of the GaAs chip.

The experimental setup is illustrated in Figure 1. The photomixer is driven by two extended-cavity diode lasers (ECDLs). Each is a commercial 100 mW 805 nm diode laser with an anti-reflection coating on the output facet. The

extended cavities are in a Littman configuration,* and the ou^ut frequency of the laser is adjusted by tilt and translation of

the mirror. Adjustment screws on the mirror mount provide coarse tuning with a range of 14 THz, and piezoelectric actuators provide fine tuning. Single nKxie scans of 19 GHz are possible in the present system by electronically matching

the ratio of tilt and translation to synchronize the bandpass firequency determined by the grating with the frequency of an extended-cavity mode. This tuning range is determined by the 9 ^m translation range of the piezoelectric actuators used and

the cavity dimensions. Special lasers designed for long-scanning range have demonstrated multi-terahertz continuous

scans. For phase-locking, electronic feedback to the injection current provides fast frequency control with a 3 dB bandwidth

of approximately 2 MHz.

The two laser beams are combined by a beam splitter and then circularized with an anamorphic prism pair. After passing through two Faraday isolators, the combined beam is resized by a telescope and focused on the photomixer by a

lens. The beam size and lens focal length were chosen to produce a 7 nm spot size on the photomixer. Typical powers

from each of the lasers are 9 mW and 22 mW. The performances of the two lasers differ due to differences in the quality of

their anti-reflection coatings.

The dc photocurrent and the millimeter-wave output power both increase with increasing dc bias across the photomixer electrodes. At 30 V bias the responsivity was 14 mA/W. Electrical or thermal burnout of the photomixer

becomes likely at higher bias voltages or at total optical power levels above 100 mW.

56 TN-233
The output radiation of the photomixer is focused by an off-axis paraboloid onto the long-wire

whisker antenna of a point-contact Schottky diode. A 9 1 GHz local oscillator signal from a Gunn diode

is also coupled onto the whisker. The Schottky diode

down-converts the millimeter or submillimeter

radiation from the photomixer by mixing it with a harmonic of the local oscillator. The downconverted signal near 1 GHz is ampliOed, filtered, and then sent to a spectrum analyzer and a phaselocking circuit.

3. RESULTS

The power produced by the photomixer was

measured by focusing it onto an InSb bolometer with

a polyethylene lens; the result of these measurements

is shown in Figure 2. The bolometer's response was

calibrated at S26 GHz and 812 GHz by using an

attenuated methanol laser whose full output power was measured separately with a broadband power

meter.'

0.4

OJ

a-0.2

0.1

0.0

• 'lO* • •10' Fr9qu«ncy (GHz)

Figure 2. Photomixer output vs. Erequency. Power

measurements were made with a 4 K InSb bolometer which was

calibrated at 526 and 812 GHz with a methanol laser.

Figure 3 shows the signal-to-noise ratio of the down-converted signal as a function of local oscillator harmonic

number. The signal-to-noise ratio in the present system is sufficient to maintain an offset phase lock of one of the lasers to

the other for harmonic numbers up to 5. Figure 4 shows the down-converted signal with the lasers locked using the fourth harmonic, an offset of 366 GHz. The linewidth of the submillimeter wave signal is limited by the phase noise of the 9

1

GHz Gunn diode local oscillator. If the Gunn diode had been locked to a low phase-noise synthesis chain, the linewidth

could have been as narrow as a few hertz.

'°

40

One method for sweeping the photomixer's output frequency while maintaining a phase-lock is to mix the downconverted output bom the harmonic mixer with a variable ftrquency before sending it to the phase-locking circuit. This

topology was tested for offset-frequency laser phase-locks with frequency differences up to 18 GHz by using a fast pbotodetector in place of the photomixer. Phase-locked

sweeps encompassing the full synthesizer band of 7 GHz

worked reliably. When the synthesizer switched bands, the rf ouq}ut was briefly absent Unless the phase-locking integrator was carefiiUy nulled, the system failed to automatically relock

after the band switch. If it relocked, then it was possible to sweep over the full 19 GHz electronic tuning range of the

lasers. However, without a tracking filter or a single-sideband

mixer, the signal-to-noise ratio of the signal at the phase

detector was degraded by 3 dB by the noise from the unwanted

mixing sideband. These minOT difficulties could be overcome

in a system specifically designed for long-range scans.

30

c20

zm 10

A second method for sweeping the photomixer's

output frequency while maintaining a phase lock is to sweep

the 91 GHz local oscillator's frequency. This allows a fixed- frequency filter to be used to reject the unwanted mixing

sideband. This ^proach was tested with the photomixer's

4 5 6 Haimonic number

Figure 3. Detected signal-to-noise ratio (SNR) vs. 91 GHz

local oscillator harmonic number. Phase-locks are

possible for harmonic numbers less than six.

TN-234

57
output phase-locked to the fouith harmonic of the 91 GHz local oscillator. The Gunn diode oscillator used in this experiment had only 1.10 GHz of bias tuning range. Applying a voltage ramp to the Gunn diode bias produced a phaselocked sweep of 4 GHz span centered at 364 GHz. ^ 4TTSM ta •

4. FUTURE PROSPECTS

The present system would allow free-ruiming

sweeps with a width over 1 THz with an appropriate laser. For phase-locked sweeps, sweeps broader than 4 GHz

should be possible with a local oscillator which has more

tuning range. The loss of local oscillator power that comes

with a broader timing range should not be a problem, since

the Gunn diode had significantly more power than was

necessary for these experiments.

Figure 4 shows that power measurements made by

observing the down-converted signal amplitude could have

a noise floor of 3 fW/Hz. This is much lower than a

cryogenic Si bolometer with a NEP of 0. 1 3 pWNUzJ Compared to cryogenic bolometers, heterodyne detection also has

the practical advantage of room-temperature operatioiL

.<^*i^k. ^t^ "V

""Yl MPM^ r^

*f ^

r^ ^ f> *rv Mt^

Ft ^T

F^[are 4. Power spectrum of phase-lock using the fourth

harmonic of the 91 GHz local osdDator.

As the speed of LTG GaAs material improves, photomixers with greater bandwidth will become possible. Some

recent LTG GaAs samples have shown photoconductivc lifetimes on the order of 100 fs, raising hopes for photomixers with

bandwidths of several terahertz. Improvements in the pbotomixer design may also increase their burnout threshold, so

stronger pun^s can be used to increase the output power. When combined with semiconductor diode lasers, these photomixcrswill make possible a broadly tunable, narrow-linewidth millimeter-wave source which will also be compact and

transportable. This in turn would allow new spectroscopic and coherent-detection applications.

7. ACKNOWLEDGMENTS

At NIST this work was supported by the Air Force Office of Scientific Research. At Lincoln Laboratories this wcMic was supported by NASA through the Jet Propulsion Laboratory. The authors thank Lyndon Zink and Ken Evenson

for supplying assistance, equipment, and laboratory space.

8. REFERENCES

1. F. C. DeLucia, T. M. Goyette, Terahatz source requirements for molecular spectroscopy," Nonlinear Optics for

High-Speed Electronics and Optical Frequency Conversion, pp. 239-247, SPIE, Los Angeles, CA, USA, 1994.

2. M. A. Frerking, "Submillimeter Source Needs for NASA Missions," Nonlinear Optics for High-Speed

Electronics and Optical Frequency Conversion, pp. 222-229, SPIE, Los Angeles, CA, USA. 1994.

3. R. H. Pantell. J. M. DiDomenico, O. Svelto, J. N. Weaver, "The Theory of Optical Mixing in Semi-conductors,"

Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet, N. Bloembergen, Eds., pp. 1811-

1818, Columbia Univ. Press, 1963.

4. E. R. Brown, F. W. Smith, K. A. Mcintosh, / AppL Phys. 73, 1480-1484 (1993).

5. E. R. Brown. K. A. Mcintosh, K. B. Nichols, C. L. Dennis, Appl Phys. Utt. 66, 285-287 (1995).

6. K. A. Mcintosh, et al.. Appl. Phys. Utt. 67, 3844-3846 (1995).

7. A. S. Pine, R. D. Suenram, E. R. Brown, K. A. Mcintosh. Journal ofMolecular Spectroscopy 175, 37-47

(1996).

8. M. G. Littman. H. J. Metcalf, Applied Optics 17. 2224-2227 (1978).

9. K. M. Evenson. et al., IEEE Journal of Quantum Electronics QE-13. 442-444 (1977).

10. F. L. Walls, C. M. Felton. "High Spectral Purity X-Band Source." Fourty-Fourth Annual Symposium on

Frequency Control, pp. 542-547, Baltimore, Maryland, 1990.

58 TN-235
1996 IEEE INTERNATIONAL FREQUENCY CONTROL SYMPOSIUM

A 1 GHz OPTICAL-DELAY-LINE OSCILLATOR DRIVEN BY A DIODE LASER

J. Kitching, L. Hollberg and F. L. Walls

Time and Frequency Division, 847.10,

National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80303

Abetract: Experimented results are presented on a

hybrid optical/electronic oscillator which uses an optical delay line to generate high spectral purity mi- crowave signals. At Fourier frequencies above 10 kHi,

the single sideband (SSB) phase noise spectrum decreases as roughly 1//^ attaining a value of -138 dB

below the carrier in a 1 Hs bandwidth (dBc/Hs) at 20

kHi offset. The origin of this noise is in part the fun- damental shot noise on the light itself, although other

optical noise sources such as double Rayleigh scattering and stimulated BriUouin scattering also appear to be important under certain operating conditions. The

frequency stability over several hours is dominated by

changes in the fiber ambient temperature with a coefEcient of about 10~^/K originating mostly from changes

in the fiber refractive index with temperature.

Introduction

Stable S-band and X-band oscillators play a role in numerous applications ranging from precision metrology to optical communication systems. There are several traditional methods of generating low phase noise

oscillation at these frequencies. Bulk acoustic wave (BAW) oscillators, oscillating at 5 or 10 MHi can be

multiplied up to GHz frequencies. Although the initial BAW oscillator may be extremely stable, the multiplication process usually adds substamtial additional

noise, particularly at frequencies far from the carrier,

which seriously degrades the original performance of

the oscillator. Surface acoustic wave (SAW) oscillators have been used to directly generate oscillation in the frequency range of 100 MHz to a few GHz with

somewhat inferior close-in phase noise performance

than low frequency BAW oscillators. For even higher

frequencies, up to tens of GHz, dielectric resonator

Contribution of U.S. Government; not lubject to copyright.

oscillators (DRO's) are most often used; sapphire is the dielectric material of choice for obtaining the lowest phase noise. While these methods have been, on

the whole, successful, p>articularly in producing signcils

with extremely low phase noise, their lack of tunability and difficulty of fabrication limit 4heir usefulness

in many critical applications.

Recently, a novel hybrid optical/electronic approach

to this problem wsls proposed [1, 2]. This uses an

optical fiber delay line to achieve phase noise perfor- mance competitive with the best commercially avail- able synthesizers. These optical-delay-line oscillators (ODLO's) or light-induced microwave oscillators also have a number of highly desirable features not avail- able in other oscillators: they are highly tunable; have

oscillation frequencies which can potentially range from hundreds of kHz to tens of GHz; can have moderately low phase noise; have both optical and electronic inputs and outputs facilitating their integration with

other optical systenis; and can be constructed with no

precision components other than commercially avail- able optical fiber. Another important aspect of these

oscillators is that their phase noise performance is in- dependent of oscillation frequency making them excellent candidates for generating microwave signals above

10 GHz. Recent experimental results for an 800 MHz

oscillator [3, 4] have demonstrated a SSB phase noise of less than -140 dBc/Hz at 30 kHz frequency offset and m£Lny future improvements seem likely.

The Optical Delay Line Oscillator

The ODLO takes advantage of the extremely low loss and long delay times which can be achieved in optical

fibers in order to provide the frequency discrimination

necessary for low phase noise oscillation^ A diagreim

of one of the oscillators built at NIST is shown in Fig- ure 1. An electronic signal is first translated into amplitude modulation on an optical carrier generated by

807

U.S. Government work not protected by U.S. copyright

TN-236
-10MH2

Moduiadon

i= hi bolaior "^^^ Detccu.

Figure 1: Experimental setup of one of the NIST optical delay line oscillators

a leiser. This can be done either by directly modulating the injection current of a semiconductor laser or by

using an electro-optic modulator (EOM) to amplitude

modulate an externally generated cw beam. The light

is passed through a long optical fiber and then sent

into a high speed photodetector which converts the

optical signal back into an electronic signal. The elec- tronic signal is then amplified, filtered, and sent back

into the amplitude modulator. This feedback loop defines RF "modes" which satisfy the condition that the roundtrip phase shift through the loop is a multiple of 2t. For a fiber length of 1 km, these modes are spaced

by about 200 kHa.

The transfer of RF modulation into amplitude modulated light and then back into a RF signal usually

involves some loss of RF power making the loop gain

substantially less than unity. However, as the amplifier

gain is increased one of the modes will eventually reach

threshold when the loop gain is equal to unity and

will start to oscillate. Which mode oscillates depends on the tuning of the RF filter. The filter gjun profile acts very much like the wavelength-dependent gain

provided by an atomic transition in a laser. Assuming saturation properties analogous to homogeneous

broadening in a laser, when the mode at the peak of the gain profile sees unity gain, it will steirt to oscil- late, saturating the gain, and bringing the system into equilibrium. Adjacent modes aie (usually) suppressed

by some large factor below the oscillating mode since

the mode amplitude is enormously sensitive to the net gain in the region around threshold. How and where

the gain saturation occurs depends on the exact con- figuration of the oscillator, as will be discussed below. An important property of this type of oscillator i« its ability to produce oscillation with low phase noise. This is true because very long delays are possible in an

optical fiber with very little loss. A typical single-mode

optical fiber can transmit 1.3 |i m light with as little as 0.4 dB/km of optical power loss. Since the optical

power modulation is proportional to the current modulation, this corresponds to 0.8 dB/km of RF power

loss intrinsic to the fiber (as opposed to w 1000 dB/km

for a delay line made of semi-rigid coaxial waveguide,

for example). As a result of this low loss and long

delay, the effective fractional RF energy loss per unit time in the fiber can be very small. The bandwidth

of optical fiber is also extremely large, so in principle very high frequency modulation can be delayed with- out significant increase in the RF loss. If we assume

perfectly efficient coupling of RF power into optical

modulation (that is, one optical photon per electron)

and then back into RF power at the detector end, then

the limiting loss mechanism in the loop is the fiber loss and the Q of the cold (no gain) RF "cavity" can be as high as 10* at a frequency of 10 GHi. In fact, if the

light could be modulated at the optical fiber bandwidth of S5 10 THi (by using two lasers at different wavelengths, for example), the intrinsic fiber Q for the ODLO could be as high as 10®. For practical fiber lengths, the loop losses are usually dominated by cou- pling the RF power into and out of the optical domain,

making the actual RF cavity Q in a reeil device much

smaller (a few tens of thousands).

An emalysis of the ODLO's RF power spectrum has

been made by Yao and Maleki [3], who include amplifier thermal noise, photon shot noise, and laser noise

in their model. They find that the RF power spectral

density close to the oscillating mode is equal to

^'^^^'^~ {6/2T)^ + {2xrf'y' (1)

for 2irr/' < 1, where /' is the frequency deviation

from the nominal oscillation frequency, r is the loop

delay time and 1/6 is the open- loop RF signal-to-noise

ratio at the amplifier input. If the dominant noise source is assumed to be shot noise (this is often the

case) then 6 = lelpKR/Prj, where e is the charge on an

electron, I^k is the DC photocurrent (a few mA), R is the amplifier input resitance, and Prj is the RF power

of the detector photocurrent modulation. For typical

values oilfK (2 mA), modulation index (0.3), and fiber

808

TN-237
length (1.5 km), this results in a single sideband phase

noise of about -144 dBc/H« at a frequency offSset of 20

kHi. This is competitive with current state-of-the-art commercial oscillators. An interesting aspect of this analysis is that the phase noise does not depend on

the oscillation frequency. If the mode-selection filter

is moved from 1 GHs to 10 GH« or 50 GHr, the phase

noise, in principle, stays the same.

Oscillator Description

We now turn to a description of the specific oscillator which has been built at NIST (Figure 1). This oscil- lator incorporates a number of features which make it different from the oscillator described in previous publications [3] . The m2un difference is that a semiconductor distributed Bragg reflector (DBR) laser, lasing at 650 nm, is used instead of a YAG laser and EOM. The

laser injection current is directly modulated in order

to transfer the RF signal to optical modulation. This

implementation offers a number of advantages as well

as disadvantages over electro-optic modulation. The

most obvious advantages are compactness and lower

cost. In addition, if pumped far enough above threshold, semiconductor lasers can have amplitude noise

close to, or even in some cases below, the shot noise

limit, which makes them ideal for use in the ODLO.

One disadvantage with using diode lasers is the lower

optical output power which limits the signal-to-noise

ratio at the photodetector. In addition, the maximum frequency at which diode lasers can be modulated is typically somewhat lower than can be obtained

in state-of-the-art EOM's.

The output from the laser was sent into 1.5 km of single-mode fiber and then into a high speed PIN photodiode. One technological issue encountered was the

difficulty in obtaining high speed photodiodes which

can operate with incident optical powers over a few

niW. If the laser noise is close to the shot noise limit,

then the signal-to-noise ratio at the photodetector improves as the optical power detected increases. As a

result, in order to obtain the best phase noise perfor- mance, it is desirable to operate at the highest optical

power possible. Although the laser used in the ex- periment was capable of generating 100 mW of opticed power, it had to be used at a lower power and the light

sometimes attenuated in order to avoid overloading the

detector (and also, as described below, to reduce optical scattering in the fiber). Our best results were

acheived with an output power of 95 mW and result- ing detector DC photocurrent of 1.6 mA. The currentto-current DC eflSciency from laser to photodetector

was 1.2%. The low efficiency was mostly the result of an optical attenuator placed intentionally in the beam

path in order to reduce the DC photocurrent to a level acceptable to the photodiode.

The output from the photodetector was sent into a

series of amplification stages, the final stage having a

1 dB compression output power of 79 mW. This final stage provided the saturating element in the loop, limiting the RF power so that the power modulation on

the laser was about 50% of the total power. Filtering at 1 GHs was accomplished by stub matching the 50 H

line impedance to the laser impedance of a few ohms

which provided the additional benefit of increasing the

RF coupling into the laser. The tuning stub filter had

a FWHM of 10 MHi about a 1.002 GHi center fre- quency. It is interesting to note that this impedance

matching (which can also be implemented on the detector end) can actually result in RF gain [6] in the

loop despite the presence of optical loss. Thus it seems

possible to avoid the use of RF amplifiers altogether

in this type of oscillator, drawing energy instead from

the DC bias circuits of the laser and detector.

Sources of Noise

In this section, the sources of noise which affect the performance of an OLDO are reviewed. In addition

to the three sources mentioned above, we found two

other factors related to light scattering in the fiber which limit the performance of the oscillator under

certain operating conditions. These scattering mechanisms are likely to be more important in our oscillator,

which uses light at 850 nm, than in an oscillator using

light at 1.3 /im or 1.5 /im.

The critical issue is the signal-to-noise ratio at the

input to the RF amplifier under open-loop conditions.

This signal-to-noise ratio determines not only the oscil- lator phase noise but also, for a given filter bandwidth,

the RF power in the side modes. The three noise sources mentioned previously are thermal noise in the

RF amplifier, shot noise resulting from the graininess

of the laser light, and excess noise generated by the

laser. When refered to the amplifier input, the noise- to-signal due to these sources is given by [4]

6 = [AkeTiNF) + 2e/p,,ii + Nfuffl^^R] /Pc.c (2)

where ks is Boltzmann's constant, T is the temperature, NF is the amplifer noise figure, and Nrjn is the

relative intensity noise of the laser. For many semiconductor lasers operating at a few times the threshold current, and with the DC detector current into 50 Q above a few mA, and the dominant noise source

809

TN-238
Directly Transmitted

Field

RL - IB. 88 dBi

Fl^TTT

UKR tl FRQ 9 H8.BB H H;

Rayleigb

Scattered Fiek)

Optical Fiber

Figure 2: Double Rayleigh scattering in the optical fiber generates excess photocurrent noise when

the scattered Held beats with the directly transniitted

field.

is shot noise. Assuming a constant modulation in- dex on the leiser light, the signal-to-noise ratio is then

maximized by increasing the laser output power to its highest level and reducing the optical losses between

laser and detector to a minimum. This strategy runB

into two difficulties. Firstly, as mentioned above, high

speed photodiodes can usually handle only limited optical power. Secondly, «md more importantly, however,

when high power is sent through the fiber, optical scat- tering mechanisms contribute additional noise and de- grade the oscillator performance.

The first scattering mechanism which was found to be important in our 850 nm oscillator was stimulated

Brillouin scattering (SBS). In this process, the optical

field scatters off acoustic phonons in the fiber gener- ating a backweird propagating optical field red-shifted by 21 GHz from the input. The threshold input power

for this process in our fiber was about 9 mW if no modulation was applied to the laser (if all of the optiCeil power was concentrated in a single spectral region).

When the optical power was increased above this level, the SBS gain in the reverse direction was larger than

the fiber loss, and the counter-propagating field was

amplified. When there was a significant SBS, the amplitude noise of the transmitted light increased dra- matically by several orders of magnitude. It is clear, therefore, that this process imposes a limitation on the

optical power which can be used in the oscillator and

therefore on the maximum signal- to- noise ratio which

can be achieved. Under oscillating conditions, significantly more than 9 mW of optical power could be sent through the fiber without observing the effects of SBS.

This is because the laser was being modulated with a

large modulation index (both AM and PM) which dis- tributed the optical power among several sidebands

and therefore reduced the power at any one frequency.

A second, and more serious problem, was that of

CENTER 958.88 m

•RB 3B.B kHz '\)i aee hz

SPAN 28.88 nHi ST 6.BB7 sec Figure 3: Excess noise about the RF carrier generated

by double Rayleigh scattering. Trace A shows the in- creased photocurrent noise when modulation at 958

MHs is applied to the laser. Trace B is under identical conditions to A except with additional injection current modulation at 10 MHz. Trace C indicates the noise level with no RF modulation and the background

amplifier noise level.

double Rayleigh scattering (DRS) in the fiber [7]. DRS

occurs because a small fraction of the optical power

propagating in the fiber is Rayleigh scattered twice re- sulting in a weak, delayed replica copropagating with

the original field in the fiber (see Figure 2). In fibers longer than the coherence length of the laser, this causes additional noise resulting from phase fluctua- tions of the laser. Because of the long delay, the phase

noise of the scattered field is not coherent with the noise of the directly transmitted field and when the two fields are detected simultaneously on a photodetector, excess photocurrent noise is generated. When

a single optical frequency is present in the fiber, this noise can be seen at low frequencies in a bandwidth

roughly equal to the laser linewidth (a few MHi). If the laser is being modulated (that is, the oscillator is oscillating), AM noise is also generated around the de- tected RF modulation as a result of the scattered optical sideband field beating with the directly transmitted

optical carrier (and vice-versa). Figure 3 shows this

effect. For this measurement, the loop weu open and

a RF signal from a synthesizer at 958 MHz was sent into the laser injection current. The photodiode signal was then detected with a spectrum analyzer. Trace

810

TN-239
C indic&tes the noise power with no modulation (the

two small steps on the right indicate the background

amplifier noise power). With modulation at 958 MHi

applied (trace A), the noise around the carrier clearly

increases as a result of the DRS.

There are several ways of dealing with this problem.

Since the noise is a replica of the laser linewidth (which

is true if the laser's coherence length is much shorter than the fiber length), chztnging the linewidth will obviously affect the noise. Reducing the linewidth will concentrate more of the noise close to the modulation

signal thereby increasing the phase noise of the oscilla- tor close to the carrier. On the other hand, increasing

the laser phase noise (by adding low-frequency noise

to the injection current, for example) will broaden the

noise bandwidth seen in Figure 3, Trace A, thereby

reducing the noise close to the modulation frequency

and improving the oscillator performance. This was

indeed the case. A more successful solution, however, was to add additional modulation to the laser injection current at a frequency different from the oscillation frequency

[8]. This spreads the optical power throughout a number of FM sidebands (separated by this new modulation frequency) while it propagates through the fiber. When the light is detected, part of the noise originally near the oscillation frequency is transferred to near the modulation sidebands. As a result, the AM

noise around the original 1 GHs signal is reduced by a

factor roughly equal to the number of sidebands generated by the second modulation signal. This reduction

is clearly seen in Figure 3, trace B, which is taken under identical conditions as trace A, except that current modulation of 10 MHs is abided to the laser injection current in addition to the 958 MHs original modulation. A reduction in the DR5 2unplitude noise can be

clearly seen in the figure. The added phase noise on

the transmitted 958 MHs signal was reduced by over *n order of magnitude at a frequency 10 kHz from the

carrier. Thus it seems possible to reduce, if not eliminate altogether, the effects of DRS noise using this modulation technique.

Acoustic vibrations were also found to generate oscillator noise, mostly at offset frequencies below about

^ kHi. Although we expect that compression-induced

flanges in the fiber refraictive index are in part responwble, it was also found that the oscillator frequency was very sensitive to the position of the optical beam

on the photodetector. It is thought that this sensi- "vity may be a result of the detector capacitance or *^ner transit time changing slightly as the location

the charge-carrier generation was changed. As a

result, acoustic noise changing both the detector position and also the beam pointing direction would be

expected to generate phase noise in the oscillator. The

use of fiber-coupled detectors might reduce the sensitivity to acoustic vibrations.

A final source of additional noise originating with

the fiber results from temperature fluctuations causing the fiber length and refractive index, and therefore the oscillation frequency, to change. The temperature

dependence of the refractive index for glass is about

10" '/K [9] resulting in a similar coefficient for the fre- quency deviation of the oscillator. Thus it is expected

that temperature stabilization of the fiber of the order

of sslOO /iK will be necessary to reduce the frequency

fluctuations on long time scales to below one part in

10».

Experimental Results

When the RF gain was increased enough to overcome

the optical loss and output coupling, the system os- cillated stably in a single frequency mode. A typical

mode spectrum, taken with the oscillation frequency

at 1 GHt, is shown in Figure 4. The power in the side

:ent[r frequence

sas.se^ riHz

[i m

; 3.02 khr

At

lilii'iililyliywmiiiJjiiinililniJi'

"r: UB 2.Z: kH: S"

Hr-: se:

Figure 4: Mode spectrum of 1 GHs oscillator.

modes closest to the main mode was typically between

50 and 60 dB below the main mode power (although

under the optimum conditions described above, a side mode suppression of 62 dB was measured). The side mode suppression agreed reasonably well with the fun- damental theoretical prediction which depends on the

filter bandwidth, open loop signal-to-noise ratio and

811

TN-240
2 4 6 8 10 12 14 16 18 20 Mode Number

Figure 5: Side mode eupprcMion V8. mode number

for 1 GHs oscillator. The solid line indicates the theoretically predicted 1/n' dependence of the side mode

power on the mode number n.

was also measured by mixing the ODLO output with the output from a frequency synthesiser and sending

the resulting signal into a frequency counter, with the assumption that the crystal oscillators driving the synthesiser and counter were more stable on long time

scales than the ODLO. The ODLO frequency over a period of several hoars is shown in Figure 7. One data

point was taken every second with a dead time of about

200 ms between measurements. A drift in the absolute frequency by 10 kHs can be seen in the figure.

This drift was correlated with changes in the ambient

temperature of the fiber with a measured temperature

coefficient of about 10~'/K which agrees well with the temperature dependence of the effective refractive in- dex for the glass used in optical fibers [9].

mode spacing. A plot of the side-mode suppression

against mode number, n, is shown in Figure 5, with

the solid line indicating the theoretical I In? dependence.

In order to accurately characterize the phase noise

of the ODLO, a three-cornered-hat cross-correlation

measurement was made [10]. The measurement sys- tem is shown in Figure 1 and used two frequency

synthesisers as reference oscillators which were phaselocked to the OLDO at frequencies below about 100

Hz. The resulting measured ODLO-SSB phase noise

spectrum, taken with 14 MHz modulation applied to the laser in order to reduce the noise from double

Rayleigh scattering, is shown in Figure 6. For this measurement, 1000 averages of the cross-correlation

signal were performed and the noise level calibrated

with a 1 GHz noise standard [11]. The calibration was

checked by frequency-modulating the ODLO with a known amplitude at 5 kHz and comparing the cross- correlation with the resulting calculated phase modulation power. Phase noise of -138 dBc/Hz at 20 kHz

was measured for the 1 GHz oscillator. The plot also shows the calculated phase noise which should result from 1.6 mA of DC detector photocurrent, 50% optical intensity modulation under oscillating conditions,

and open-loop detection noise at the shot noise limit. Clearly the measured noise is somewhat higher. The

origin of this excess noise is likely a combination of

double Rayleigh scattering and thermal noise in the RF amplifiers. The theoretical phase noise increase

estimated from measurements of the DRS fiber noise

(with the 14 MHz modulation applied to the laser) is also shown in the figure.

The oscillator frequency drift on longer time scales

Conclusions

The preliminary investigations described above and

previously published results [2, 3, 4], suggest that optical delay line oscillators may be competitive alter- natives to crystal and dielectric resonator oscillators

if oscillation frequencies can be increased beyond 10 GHz. Their tunability and ease of construction are additional advantages. The development of these oscil- lators is still in its infancy and substantial room for improvement remains. Specifically, the phase noise per- formance can almost certeunly be improved by using

higher optical powers from the laser and better optical

coupling from laser to detector. Diode lasers appear

compatible with ODLO's and do not themselves seem

to cause any fundamental problems. High performance

lasers [12] having large modulation bandwidths in ad- dition to useful output powers would be a great asset

in the development of these ODLO's. To some extent,

this improvement hinges on being able to find high

speed photodiodes which can handle tens of mW of optical input power. Additional reductions in the fiber-generated noise could be obtained by using optics at 1.3 /im rather

thaui 850 nm. Although lasers at this wavelength tend

to be slightly lower in optical output power, optical

fibers have substantially less loss and scattering mechanisms such as stimulated Brillouin scattering and

double Rayleigh scattering should be much weaker. A

system with these design improvements is under construction at NIST. This system should produce even

higher frequency oscillation with phase noise close to the fundamental limit set by the shot noise on the laser

light.

812

TN-241
o

w

U

"o

en

CO JC

Cu

CQ

C/2

-60

-70

-80

-90

100

110

120

130

140

150

160

Excess DRS Noise

Shot Noise, 1.6 mA, 50% modulation

102 3 4 5 103 2 3 4 5 JQ^

Frequency (Hz)

3 4 5 10-

Figure 6: Single-sideband phase noise spectrum for a 1 GHx optical-delay-line oscillator. The measurement was made using the three-cornered-hat cross-correlation technique with 1000 averages. Current modulation at 14 MHi was applied to the laser to reduce the noise from double Rayleigh scattering.

Acknowledgements

This work was funded in part by the AFOSR. We are

grateful to D. Welch at Spectra-Diode Labs for the donation of the laser used in the experiment. We also acknowledge useful discussions with S. Waltman and

K" Shuker.

References

[1] A. Neyer and E. Voges, "High- Frequency Electro- Optic Oscillator Using an Integrated Interferometer," Appl. Phys. Lett., vol. 40, pp. 6-8, Jan.,

1982.

[2] X. S. Yao and L. Maleki, "High Frequency Optical

Subcarrier Generator," Electron. Lett., vol. 30, pp. 1525-6, Sept. 1994.

[3] S. Yao and L. Maleki, "Characteristics and Per- formance of a Novel Photonic Oscillator," Proc.

of 49th Annual IEEE Frequency Control Sympo-

•luin, San Francisco, CA, May 31 - June 2, 1995.

[4] X. S. Yao and L. Maleki, "Converting Light

into Spectrally Pure Microwave Oscillation," Opt.

Lett., vol. 21, pp. 483-5, April, 1996.

[5] The product information given is for techniced ref- erence only and does not constitute an endorsement of the laser or detector used in the experi- ment.

[6] M. F. Lewis, "Novel RF Oscillator Using Optical

Components," Electron. Lett., vol. 28, pp. 31-2,

Jan., 1992.

[7] S. Wu, A. Yariv, H. Blauvelt and N. Kwong,

"Theoretical and Experimental Investigation of Conversion of Phase Noise to Intensity Noise by

Rayleigh Scattering in Optical Fibers," Appl.

Phys. Lett., vol. 59, pp. 1156-1158, Sept., 1991.

[8] A. Yariv, H. Blauvelt and S. Wu, "A Reduction

of Interferometric Phase-to-intensity Conversion

Noise in Fiber Links by Large Index Phase Modulation of the Optical Beam," J. Lightwave Tech.,

vol. 10, pp. 978-81, July, 1992.

813

TN-242
10000 20000 30000 40000 50000

TiiDe(t) Figure 7: OpticaJ-delfty-line oscillator frequency vari- ation over several hours. The frequency drift was cor- related with the fiber ambient temperature with a coefficient of about lO-'/K.

[9] J. J. Carr, S. L. Saikkonen and D. H. Williams,

"Refractive Index Measurements on Single- Mode

Fiber as Functions of Product Parameters, Tensile Stress, {md Temperature," Fiber and Inte- grated Optics, vol. 9, pp. 393-396, 1990.

[10] W. F. Walls, "Cross-Correlation Phase Noise

Measurements," Proc. of 46th Annual IEEE Fre- quency Control Symposium, Hershey, PA, May

27-29, 1992, pp. 257-261.

[11] F. L. Walls, "Secondary Standard for PM and AM

Noise at 5, 10, and 100 MHz," Proc. of 46th Annual IEEE Frequency Control Symposium, Hershey, PA, May 27-29, 1992, pp. 290-299.

[12] T. R. Chen, P. C. Chen, J. Ungar and N. Bar-Chaim, "High Power Operation of MultiQuantum Well DFB Lasers at 1.3 ^m," Elerton.

Lett., vol. 31, pp. 1344-5, 1995; J-M Verdiell, D. F. Welch, B. Piano and K. Duncan, "HighPerformance 1.3 /xm Lasers for Analog and Digital

Applications," Proc. LEOS 1995 Annual Meeting,

pp. 169-70, 1995.

814

TN-243
August 15, 1997 / Vol. 22, No. 16 / OPTICS LETTERS 1211

Continuous-wave frequency tripling and

quadrupling by simultaneous three-wave mixings in

periodically poled crystals: application to a

two-step 1. 19-10. 71-yL6m frequency bridge

O. Pfister

JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440

J. S. Wells, L. Hollberg, L. Zink, and D. A. Van Baak*

National Institute of Standards and Technology, Boulder. Colorado 80303

M. D. Levenson

Department of Electrical and Computer Engineering, Rice University. Houston, Texas 77251

W. R. Bosenberg

Lightwave Electronics Corporation, Mountain View, California 94043

Received April 3, 1997 We observed cw third-harmonic generation in a periodically poled LiNbOs crystal by cascading optimally

phase-matched second-harmonic and sum-frequency generation. Other processes, such as fourth-harmonic

generation, are allowed by the flexibility of quasi-phase matching. We demonstrate a divide-by-nine (1.19-

10.71-/im) frequency chain that uses only two lasers.

Precise measurement of optical frequencies requires

connecting laser frequencies to well-known standards

by means of a frequency chain. Because of the

large frequency intervals involved, these systems

can be extremely complex, but they are required

for future optical clocks and tests of fundamental

physics.^ Therefore there is a need for new and

efficient optical mixing schemes compatible with cw, low-power frequency-stabilized lasers. Our interest

is also in frequency connections in a 3:1 ratio, which

would bridge gaps between excellent existing stan- dards such as the CO2 laser locked on OSO4 at 10 /im,

the He-Ne laser locked on CH4 at 3.39 /nm, and the

Nd:YAG laser locked on I2 at 1 /nm.

Nonlinear mixing in crystals is a good way to con- nect optical frequencies.^ One promising technique is quasi-phase matching^'' (QPM) in periodically poled

(PP) crystals,' such as LiNbOg (LN), KTiOP04 (KTP),

and RbTiOAs04 (RTA). QPM has well-known advantages such as access to the largest nonlinear coeffi- cients, suppressed walk-off, and great flexibility in the

choice of the wavelengths involved in the mixing.

Because of these properties, simultaneous QPM of

different interactions is more probable than one might

at first suppose. We envisaged third-harmonic generation (THG) by cascading^ second-harmonic generation (SHG; (o 1-^ 2cd) and sum-frequency generation

(SFG; oj + 2aj ^-» 3co), which of course realizes a 3:1 fre- quency connection. Another possibility (using a sin- gle input beam as well) is fourth-harmonic generation

(FHG) by cascading SHG twice. Considering simple

poling (50% duty-cycle period) and first-order collinear

QPM^ as well as birefringent phase matching (BPM),^

and allowing different polarizations, we find 12 THG

and 10 FHG coincidences in PP LN (Fig. 1 and Table 1), 8 and 2 coincidences in PP KTP, and 14 and 5

in PP RTA (Table 2). Given our low initial power Pico), the THG power is P{3oj) = 'i?sHG'?SFG-P(w)^, where tjshg.sfg are the SHG

and SFG efficiencies, each of the form [;^''^'sinc(Ak •

1/2)]^. Ak is the phase-mismatch vector and 1 is a vector of modulus the effective crystal's length, perpendicular to the walls of the poled domains. Although

this model takes into account noncollinear QPM (angle tuning)'* and the temperature dependence of the

35r

1500 2000 2500 3000 3500 4000

Fundamental wavelength X (nm) Fig. 1. QPM curves for THG in PP LN: The optimal

poling period A is calculated versus the input wavelength

A for SHG and SFG and several polarizations. These

curves are based on the Sellmeier coefficients* that gave

predictions closest to our experimental results at room

temperature. Arrows point to the THG coincidences. As

in the tables, polarizations (o, e) are given for a)co2a) and

w2w3a;.

TN-244
1212 OPTICS LETTERS / Vol. 22, No. 16 / August 15, 1997

Table 1. THG and FHG Coincidences in PP LN

THG in PP LN FHG in PP LN

'^in '^out A Polarizations '^in ''out A Polarizations

1056 352 00/1.2 ooejoeo 1755 439 11.0 eoo/ooe

1122 374 4.6 eoo/ooe 1897 474 23.3 ooo/ooe

1231 410 9.0 ooo/ooe 2113 528 13.8/a> eoo/ooe

1500 500 8.5/a) eoo/ooe 26.4/^ ooo/ooe

5.3/00 ooo/ooe 2524 631 29.1 ooo/ooe

1907 636 23.5 ooo/ooe 3240 810 17.8 eoo/ooo

2118 706 13.9 oeo/ooo 3759 940 ^/27.1 ooe/eee

3158 1053 28.2 ooo/ooe 3893 973 24.8 ooo/ooe

3527 1176 18.0 eoo/eoo 3941 985 24.5 ooo/ooo

26.6 ooo/ooo 3979 995 29.2 eee/eee

3561 1187 31.6 eee/eee

3759 1253 0O/13.0 ooe/oeo

"'^in.out in nanometers; poling period A (or Ashg/Asfg) in micrometers. A — «; indicates BPM. Polarizations (o,e) are given for ww2ai/ai2ai3a) for THG and for (wai2ai/2a)2ai4(ij for FHG. Nonlinear efficiencies ^ (c/22)^ tooo) < (dsi)^ (ooe,oeo,eoo) « (^33)^ (eee). The boldface number is the wavelength at which the experiment was performed (see text).

Table 2. THG and FHG Coincidences in PP KTP

and PP RTA°

'^in '^out A Polarizations

THG in PP RTA

1143 381 ^/\n zxx/xxz

c»/5.9 zxx/zxx

1244 415 «=/2.2 zyy/yyz

1368 456 6.0/c» xxz/xzx

1492 497 7.4/a> yyz/yzy

1720 573 54.7 zxx/zxx

1916 639 75.1 zyy/zyy

2196 732 67.2/^ zxx/zxx

3312 1104 1290 zyy/zyy

3394 1131 ^/12.4 zyy/yyz

3603 1201 00/00 zxx/zxx

3604 1201 ^/12.3 zxx/xxz

3630 1210 455 zyy/zyy

3658 1219 43.4 zzz/zzz

FHG in PP RTA

2424 606 12.6 xxz/zzz

2501 625 13.9 yyz/zzz

3394 849 ~/8.9 zyy/yyz

3604 901 '^/17.3 zxx/xxz

4091 1023 40.1 zzz/zzz

THG in PP KTP

1082 361 ^/4.6 zyy/zyy

1213 404 4.6/00 xxz/xzx

1325 442 5.6/» yyz/yzy

1473 491 36.5 zxx/zxx

1623 541 47.8 zyy/zyy

1824 608 40.9/^ zxx/zxx

2052 684 ^/6.0 zyy/yyz

59.0/^ zyy/zyy

FHG in PP KTP

2161 540 9.8 xxz/zzz

2227 557 10.8 yyz/zzz

"Same as in Table 1. Nonlinear efficiencies ^ (d2if(xxz,xzx,

zxx) < (d:^2f(yyz,yzy,zyy) « (^33)^ (222). Note, in RTA, the THG and FHG of the He-Ne/CH4 standard (3392 nm) and the

rare BPM-BPM THG (3603 nm).

indices®^ and of the length ^"^ of the crystal, it did not

fit our experimental results well, probably because

the Sellmeier coefficients®'^ are not accurate beyond

3 /mm. Still, one set of coefficients^ enabled us to predict qualitatively that higher temperatures should

give THG at longer wavelengths and incidences closer

to normal, a prediction confirmed by the experiment.

We demonstrated experimentally THG coincidence

eee/eee in PP LN (Fig. 1, Table 1). A CO overtone

laser,"'^2 emitting on its u' = 30 -* i; = 28 band (3.54-

3.61 /um) with an output power of ^250 mW, was fo- cused to a 50-/xm waist in our 20 mm x 15 mm x 0.5-mm PP LN sample. The crystal was poled with a

period A = 31.5 /^m and antireflection coated at 1.8 and 1.2 /uLin. The output SHG at 1.8 /xm was measured with an InGaAs photodiode with a 2.2-yam cutoff. The efficiency inside the crystal was P(2aj)/Piaj)^ >

5.4 lO"'* W"^ The third-harmonic signal was then

detected and measured with an optical spectrum analyzer. The light was brought to it by a 400-^tmdiameter multimode fiber. This large fiber core was

most convenient for optimizing the mixing (crystal angles, focusing) for maximum THG signal.

By measuring the THG efficiency for different CO

laser lines, we determined that the optimum THG co- incidence point occurs at a shorter wavelength than

expected from the theory (Table 1). At room temperature the THG coincidence point for our crystal is at <3.54 /xm, which is in the gap between the 29 — 27 and

the 30 — 28 bands of our CO overtone laser. Even so, —200 mW out of the CO laser still produces a maximum

THG power of —0.5 nW at 22 °C and -15-deg incidence.

We were then able to temperature tune the optimum

coincidence point to 3.56 /xm [P28(9)], for a temperature

of 133 °C and nearly normal incidence. We obtained

a THG power of —7.3 nW (sufficient for phase-locking

purposes) for a CO power of 195 mW (Fig. 2), which

corresponds to a THG efficiency inside the crystal of

P{3uj)/P{a)f < 10"^W-2. This optimized efficiency

corresponds to normal incidence, i.e., maximum interaction length (collinear QPM) in our crystal.

As the first stage in using THG for optical frequency

synthesis we made a two-step, divide-by-nine frequency

conversion between 10.71 and 1.19 /xm. The CO over- tone laser, emitting at 84 THz on P28(ll) (3.57 /im),

TN-245
August 15, 1997 / Vol. 22, No. 16 / OPTICS LETTERS 1213

10 1

0.1 -

<3X

0.01 -

1180 1196

Fig. 2. THG power, at 133 °C, for several CO overtone

frequencies. The width of the signals is the resolution

of the optical analyzer, fixed by the fiber's diameter (in- put slit).

I[

. 1 mt^ wfWf m^ wV4i#M

^*

Fig. 3. MIM-diode voltage of beat note fco - ^fcOi- Vertical linear scale. Center frequency, 796 MHz; scan, 10 MHz; resolution and video bandwidths, 100 and 30 kHz,

respectively.

was frequency tripled in PP LN to 252 THz (1.19 /im).

It was also connected to a ^^C^^02 laser emitting on Pi(40) (28 THz, 10.71 /tm) by use of a metalinsulator-metal (MIM) diode; the electrical IF signal

from the diode corresponded to the beat note between

the tripled CO2 laser and the CO laser. ^^ The two

laser beams were focused on the MIM diode at or- thogonal angles, as has proved to be optimum. ^^ The

laser powers and the resultant rectified voltages in the

MIM were 70 mW and 0.5 mV for the CO laser and

200 mW and 5 mV for the CO2 laser. We obtained

a 796-MHz beat note with a signal-to-noise ratio of

~25dB in a 100-kHz detection bandwidth (Fig. 3), which should be adequate for phase locking the CO

laser. CO2 lasers have now been stabilized to the

hertz level on the short term, with subhertz Flicker

plateaus and reproducibilities of < 10 Hz.^* Phase

locking a CO laser to such a reference would yield a short-term stability of —10 Hz at 1.19 /xm.. We have demonstrated a new use of QPM in PP crystals for optical frequency mixing. One can remove the

constraint of finding coincidences by juxtaposing dif- ferent gratings in the same crystal, each grating corre- sponding to each desired mixing. This procedure can

also lead to an optical equivalent of rf diode mixers that

generate the sum, difference, and second harmonics of

two input frequencies. We have observed all four of

these mixings (occurring at different angles and QPM

orders) out of a single-grating PP LN crystal with in- puts from an 800-nm diode and a 1064-nm Nd:YAG

laser. More generally, Fejer et al. proposed an elegant

design method of phase matching curves by Fourier

analysis of spatial poling frequencies.^ Hence QPM

opens many new possibilities in optical frequency S5mthesis and high-resolution spectroscopy, especially be- cause these applications do not usually require high

power. Optical beat notes can be detected with >1 nW

of power, and ultrahigh-sensitivity saturation spec- troscopy can now be achieved with low initial power

by use of buildup in high-finesse optical resonators. ^^ We thank L. E. Myers, R. W. Fox, S. Waltman, A. Bredsford, K. Petrov, and J. L. Hall for significant

contributions to this research, which is supported in

part by the U.S. Air Force Office of Scientific Research.

*Permanent address, Calvin College, Grand Rapids,

Michigan 49546.

References

1.2.

3.

5.

6.

A detailed list of references is given in Ref 2. O. Pfister, M. Miirtz, J. S. Wells, L. Hollberg, and

J. T. Murray, Opt. Lett. 21, 1387 (1996), and references

therein.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and

P. S. Pershan, Phys. Rev. 127, 1918 (1962).

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer,

IEEE J. Quantum Electron. 28, 2631 (1992).

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer,

W. R. Bosenberg, and J. W. Pierce, J. Opt. Soc. Am. B

12, 2102 (1995), and references therein. For cascading three-wave mixings, see E. Yablonovitch,

C. Flytzanis, and N. Bloembergen, Phys. Rev. Lett. 29,

865 (1972); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae,

G. Stegeman, and E. Van Stryland, Opt. Lett. 17, 28

(1992). Optimally phase-matched cascading three-wave

mixings in nonresonant crystals (as here) is new: M.

Asobe, I. Yokohama, H. Itch, and T. Kaino, Opt. Lett. 22,274(1997)

7. We are grateful to one of the referees for pointing out

the existence of hybrid QPM-BPM coincidences in a

crystal whose length is partially poled.

8. M. V. Hobden and J. Warner, Phys. Lett. 22, 243 ( 1966).

9. G. J. Edwards and M. Lawrence, Opt. Quantum

Electron. 16,373(1984).

P. K. Gallagher, H. M. O'Bryan, E. M. Gyorgy, and

J. T. Krause, Ferroelectrics 75, 71 (1987).

E. Bachem, A. Dax, T. Fink, A. Weidenfeller, M.

Schneider, and W. Urban, Appl. Phys. B 57, 185 (1993). A. Dax, J. S. Wells, L. Hollberg, A. G. Maki, and W.

Urban, J. Mol. Spectrosc. 168, 416 (1994). K. M. Evenson, M. Inguscio, and D. A. Jennings, J. Appl. Phys. 57, 956(1985).

V. Bernard, P. E. Durand, T. George, H. W. Nicolaisen, A. Amy-Klein, and Ch. Chardonnet, IEEE J. Quantum

Electron. 31, 1913 (1995); O. Acef, Opt. Commun. 134,

479(1997).

15. J. Ye, L. S. Ma, and J. L. Hall, IEEE Trans. Instrum. Meas. 46, 178(1997).

10

11

12.

13

14

TN-246
PartV

Multiphoton Interactions and Optical

Coherences

1456 a reprint from Optics Letters

Optical probing of cold trapped atoms

R. W. Fox, S. L. Gilbert, L. Hollberg, and J. H. Marquardt

National Institute of Standards and Technology, Boulder, Colorado 80303

H. G. Robinson

Department of Physics, Duke University, Durham, North Carolina 27706

I

Received April 6, 1993

Transitions between excited states of laser-cooled £ind laser-trapped rubidium and cesium atoms are probed by

use of fiber and diode lasers. High-resolution Doppler-free spectra are detected by observation of the absorption

Eind fluorescence of light from the intermediate level of two-step cascade systems. The optical double-resonance

spectra show Autler-Townes splitting in the weak probe limit and more complicated spectra for a strongly

coupled three-level system.

The potential, and even the requirement, for the use of laser-cooled atoms in the highest-resolution

optical spectroscopy is well recognized,^ but little high-resolution optical spectroscopy has been done on laser-cooled neutral atoms. This is in marked

contrast to impressive demonstrations of extremely

high-resolution optical spectroscopy on laser-cooled

trapped ions.^ With room-temperature atoms and

Doppler-free techniques such as saturated absorption and two-photon transitions, the ultimate reso- lution and spectroscopic accuracy is usually limited

by velocity-dependent effects, such as transit time

broadening, second-order Doppler shift, and wavefront curvature.^ These limitations can be avoided

by the use of low-velocity atoms. Trapped-atom sys- tems also operate at low pressures, which should significantly reduce the pressure shifts that often plague

gas-cell wavelength measurements and stability.

Two important technological advances have greatly

simplified experiments with low-velocity atoms.

These are magneto-optic traps'* (also known as Zeeman-shift optical traps) emd the implementation

of these traps in a relatively simple vapor cell.^ Recent research with neutral atom traps has demonstrated very-high-resolution microwave spectra,^ nar- row Raman spectra,^ and optical spectroscopy out

of the ground state.® To our knowledge, our

experiments demonstrate the first high-resolution

optical spectroscopy of excited states of laser-trapped

and laser-cooled alkali atoms. By probing the

excited state of the trapping transition, we have an independent diagnostic of the conditions of the

trapped atoms.

In our experiments, cesium or rubidiiun atoms

are trapped in separate vapor cells by use of diode

lasers tuned to resonance lines of the atoms. Additional lasers are then used to probe the trapped

atoms in the excited state of the trapping-cooling

transition. The transitions of interest are shown

on simplified energy-level diagrams in Fig. 1. Most

of the experimental conditions are common to both

systems and are similar to those described in the

literature. ^'^ Small ion-pumped cell traps operate at

background alkali pressures that range from 10"^

to 10"^ Pa (« 10"^ -10-8 Torr). The trapping laser

beams are approximately 1 cm in diameter, with

—2-5 mW in each beam. In each experiment, an

elliptically polarized probe beam copropagates with

one of the trapping beams. These systems t3rpically

confine between 10' and 10® atoms in a 1-2-mmdiameter cloud at temperatures of a few hundred

microkelvins.

The study of rubidium is part of a program to develop a wavelength standard for optical communications in the 1.5-/u.m region.^" Atoms are trapped

with the use of two 780-nm diode lasers. The trapping laser is tuned to the low-frequency side of the

5Si;2, F = 2 ^ 5P3/2, F = 3 rubidium (®'Rb) cycling

transition and cools and traps the atoms. The re- pumping laser, tuned to the 5Si/2, F = 1 —» 5P3/2, F =

2 transition, prevents the atoms fi-om accumulating

in the F = 1 groxmd state. The trapping laser was

locked to the low-fi-equency side of the cooling transition by use of a signal from a saturated-absorption

spectrometer. The 1.529-)u,m 5P3/2 — 4D5/2 transitions were probed with the use of a tunable erbivmidoped fiber laser that has a fi-ee-running linewidth

of 1 MHz.^^ We observed these transitions by measuring their effect on the 780-nm trap fluorescence.

When the fiber laser is timed into resonance, it re- moves population from the 5P, F = 3 level and

Cs Hyperfine Levels Rb Hyperfine Levels

Fig. 1. Diagram of relevant energy levels of cesium

(^^^Cs) and rubidium (®''Rb) with the trapping- cooling (t), repumping (r), and probe (p) transitions indicated. TN-247
September 1, 1993 / Vol. 18, No. 17 / OPTICS LETTERS 1457

causes a reduction in the 780-nm fluorescent light

emitted by the trapped atoms. The fiber laser's ef- fect on this fluorescence can be quite large for the

5P, F = 3 — 4D, F = 3 and 2 transitions because

it optically pumps the atoms into the 5S, F = 1 state, removing them from the strongly fluorescing

5S, F = 2 ^ 5P, F = 3 — 5S, F = 2 cycle. The

atoms must then be pumped back into the cycling

transition by the repumping laser. When the re- pumping rate is relatively small, this depopulation

technique greatly enhances the sensitivity for detection of weak signals. ^^ ^he 5P, F = 3 ^ 4D,

F = 4 signal, however, is not enhanced because this

transition does not optically pump the atoms into the

F = 1 ground state. The 5S, F = 2, 5P, F = 3 and

AD, F = 4 levels compose a closed system of three

levels that are strongly coupled in the presence of

the two laser fields. A small modulation was applied

to the fiber-laser frequency, and the first derivative

of the 780-nm trap fluorescence was obtained by

use of phase-sensitive detection. Figure 2(a) shows

this derivative signal as the 1.529-/i.m fiber laser is scanned through the resonances. The trapped atoms in the cesium experiment

are probed by observation of absorption out of the

upper state of the 6Sl/2, F = 4 — 6P3/2, F = 5

trapping -cooling transition. We used both direct

absorption and derivative techniques to interrogate

the red 6P3/2, F = 5 ^ 98^2, F = 4 transition

at 658.8 nm. Approximately 1.5 mW of power at 658.8 nm was provided by an extended-cavity diode

laser that was frequency stabilized to a reference cavity, resulting in a short-term linewidth of —500 Hz.

The laser's asymmetric spatial mode was filtered

by a single-mode fiber used to deliver the light

to the trap. The probe beam diameter was set to be approximately the same size as the trappedatom cloud. After frequency stabilization, spatial

filtering, and amplitude noise subtraction, the probe

laser power at the trap was —40 ^(,W. Absorption

by the trapped cesium atoms was typically 1% and

provided a signal-to-noise ratio of ~ 10 in a 200-kHz

detection bandwidth. The power in the probe laser

is low enough so that it does not appear to perturb

the trap dynamics or the absorption line shape.

We accomplished precise detuning of the 852-nm

cesium trapping laser by offset locking the laser

(using an acousto-optic modulator) to a saturatedabsorption crossover resonance. Figure 2(b) shows

cesium absorption of the 658.8-nm probe light.

These cesium and rubidium cascade two-photon

transitions have high signal-to-noise ratios and,

because of the laser cooling, are free of Doppler

broadening and associated effects. The obvious

double-peaked nature of these signals is due to Autler-Townes splitting of the P states that is caused by the relatively strong trapping laser

light.13-15 Tj^g cesium 6P, F = 5 ^ 9S, F = 4

transition and the rubidium 5P, F = 3 —* 4D, F =

3 and F = 2 transitions are representative of the

moderately weak probe regime, in which the Rabi

frequency owing to the probe light is much less than the Rabi frequency owing to the trapping laser. The 5P, F = 3 — 4D, F = 4 rubidium transition

is in the moderately strong probe regime because

of the larger matrix element for this transition.

This strong coupling results in an asymmetic line shape. The observed linewidths are influenced by

power broadening owing to the lasers, the magneticfield gradient that causes splitting of the Zeeman

levels, and nonuniform laser-field strength across the volume of the trap. From our measurements of

linewidths with the magnetic field off, we conclude

that broadening that results from the splitting of

Zeeman levels is less than 1 MHz. We estimate that

the residual Doppler broadening is less than 300 kHz.

It is actually remarkable that the experimental

line shapes are so narrow; linewidths as narrow

as 3.1 MHz FWHM were observed on the 658.8-nm

transition in cesium. This is to be compared with

a natural width for the P state of 5.3 MHz. The

ultimate probe transition linewidth is not affected by

the intermediate-state lifetime; instead, it is limited

by the natural linewidth of the upper level, ^^ which

is —0.97 MHz for the 9Sv2 state of cesium and — 1.8 MHz for the 4D5/2 state of rubidium.

50 100 150 Fiber Laser Tuning (MHz)

(a)

0^0

(b)

Fig. 2. (a) Rubidium line shape showing the derivative

of the 780-nm fluorescence signal as the 1.529-/i.m fiber laser was scanned through the 5P3/2, F = 3 — 4D5/2, F = 4,

3, and 2 transitions. The trapping laser detuning was

- 11 ± 1 MHz, and the Rabi frequency was 8.5 ± 0.5 MHz.

The fiber-laser intensity was 0.7 ± 0.2 mW/cm^. (b) Ce- sium absorption at 658.8 nm as a function of the probe

laser frequency for various trap laser detunings. We

improved the signal-to-noise ratio by averaging 200 scans

at each detuning. The large peaks on successive lines were aligned to display clearly the change in splitting.

TN-248
1458 OPTICS LETTERS / Vol. 18, No. 17 / September 1, 1993

10 20 30 40 50 60 658.8-nm Tuning (MHz)

70

Fig. 3. Theoretical cesium-absorption line shape and ex- perimental data points for 9-MHz detuning of the trapping laser and a Rabi frequency of 11 MHz. The ex- perimental data show sidebands at 4 and 54 MHz that

result from 25-MHz modulation of the probe laser. These

sidebands are used for determining the frequency scale.

A density matrix model with five energy levels was

used to calculate theoretical line shapes for the twophoton resonances. Three of these levels, 1 1), |2), and

|3) with energies El < E2 < E3, form the cascadelevel system that is coherently excited by two lasers. The remaining two levels, |4) and |5), are artificial levels that represent decay channels from |2) and

1 3) and can themselves decay only to the ground

state |1). These artificial levels approximate the real

effects of decay through other hj^erfine levels and

the repumping by a third laser. The parameters

entering the theory include the trap laser detuning

from resonance, the probe laser frequency (which was

swept), the Rabi frequencies for the two applied laser

fields, and the six relaxation coefficients between

states. The relaxation coefficients and radiative decay constants come from known Einstein A values.

Our analysis follows that of previous research^^ with some extensions.

To make the analysis tractable, we assume motionless atoms, uniform laser intensity, no collisions,

and no trap dynamics. A simplified model of Zee- man broadening and magnetic-field gradients has

been included. The general features of the theoretical line shape agree with the experimental results

(see Fig. 3), but quantitative agreement is not found

within experimental uncertainties. Our model contains no free parameters, other than signal size,

and generally gives line shapes that are too narrow.

Quantitative agreement of the line shapes should

yield illuminating details of the djniamics of the

trapped atoms, but will require more sophisticated

models of the conditions within the trap. The most

significant simplification in our model is the lack

of averaging over the three-dimensional atom density and laser field and hence over the variation in

Rabi frequency. These spatial variations may ac- count for the difference between observed and cal- cvdated linewidths.

The potential accuracy in determining the line center in these narrow two-photon transitions is yet

to be determined. Though essentially free from sys- tematic effects owing to pressure, Doppler, transit,

and wave-front perturbations, the transitions are af- fected by ac Stark shifts resulting from the trapping

laser and, to a lesser extent, by the trap's magnetic

field. These problems could be reduced by temporarily turning off the trapping fields while probing the

atoms with weak laser fields. These experiments have demonstrated the potential for high-resolution optical detection of narrow

transitions in trapped neutral atoms. Experimental

line shapes give good qualitative and fair quantitative agreement with calculations based on a simple

model. Trapped neutral-atom spectroscopy yields

Doppler-free signals and diagnostic information

about the conditions of the trapped atoms; the

Autler-Townes-split line shape provides information on the average square of the laser electric field that

the atoms experience. As with trapped ions, we can

anticipate that spectroscopy in these systems will soon measure resonances for which the accuracy and

precision are not limited by the atom's environment.

We gratefully acknowledge the helpful comments

of C. Wieman, C. Weimer, J. L. Hall, and J. Bollinger

and the support of the U.S. Air Force Office of Sci- entific Research, NASA, and the Naval Command,

Control and Ocean Surveillance Center.

References

1. J. L. Hall, M. Zhu, and P. Buch, J. Opt. Soc. Am. B 6, 2194 (1989); W. Ertmer and S. Penselin, Metrologia

22, 195 (1986).

2. J. C. Bergquist, W. M. Itano, F. Eisner, M. G. Raizen,

and D. J. Wineland, in Light Induced Kinetic Effects in Atoms, Ions and Molecules, L. Moi, ed. (ETS Editrice,

Pisa, Italy, 1991), p. 291; W. Nagoumey, N. Ya, and

H. Demelt, Opt. Commun. 79, 176 (1990).

3. C. J. Borde, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).

4. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D.

Pritchard, Phys. Rev. Lett. 59, 2631 (1987).

5. C. Monroe, W. Swann, H. Robinson, and C. Wieman,

Phys. Rev. Lett. 65, 1571 (1990).

6. C. Monroe, H. Robinson, and C. Wieman, Opt. Lett. 16, 50 (1991); A. Clairon, C. Salomon, S. Guellati, and

W. D. PhilUps, Europhys. Lett. 16, 165 (1991); K. Gibble and S. Chu, Phys. Rev. Lett. 70, 1771 (1993).

7. D. Grison, B. Lounis, C. Salomon, J. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991); J. Tabosa,

G. Chan, and H. Kimble, Phys. Rev. Lett. 66, 3245

(1991); L. Hilco, C. Fabre, and E. Giacobino, Europhys.

Lett. 18, 685 (1992).

8. M. Zhu, C. W. Gates, and J. L. Hall, Opt. Lett. 18,

1186 (1993).

9. K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).

10. S. L. Gilbert, Proc. Soc. Photo-Opt. Instrum. Eng.

1837, 146 (1993).

11. S. L. Gilbert, Opt. Lett. 16, 150 (1991).

12. D. J. Wineland and W. M. Itano, Phys. Lett. 82A, 75

(1981).

13. S. H. Autler and C. H. Townes, Phys. Rev. 100, 703

(1955); R. M. Whitley and C. R. Stroud, Jr., Phys. Rev. A 14, 1498 (1976).

14. J. L. Picque and J. Pinard, J. Phys. B 9, L77 (1976).

15. P. R. Hemmer, B. W. Peuse, F. Y. Wu, J. E. Thomas,

and S. Ezekiel, Opt. Lett. 6. 531 (1981).

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Volume 75, Number 8 PHYSICAL REVIEW LETTERS 21 August 1995

Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum

Interference in Rb

A.S. Zibrov,''2-^-5 M.D. Lukin,'-^'^ D. E. Nikonov,'-^ L. Hollberg,^ M.O. Scully,'-^ V. L. Velichansky,'^

and H. G. Robinson'^

^ Department of Physics, Texas A&M University. College Station, Texas 77843

^Texas Laser Lab, HARC, The Woodlands, Texas 77381

^ Max-Planck-Institut fiir Quantenoptik, D-85748 Garching, Germany

'^National Institute of Standards and Technology, Boulder, Colorado 80303

^Lebedev Institute of Physics, Moscow, 117924 Russia

(Received 23 February 1995)

Laser oscillation without population inversion is demonstrated experimentally in a V-type atomic

configuration within the D\ and Di lines of Rb vapor. It is shown that the effect is due to the atomic

interference. The experimental results, as first predicted by careful theoretical analysis, are in a good

agreement with detailed calculations.

PACS numbers: 42.50.-p, 42.55.-f

In the present work, laser oscillation without population

inversion (LWI) [1] is reported for the first time. Our

demonstration makes use of noninversion gain in a Vtype [2] cw amplifier. In order to obtain a clear proofof-principle demonstration of LWI oscillation, we carried out a set of experiments which include the following:

the observation of inversionless amplification of a weak

probe light by a coherently prepared atomic medium,

experimental verification of the absence of inversion, and,

finally, observation of noninversion laser oscillation in a cavity.

Several recent experiments [4,5] have already demonstrated the possibility of noninversion amplification.

These experiments were based on observation of amplification in A-type systems [6] which involved coherent

population trapping and can therefore be viewed as amplification with inversion in a dressed state basis. V-type inversionless amplification is itself conceptually

interesting in that the physics of resonant V-type LWI is the cancellation of absorption via quantum interference. And there is, in general, no dressed state basis in which

there is a "hidden" inversion. Furthermore, the present

work is a technical advance, in that it is the first observation of gain without inversion using low power cw

diode lasers. The present experiment was suggested and modeled

by a detailed theoretical analysis, the results of which

may be understood by considering the four-level model

of Fig. 1 (a), although the actual calculations were carried out using a realistic model of Rb^' with all hyperfine

and Zeeman sublevels included. Two sublevels of the ground state are coupled to a pair of excited states via

three fields. A strong driving field with Rabi frequency

(1^ and a weak probe field with Rabi frequency n„ are assumed to be quasimonochromatic. These fields have

linewidths A^c and lS.Va, both of which are much less than atomic radiative decay rates. The third (pump) field

is taken to be incoherent, i.e.. it has a very broad linewidth

(At-pump ^ ya^Jc) and is represented by an incoherent

pumping rate r [see Fig. 1(a)]. In the absence of the incoherent pump field, almost all the population is optically pumped into the state b' by

the strong driving field. The incoherent pump destroys

this optical pumping by populating the upper state a, and

thus state /?, via spontaneous decay. Hence the population

difference paa ~ Pbb is determined by the rates with

0.2 0.4 0.6 0.8 Pumping (l/lsat)

(a) (b)

FIG. 1. (a) Simplified four-level model for lasing without

inversion. In our realization of the model in Rb*^ \a)

corresponds to sublevels |Pi/2, F = 2), \c) = IP3/2, F = 2) and the two sublevels of ground state \b) = \S\/2, F = \) and

\b') = ISi/2, F = 2). Driving field Q, is tuned to the Di

resonance from the F = 1 ground state to F = 2 of excited

state, probe field fta couples the same sublevels of the ground

state with levels having F = 2 of the F1/2 excited state. Polarizations of the fields are described in the text. ( b) Results of numerical modeling for the realistic 32-level scheme of Rb. Gain X Sv/NA'L (solid line) and inversion per atom (dashed

line) as a function of the incoherent At- = 50 MHz pump

laser intensity; parameters are |n,| = 30 MHz, H- = lO'^'T.

All fields are in the exact resonance with corresponding

transitions in the center of the Doppler profile. Inversion

is defined as the sum of populations of levels F]/2, F =

2, Mf = 0, ± 1 minus populations of ground state sublevels having F = 1 with corresponding My. Incoherent pumping

rate is expressed in terms of Rabi frequency and a linewidth of

a pumping laser as / = l\£i^^n.,^\^ l{S.v -F yal2)ya0031 -9007/95/75(8)/ 1499(4)$06.00 © 1995 The American Physical Society

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1499
Volume 75, Number 8 PHYSICAL REVIEW LETTERS 21 August 1995

which atoms leave and decay into the states a and b. Note

that in the limit of a weak probe field, atoms can leave state b only via state c. Thus the population difference above

is determined by the ratio of decay rates from level a to level b and from level c to level b'. If level c decays more

slowly than level a, an inversion on the transition coupled

by the^weak probe field cannot be created. Amplification of a weak probe field on the a io b

transition is. however, possible, due to the presence of

atomic coherence between upper levels a and c. The

physical origin of this mechanism is to be interpreted

as a quantum interference cancellation of absorption.

Alternatively, reduction of absorption and enhanced gain can be viewed as a result of a Fano-type interference

between the dressed states [2]. The gain (absorption) coefficient for a weak probe field on the a to b transition is proportional to the imaginary

part of the off-diagonal element of the atomic density

matrix p^fc- In the weak probe field limit, and under

conditions of exact resonance, we obtain the gain

G =

3\~NLya Impat ^

477 ria Ait

(Paa ~ Plb) + \^c\-lyacybAplb X pD

Jab + \^c\'/yac

(1)

where p„ is the population of level / calculated to the zeroth order in the probe field. y,y is the relaxation rate of

the density matrix element p,y, A'^ is the density of atoms,

L is cell length, and A is the probe laser wavelength.

From the second equality in Eq. (1) we see that there are two contributions of the upper-level coherence

which modify the usual gain or absorption. The first

is the dynamical Stark effect [7], studied theoretically

a

-3O0 -2D0 -100 100 200 300 400

Ovtunrng (IfHz)

-190 (90 3n rX) 760

(iequency of the probe (MHz)

frequency of

the probe

(a) (b) (c)

FIG. 2. (a) Calculated absorption (gain) coefficient for a weak

probe field as a function of its frequency in the vicinity of

1 — 2' resonance of the D\ line. Parameters and scaling

correspond to those of Fig. Kb). Detuning is from the center of the absorption line. Upper curve, without incoherent pump; lower curve, r = 0.4. (b) Experimentally measured

transmission of the probe laser as a function of its frequency. Curve a, without the incoherent laser; curve b, with incoherent

laser. Estimated parameters for the experiment are fi, ~

30 MHz, n,, ~ 0.1 MHz, r ~ 0.4. (c) Experimental results for transmission of the probe field showing the influence of

a probe laser linewidth on its transmission spectrum. Curve

a, without modulation of current; curve b, with modulation of

current [Ivp ~ 10 MHz).

1500

and experimentally m a V-type configuration in [3]; it is responsible for the lO^-l" term in the denominator.

There is, however, another important effect which modifies the properties of the V scheme. This contribution is represented by the term proportional to the Ifld" in the numerator of Eq. (1) and is precisely due to the quan- tum interference of absorption mentioned above. It fol- lows from Eq. (1) that absorption interferes destructively

if phh ~ PcL > 0. This leads to a reduction of absorption and enhances the gain. As a result the probe field can be amplified even if paa ~ Pbb < 0- We would like to underscore the fact that quantum interference is the only reason for inversionless gain in the V scheme, i.e., there is no inversion in any dressed state picture (provided

the drive and the probe fields are equally detuned from

resonance).

Motivated by these simple considerations, we choose

for the present experiment in Rb*^ the following combination of the fields. The coherent drive is Jc polarized and couples sublevel 1 [8] of the 5i/2 state with

sublevels of the P3/2 state (the power ranged from 1 to 20 mW in 0.9 mm spot). The probe laser is z polarized

and couples sublevels 1 — 2' (the probe power ranged

from 0.5 to 50 /o^W in a 0.7 mm spot). The third beam

(incoherent pump) comes from a solitary diode laser that had a broad variable linewidth of 50-200 MHz, an out- put power 10 mW, and a diameter in the cell of 8 mm,

which encompassed both the probe and pump beams. All

fields propagate in the same direction, hence, for suffi- ciently strong drive field the amplification peak is essentially Doppler free. To obtain amplification without inversion in our scheme, a weak magnetic field in the z direction is re- quired. This field destroys Zeeman coherences within the F = 1 ground state manifold created by an x polarized

incoherent pumping field. Without the magnetic field population tends to collect in certain coherent superpositions of sublevels of this manifold. We found that the optimum range (for the given linewidth of the incoherent

field) of the magnetic field //; is of order 10"'* T. To investigate the possibility of LWI in this scheme we have numerically solved density matrix equations

for the 32-level scheme of Rb, taking into account all relevant Clebsch-Gordan and Racah coefficients, field polarizations, Zeeman sublevels, and Doppler broadening.

The results of the modeling are presented in Fig. 1(b). The results, for this particular field configuration, turn out to be very similar to those obtained from the simple

four-level model of Fig. 1(a). As shown in Fig. 1(b)

the gain increases as a function of the incoherent pump

intensity, while inversion is negative and decreases within

incoherent pump intensity.

A remarkable feature of the amplification peak in Figs. 2(a)-2(c) is its narrow width. This is determined

in our case by the Rabi frequency of the driving laser. In contrast, the optical pumping peaks are broader, since

their width is determined by the optical pumping rate

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Volume 75, Number 8 PHYSICAL REVIEW LETTERS 21 August 1995

of the driving field and the slow ground state relaxation

rate. The calculated spectrum for the probe transmission

is presented in the Fig. 2(a). Agreement between theory

and experiment is excellent. In the experiment we use a 4 cm long Brewster cell containing natural Rb heated to —60 °C. The driving

and probe lasers are tunable extended cavity diode lasers, having short-term linewidths on the order of 100 kHz.

The drive and probe beams were separated after the cell with a diffraction grating. In the first set of experiments the transmission of the probe field was measured as a function of its frequency.

The frequency of the driving laser was tuned within

the Doppler profile of the D2 absorption line, while the frequency of the probe laser was swept through the D\

line. The results of the transmission measurements are shown in the Fig. 2(b). This figure shows the portion

of the transmission spectrum which corresponds to the coupling of the probe field to the 1 — 2' transition within

the D\ line. The first experiment was done without the incoherent

pump laser [curve a in Fig. 2(b)]. On the broad Doppler

profile apparent in the transmission spectrum of the probe

beam we see two transmission peaks. They are due to the

optical pumping of specific velocity groups by the drive

laser. There are three such groups within the velocity

distribution; for one of these groups the drive field is resonant with 1 — 2" transition [left peak in Fig. 2(b)]

and for others it couples levels 1 with 1" and 1 with

0". Since the frequency separation between the last two

transitions is small, both of these groups contribute to the

right optical pumping peak.

In the second experiment [curve b in Fig. 2(b)] the incoherent pump was added and its frequency was tuned

such that it couples 2 —* 2' transition. We clearly observe an increase in the transmission of the probe corresponding

to amplification of the weak probe field in the vicinity of

1 —* 2" optical pumping peak. The amplification occurs

in spite of the fact that the results of optical pumping

(a)

wavelength of driving laser

(b)

FIG. 3. (a) Schematic of the ring resonator closed by a polarization beam splitter cube for the LWI oscillator experiment;

ref is a reference cell with Rb; output from the cavity is ana- lyzed using a monochromator. ( b) Dependence of the driving

field absorption (curve "a") in the reference cell and the cor- responding dependence of the cavity output power at 794 nm

(curve "^") as a function of the frequency of a driving field. Three peaks of the curve a correspond to the three longitudinal

modes of the cavity (with frequency separation —170 MHz).

are destroyed by the incoherent laser. Because of the reverse optical pumping effect, the absorption of the probe

increases in all other parts of the spectrum. We also notice

that the amplification peak has a much narrower width

[—30 MHz in Fig. 2(b)] than the pure optical pumping

peaks of curve a. With present experimental conditions we observe approximately 8% to 16% gain per pass. To verify the absence of a population inversion we carry out an experiment with different linewidths for the probe

laser. Since the probe field is weak, it does not affect the population distribution in our system. However, its phase fluctuations do affect the coherent contribution to the gain coefficient [9]. This is due to fact that phases of

atomic coherences cannot follow fast phase fluctuations of

the fields and therefore, on average, coherent contributions

are reduced. Indeed, the probe laser linewidth adds to the decay rate of the upper-level coherence. Consequently,

if At-a > ya,b-, the linewidth contribution dominates the coherence decay rate, and therefore reduces the contribution due to atomic interference in the gain coefficient. In the limit At'a » ya,b the interference contribution vanishes, and therefore amplification without inversion should

disappear.

In our original experiment the linewidths of probe

and driving lasers are relatively narrow (At- —

100 kHz « 7a = 5.4 MHz, jb =5.6 MHz). However, we can change these linewidths from 100 kHz to 50 MHz by modulating the diode laser's injection current with a noise signal. Figure 2(c) shows the result of such

a modulation of the current to the probe laser. In this experiment all three lasers are present in the cell, and

therefore without the additional modulation we see the

typical amplification peak [curve a in Fig. 2(c)]. In the presence of the current modulation the linewidth of the probe laser was —10 MHz, and we observe that the amplification disappears (curve b). Since the populations of

the levels are not changed, this proves that the observed

amplification is not due to population inversion, i.e., it is LWI due to quantum interference effects. Having observed the amplification of a weak probe field and having verified the absence of a population inversion, we are able to demonstrate the buildup of laser oscillations

in a cavity at the frequency corresponding to the 1 — 2' transition of the D\ line. To this end the Rb cell was

placed inside the ring cavity [Fig. 3(a)]. One mirror of

this cavity was formed by a polarization cube in order to allow for a substantial transmission of Jc -polarized driving

field, and, at the same time, high reflectance for a z- polarized lasing field. The laser radiation at 794 nm was

selected at the cavity output by using a monochromator.

The frequencies of driving and incoherent pump lasers were controlled by using additional reference cells with

Rb. The typical dependence of the output power from

the cavity at 794 nm and corresponding absorption of

the driving field in the reference cell is presented in the Fig. 3(b) as a function of driving field frequency.

When driving laser (780 nm) is tuned near the center

1501

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Volume 75. Number 8 PHYSICAL REVIEW LETTERS 2i August 1995

of the D: absorption line (1 — 2" transition), the laser oscillation at 794 nm appears in the ring cavity. This

laser field oscillates at the frequency corresponding to the

1 —< 2' transition of the D\ line as was verified by making

a beat note with an independent laser. The beat note measurement shows a direct one-to-one correspondence

of the tuning of 795 nm laser with the frequency of the driving laser, which again confirms that the observed

lasing is caused by coherent interaction of the drive

laser with atoms. This tuning, along with the fact that the incoherent pump is spectrally broad, rules out the

possibility that the lasing is due to Raman gain. Under

conditions similar to that of the pump-probe experiment

except with no probe present we observed approximately

30 yuW of lasing power at 794 nm.

In conclusion, we have experimentally shown inver- sionless amplification and lasing in a Rb gas cell coherently prepared by a cw diode laser. To prove that the gain

is "without inversion" we performed measurements with

various linewidths of the probe laser, showing that when

the linewidth of the probe laser exceeds the radiative de- cay rate, the amplification peak disappears. This establishes the LWI nature of the observed amplification and

the absence of population inversion. And, finally, self- generated laser oscillation was observed when the inver- sionless gain medium was placed inside a laser cavity that was resonant with the appropriate transition of the D\ line. The authors gratefully acknowledge useful discussions

with E. Arimondo, M. Fleischhauer, E Fry, T. Hansch,

and A. Weis, valuable assistance of T. Zibrova, and the support from the Office of Naval Research, the Welch

Foundation, the Texas Advanced Research Program, and

the Air Force Office of Scientific Research.

[ 1 ] For recent theoretical work on LWI in multilevel schemes

see, e.g., O. A. Kocharovskaya and Ya. I. Khanin, Pis'ma

Zh. Exp. Teor. Fiz. 48, 581 (1988) [JETP Lett. 48, 630

(1988)]; S.E. Harris, Phys. Rev. Lett. 62, 1033 (1989);

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, ibid. 62, 2813 (1989); A. Imamoglu, J. E. Field, and S.E. Harris,

ibid. 66. 1154 (1991). For a review of the subject, see O. Kocharovskaya, Phys. Rep. 219. 175 (1992)

[2] Interaction of optical fields in a V-type atomic configuration was studied long ago [3] but recently attracted renewed attention and was investigated theoretically in

the context of LWI, see. e.g.. O. Kocharovskaya and

P. Mandel. Opt. Commun. 84, 179 (1991); M. Fleis- chhauer etaL. Phys. Rev. A 46. 1468 (1992); W. Tan, W. Lu. and R.G. Harrison, ibid. 46, 3613 (1992); G.A.

Wilson. K. K. Medun. P. B. Sellin. and T. W. Mossberg,

ibid. 50. 3394 (1994); M. Fleischhauer. T. Mclllrath, and

M.O. Scully, Appl. Phys. B (to be published).

[3] I.M. Beterov and V. P. Chebotaev, Sov. Phys. JETP Lett.

9, 127 (1969); T. Hansch et ai. Z. Phys. 226, 293 (1969);

T. Hansch and P. Toschek, ibid. 236. 213 (1970); M.S.

Feld and A. Javan, Phys. Rev. 177. 540 (1969).

[4] Xingfu Li et ai, in Proceedings of the International Conference on Lasers '92, Houston, 1992 (STS Press, McLean, VA 1992), p. 446; A. Nottelmann, C. Peters, and W. Lange, Phys. Rev, Lett. 70, 1783 (1993); E.S. Fry

et at., ibid. 70, 3235 (1993); W.E. van der Veer etaL.

ibid. 70, 3243 (1993).

[5] Some interesting experimental studies of LWI continue to be a source of discussion. For example, in the interesting

experiments of J. Gao et al. [Optics Commun. 93, 323

(1992)] and Gao et al. [ibid. 110. 590 (1994)] it is difficult to assess experimental evidence for the absence

of inversion. Moreover, theoretical modeling which takes

into account Zeeman sublevels shows that simple LWI of

the type studied theoretically by L. Narducci et al. [Opt.

Commun. 81, 379 (1991); 86, 324 (1991)] cannot, in fact, be observed under the conditions of these experiments,

see, e.g., G. M. Meyer et ai. Quantum Opt. 6. 231

(1994). Interpretation of some of the results in the recent expjeriment of J. A. Kleinfeld and D.A. Streater, Phys. Rev. A 49. 4301 (1994), are also complicated

from the theoretical point of view for a similar reason. Nevertheless, coherence effects were observed in these experiments. Further theoretical considerations along

these lines will be published elsewhere.

[6] G. Alzetta, A. Gozzini, L. Moi. and G. Orriols. Nuovo

Cimento B 36. 5 (1976); E. Arimondo and G. Orriols. Nuovo Cimento Lett. 17, 333 (1976); H. R. Gray. R.M.

Whitley, and C. R. Stroud, Jr., Opt. Lett. 3, 218 (1978).

[7] S H. Autler and C. H, Townes. Phys. Rev. 100. 707 (1955).

[8] In the present paper we use the following notations

to distinguish different sublevels of Rb'*^. 1 and 2 denote the F = 1 and F = 2 hyperfine components of

the 5i/2 ground state, 1' and 2' are hyperfine components

of the first excited state P,/:. and 0". 1", 2". and 3" are sublevels of the P-m state with corresponding F.

[9] G.S. Agarwal, Phys. Rev. A 18, 1490 (1978); B.J. Dalton and P. L. Knight, Optics Commun. 42. 41 1 (1982); M. Fleischhauer et ai, ibid. 110. 351 (1994).

1502

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1384 J. Opt. Soc. Am. B/Vol. 13, No. 7/July 1996 Marquardt et al.

Line shapes of cascade two-photon

transitions in a cesium magneto-optic trap

J. H. Marquardt, H. G. Robinson, and L. Hollberg

National Institute of Standards and Technology, Boulder, Colorado 80303

Received August 16. 1995; revised manuscript received November 30, 1995 We present a study of a two-photon double-resonance transition in cold cesium atoms in a magneto-optic trap. A closed five-level density matrix model of the system is developed to characterize the double-resonance Autler-Townes-split absorption line shape. Comparing this model with experimental spectra, we gain

insight into the dominant process involved in trapping atoms, in particular, the importance of the interference

of the six trapping laser beams. This system is used to probe transient effects in the trap as well as collective

effects of the trapped atom cloud resulting from the intentional misalignment of the trapping beams.

1. INTRODUCTION

We investigate the detailed line shapes of cascade two- photon transitions in laser-cooled and trapped atoms. There has been much research on the use of cold, trapped

atoms for microwave frequency standards,^ ultracold atom collisions,^ and spectroscopic dynamics of cold, trapped atoms.^ Some of this research has lead to sur- prising results in terms of narrow optical resonances, evidence of quantized motion, atomic localization in atom

traps,* and other effects. Various mechanisms that pro- duce low temperatures in these traps are now understood.

In addition, some theoretical models are now able to cal- culate detailed line shapes of the spectroscopic features observed on the cooling and trapping transitions.^ Other

effects, including some aspects of the collective behavior

of trapped atoms and unusually long relaxation times

remain unexplained. Further detailed spectroscopic in- vestigations of cold, trapped atoms promise new surprises as we learn more about their environment.

Our experiment consists of optically probing cold, trapped cesium atoms, which are excited to the 6P3/2 state by the absorption of the cooling and trapping laser. A probe laser, tuned to the 6P3/2 —» 9Si/2 transition at 658.8 nm, is sent through the trapped atoms, creating a doubly resonant two-photon transition (Fig. 1). The

probe field is weak and nonperturbing and completely

independent of the trapping laser fields. In our experimental work we observed relatively narrow Rabi-split

two-photon line shapes that are reminiscent of atomic

beam studies of Gray and Stroud and of Hemmer et al.,^ except that in our case the atoms are cooled and trapped

by the resonant radiation and a weak magnetic field. The system consists of magnetic-field gradients and

strong laser fields at 852 nm necessary for the trapping of the atoms in the usual cr^-cr magneto-optic

trap (MOT) configuration. The signal that we observe

is the absorption of the 658.8-nm laser as it is tuned

across the two-photon resonance. Because the splitting

and the shape of the absorption signal depend on the

properties of the trap, understanding the features of the

line shape provides knowledge of the local environment of the atoms. Independently probing the perturbing effects

of the trapping fields will be important in future realiza- tions of optical frequency and length standards based on

laser-cooled and trapped atoms.

Initially, we developed a simple theoretical model

describing this double-resonance experiment,^ which

showed the qualitative features of the experimental line shape but quantitatively was not in good agreement with

the experimental results. We have improved the model

by including important additional effects, such as the

three-dimensional nature of laser field and intensity dis- tributions and the effects of laser beam phase fluctuation. In this paper we present a detailed description of

this improved model and its comparison with the experimental data.

2. EXPERIMENT

The cesium atoms are cooled and trapped in a standard

vapor-cell MOT. Our MOT is similar to those described

in the literature* and is shown schematically in our ex- perimental setup in Fig. 2. We use two extended-cavity

diode lasers for the trap, one relatively powerful laser (—30 mW) for cooling and trapping and a second laser (~1 mW) to recirculate atoms that have fallen into the

F = 3 h5T)erfine ground state. The cooling and trapping light is tuned to the low-frequency side of the 6S1/2, F = 4 —> 6P3/2, F = 5 cycling transition. To lock the

trapping laser at a specific detuning, the laser beam is sent through an acousto-optic modulator (AOM), where

a small percentage of the light is frequency shifted and

sent through a separate cesium cell used for saturated absorption. The laser is locked to the saturated-absorption

signal corresponding to the nearest crossover resonance to the 6S1/2, F = 4:—> 6P3/2, F = 5 transition. The frequency

of the trapping laser is controlled by use of a rf synthesizer to drive the AOM. The repumping laser is tuned

to the 6S1/2, F = 3^ 6P3/2, F = 3or F = 4 transition and

locked to the side of the cesium Doppler profile in a sec- ond, separate cesium cell. The 6P3/2 state of the trapped

atoms is then interrogated by direct absorption of a diode

laser tuned to the excited 6P3/2, F = 5 — 9Sy2, F = 4

transition at 658.8 nm. Approximately 1.5 mW of 658.8- nm light was provided by an extended-cavity diode laser.

TN-254
Marquardt et al. F=4^

9 %,,

F=3 \

\

\ probe

658.8 nm\ i"ef

6V,

Fig. 1. Relevant cesium energy levels and the hyperfine structure, showing the lasers used for the magneto-optic trap and the cascade two-photon transition.

This laser was frequency stabilized to a reference cavity, which resulted in a short-term line width of —500 Hz

with low-frequency jitter of ~5 kHz. The laser's spatial

mode was filtered by an optical fiber, which delivered the

light to the experiment. The probe laser was elliptically

polarized and copropagated with one of the six trapping

beams. The diameter of the probe beam was set approximately equal to the diameter of the trapped atom cloud. After spatial filtering, frequency stabilization, and amplitude noise subtraction, the probe laser power avail- able at the MOT was —40 ijlW. The absorption on the

658.8-nm transition by the cesium-atom cloud ( — 10^ cold atoms) was typically —1%. (Fluorescence detection could

have been chosen as well but would have required good

imaging optics, filtering of the strong 852-nm Ught, etc. Absorption detection was chosen because of its relative simplicity.) The power of the probe beam was low

enough that it did not appear to perturb the trap dynamics or the profile of the absorption line shape.

A typical absorption spectrum of the 658.8-nm probe

laser is shown in Fig. 3. The doubly peaked profile of

this transition is attributed to the optical Autler-Townes

effect (ac-Stark splitting). Because of the strong trapping laser fields, we expect a doublet structure of the cou- pled ground and the first excited states. These states exhibit a well-defined generalized Rabi splitting that de- pends on the detuning and the Rabi frequency of the trapping laser and the decay rates of the atomic states (the

Rabi frequency is given by a2i = /X2i^2i/^, where iX2\ is the dipole matrix element and E21 is the amplitude of the

laser field driving the 6S1.2 —' ^Pm transition).

The characteristics of the line shape were investigated

as functions of various trap parameters. For example,

Fig. 4 shows the variation of individual 658.8-nm absorption line shapes with detuning of the trapping laser fre- quency. In this figure the centers of the larger peak

were aligned fin frequency space) to show clearly the

dependence of the splitting on the trap detuning. We

can compare these individual line shapes with theory to

Vol. 13, No. 7 /July 1996/ J. Opt. Soc. Am. B 1.385

evaluate our model of the trapping environment. In particular, we studied the Autler-Townes splitting, the peak

height ratios, and the widths of the absorption peaks as a function of the trap parameters. This gave valuable

information about the local fields in the trap. The de- tuning of the trapping laser was limited by the range

of stable trap operation. The overall height of the sig- nal in the figure varied with the number of trapped

atoms, obviously a function of the detuning. The maximum signal corresponded to a magnetic field gradient of -15 X 10"* T/cm (- 15 G/cm) and a detuning of ~2r to the low-frequency side of the transition {Y/2tt = 5.1 MHz

is the natural linewidth for this transition in cesium).

3. THEORY

We have developed a theoretical model of the two-photon

transition that includes many of the physical processes that affect the atomic spectra of the trapped atoms. It

Trapping

Laser 852 nm

Sat. AbsJ I RF

-XT

^

AOM

Side Lock

Repumping 852 nm - !• , Laser i - r

-

To Trap

Detector

MOT

Probe

Laser V > Fiber 658.8 nm /

\ > Cavity

J

Fig. 2. Schematic diagram of the experimental laser setup. The trapping laser is locked to a saturated-absorption crossover

feature in a separate cesium cell. The AOM is used to frequency offset the lock point from the saturated-absorption

<Sat. Abs.) feature. The repumping laser is locked to the side of the Doppler profile in a different cesium cell. The dashed lines represent servo loops needed to lock the lasers. The vertical pair of trapping beams and the magnetic-field coils are not shown. The detectors are used to monitor direct absorption of the probe beam and trap fluorescence.

20 30 40 50

658.8 nm Tuning (MHz)

Fig. 3. Typical absorption spectrum taken in our MOT with standard cr^/cr" laser polarizations. The trap detuning

(52i/2n-| was 10 MHz; oBtrap/^^ = 16 x 10"-* T/cm (16 G/cmi.

Cloud diameter —3.5 mm, —2.5 mm in height, —10* atoms,

effective Rabi frequency a2i of 15.5 MHz. The 658.8-nm laser

is swept through the resonance with the trapping lasers kept

fixed. The x axis shows the relative tuning of the 658.8-nm

laser. The selection of the origin is arbitrary. To improve the

signal-to-noise ratio this spectrum is averaged over 20 scans.

TN-255
1386 J. Opt. Soc. Am. B/Vol. 13, No. 7/July 1996 Marquardt et al.

fo5%

Fig. 4. Probe absorption as a function of trapping laser detuning, S2i/2tt. The large peaks were aligned to show clearly the dependence of the cascade two-photon line shape on the trap laser detuning. The signal height depends on the number of atoms

in the trap, a function of the detuning. The small features at —20 and —70 MHz are sidebands put on the 658.8-nm laser as a frequency reference. These spectra were averaged over 200

scans to improve the signal-to-noise ratio. The figure is adapted

from Ref. 7.

would be extremely difficult to analyze the complete sys- tem theoretically, including all relevant atomic levels in cesium, six strong laser fields, laser polarizations, the

three-dimensional variation of the magnetic field Btrap, and the distribution and the residual motion of the cold atoms in the trap. To analyze a more tractable sys- tem we have made some assumptions and simplifications. We have assumed (to a good approximation) that

the laser fields are plane waves, the atoms are motionless, and the coUisional effects are negligible. We in- clude spatial effects for the three-dimensional trapping

laser fields and the variation of Btrap over the trapping

volume. The Zeeman structure for each radiatively cou- pled level is approximated by use of only the mp = ±F

(stretched state) Zeeman coefficient for each of the three

coupled levels. The validity of our assumptions and simplifications is discussed later in this paper. We have

further simplified the complicated cesium energy-level

spectra to a closed five-level system (Fig. 5). Three of these levels, |1), |2), and |3), correspond to the three cou- pled levels of the doubly resonant, cascade configurations 6S1/2, F = 4^ 6P3/2, F = 5 ^ 9Si/2, F = 4. The

remaining two levels, |4) and |5), are artificial and rep- resent all other decay channels out of the cascade sys- tem, which are due to the other atomic states and to the

relevant hyperfine structure of the three coupled levels. The hyperfine structure permits population decay out of the 6S1/2, F = 4 —> 6P3/2, F = 5 cycling transition by off- resonant absorption and decay to the 6S1/2, F = 3 ground

state. This loss mechanism and the presence of the re- pumping laser are represented in our model by the addition of level |5). The rate at which atoms enter the

other h5rperfine states can be calculated and is repre- sented in the model by 725- Similarly, we have added

level 1 4) to represent other decay channels out of the excited, 9Si/2, F = 4, state to the other noncoupled states. This rate is represented by 734 and shown in Fig. 5. Fol- lowing the standard approach, we model our system by us- ing the density matrix formalism.^ Some additions and

modifications to this approach are necessary for the conditions relevant to this experiment.

The time evolution of the density operator can be rep- resented by

dt

dp

= -tIH, p]„n + ZSyknPkk - ynkPnn) for U =

TT~ — ~T"[-f^> P]nm ~ ^nmPn for n "^ m .

(1)

Here the H is the Hamiltonian operator of the system and

jnm is the decay rate from state n to state m. (In this representation jnm ^ Jmn- If state n is a higher-energy

state than state m, then jmn = 0.) The damping rate Tnm

of the off-diagonal elements can be written as

^ nm cy w n ' Tm/ ' Tni

col (2)

where 7„ and jm represent the total decay rates out of

levels n and m and ynm'^°^ is the dipole dephasing term that

is due to processes such as collisions (which we neglect).

We can write the Hamiltonian operator as H = Ho + V(t)

,

(3)

where Hq is the atomic Hamiltonian and V{t) represents

the interaction energy of the atom with the electromagnetic field. V(t) can be represented by

^ nm\^ ) -^nm COS ii;j^t = ~^'""^^'"" [expi-in„„t) + expm^^t)] , (4)

where £„„ is the incident laser field with frequency Cl^ni and fj-nrn is the dipole matrix element corresponding to the transition from level m to level n. The rotating- wave approximation allows us to neglect the last term

in Eq. (4). After inserting the full Hamiltonian H into Eqs. (1), we can write

_6D„

6D„

-SD,„

'5D„;

Cesium Energy Levels Model Energy Levels

Fig. 5. Relevant cesium energy-level diagram showing the cas- cade two-photon transition, the lasers used in the experiment,

and the corresponding energy levels of the model. The energy

levels of the model consist of three levels that are coupled by

laser radiation, |1), |2), and |3), and two artificial levels, |4) and

|5), representing all the other decay channels out of the cascade

system. The y are the decay rates between levels, and the a

are the Rabi frequencies of the lasers used in the model.

TN-256
Marquardt et at Vol. 13, No. 7 /July 1996'.J. Opt. Soc. Am. B 1387 — + lOJnm \Pnm + T zL'^^nkPkm " Pnk'^km)

Y^iYknPkk - YnkPnn) ioV U = TTl

" 1 nmpn for n i^ m

(5)

where a;„m = £„ - Em/fi is the transition frequency be- tween levels ;i and m. Introducing the slowly varying

quantity cr„^, such that

Pnm(t) = an^{t)eX^{-lU.nrnt), (6)

we look for steady-state (danm/^t = 0) solutions to Eq. (5); these yield

k

'^ h for n = m ,

for n ^ m , (7)

where O^m = -fi^^ and ar,m = -Tnm/fi- in this notation. Equations (7) describe a 25 x 25 matrix for our five- level system. Fortunately, many of the levels are not coupled by radiation or decay, so some simplifications can be made. In the steady state many of the density

matrix states can be written in terms of other states. For

example 0-44 can be eliminated by use of the relation for dcr44/di:

do"44 _ „ y.34 J . — y4lO"44 ~ 734 C33 = U —> 0-44 = 0-33 . d^ 741

(8)

Similarly, the other states that are not coupled by laser radiation can be represented in terms of coupled states. This simplifies the 25 x 25 matrix into a 9 x 9 matrix (shown in Table 1), which can be solved for each of the remaining density matrix components. In the table 5„m = ilnm " (^nm represents the detuning of the lasers from exact resonance for the given transition (52i < for trap operation). The signal is then calculated as a function of the probe laser detuning 532. Solving this 9x9

density matrix gives the specific values of cr^„. The sig- nal that we observe experimentally is the absorption from

level |2> to level |3), which is dependent on the imaginary

part of cr32.

4. NUMERICAL IMPLEMENTATION

OF THE THEORY

This solution for the imaginary part of 0-32 gives only part

of the total line shape because the three-dimensional na- ture of the trapping laser and the magnetic fields of the MOT have not yet been included. Because the diameter of the probe beam is set approximately equal to the

size of the cloud of trapped atoms, every atom in the trap can contribute to the absorption line shape. The

energy levels of the atoms in the trap are position de- pendent because of both the magnetic-field gradient and

the wavelength scale variations of the electric field and

polarization. The magnetic-field gradient dBtrap/or ef- fectively alters the detuning of the trapping laser 821 as a function of the distance from the center of the trap (where

IBtrapl = 0). Thus, for a fixed trap detuning, the actual detuning of the trapping laser depends on atomic Zeeman

structure as

821 =821 + — Btrap( p, zH gF'^orriF' - gF=\rnF) (9)

Here Btrap( p, z) is the local magnetic field at point ( p, z), gF'=5 = 0.4 and gF=4 = 0.25 are the Lande g factors,

fiB is the Bohr magneton, and itif' and mp are the Zee- man sublevels of the excited state and the ground state, respectively. For the anti-Helmholtz configuration the magnetic-field strength IBtrapl varies approximately lin- early with distance from the center of the trap. The

atoms at the center of the trap have a detuning that cor- responds to the trapping laser detuning, 82i'( p = 0) = 821, whereas other atoms experience a different detuning, de- pending on the magnetic-field gradient and the position of the atom. We call the most probable value of ^21' the

effective detuning. Larger magnetic fields correspond to smaller effective detunings (for ^21 < Ol, which naturally

affect the cascade two-photon line shape. Of course, it is possible to switch off the magnetic field to eliminate the magnetic-field-dependent effects, but we dedicate most of

this discussion to the steady state, which includes the magnetic field. Unlike that of the magnetic field of the trap, which

varies over macroscopic dimensions, the electric field's magnitude changes on a scale smaller than the optical

wavelength. The interference of the laser fields in the trap is generated by the intersection of the six circu- larly polarized laser beams. This interference pattern

depends on the relative amplitudes and phases of the six beams and varies significantly, both in magnitude and in polarization, over an optical wavelength. In our model

Table 1. Density Matrix

0"33 0"32 0-31 0"21 0-11 (J12 cri3 a'23 (722

<'"33 -734 - 732 -ia2: /2 (032/2

0-32 -ia32/2 iS32 - r32 -/ai2/2 (032/2

0"31 -ia2i /2 iiS32 + S21] -

Tsi i 032/2

0-21 £"23/2 iS2i - r2i (021/2 -(021/2

O-U 734 iai2/2 -(021/2 721 + 725

0-12 -iai2/2 -(521 - r2i -i032/2 (012/2

0'13 -(Q23/2 -i(532 + 521 ) - r3i (012/2

a"23 ia23/2 t02i/2 -(532 - r32 -(023/2

a"22 732 '032/'2 -ia2i/2 (012/2 -('032/2 -721 - 725

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1388 J. Opt. Soc. Am. B/Vol. 13, No. 7/July 1996 Marquardt et al.

we neglect any polarization dependencies that would

contribute to optical pumping of the atoms to other Zee- man states. A more exact model that includes all the

magnetic sublevels and polarization dependencies of the

transitions was not attempted because of its complexity.

We can write the a^ and a~ beams as

Ta+iz) = Eoii cos{kz - cot + 4>i) - j sin(^2 - wt + <f>i)],

X(r-[z) = Eo[i cos(kz - ii)t + (t>2) + j sin(^z - wt + cf)^)],

(10)

for waves traveling along the positive z axis. The total

field is given by the vector sum of the six intersecting

beams with the proper polarization and direction. Initially, choosing all the phases to be (</>„ = 0) allows us

to write the total field for our MOT as

Ttot = 2£Jo cos o)t[i(cos kz + sin ky) + j{cos kx - sin kz) + ^(cos ky + sin kx)]. (11)

We are interested in the time-averaged magnitude of this three-dimensional field, which can be written as

lEiaserl — y'^tot ' ^tot = Eo[6 + 4(cos kz sin ky - cos kx sin kz + cos ky sin kx)f^. (12)

Figure 6(a) shows Eq. (12) plotted as a function of x and

y with a fixed value for z (kz = 37r/4). The actual in- terference pattern depends on the relative phase of each

of the six trapping beams and can easily be included in Eq. (12). In the experiment the relative phase of each

of the laser beams is unknown and is continually changing owing to mechanical vibrations. These vibrations are important because of the finite sweep speed of the

probe laser (generally <200 Hz) and must be taken into account. Using the laser field distribution above, we generated

a Monte Carlo histogram of the probability of finding a

specific laser field lEiaserl in the trap. An initial his- togram was calculated with a specific phase distribution

(0n = 0). To approximate phase-changing mechanical

vibrations, we calculated separate histograms for many

different phase distributions. These were combined and

normalized to form a composite distribution representative of the electric fields in the trap. This composite dis- tribution is shown in Fig. 6(b). With this distribution we

can integrate over the fields with the proper weighting of the Rabi frequencies to give the final line shape.

Because of the spatial dependence of the trap's magnetic and electric fields, we need to include all the fields in the spatial distribution to calculate the measured two- photon line shape. We accomplish this by numerically

integrating over the magnetic-field contributions while

simultaneously integrating over the microscopic interfer- ence pattern of the electric field. The total line shape can

be represented as a sum of many individual line shapes,

each of which corresponds to atoms in different electric and magnetic fields. These line shapes are additionally

weighted to ensure that each individual line-shape con- tribution reflects the number of atoms present in similar

fields. We assume that the distribution of atoms is pro- portional to the intensity of the local electric field. ^^ By

stepping through the possible values of the electric and

the magnetic fields and calculating a separate line shape

for each value, we combine these line shapes with the

proper weighting to create a final line shape. This ab- sorption line shape S can be represented by

S ^ I f I

lTn[a32]P{E)I pdEdpdz , (13)

where P{E) is the probability of finding a certain electric field E in the trap [from Fig. 6(b)], I is the intensity of the radiation, and p and z are the radial and the

axial positions, respectively, in the trap.^^ We numerically integrate relation (13) over all electric and magnetic

fields (all positions in the trap). This procedure produces

a line shape that we can compare with experiment. This

position-dependent integration (Eiaser, 4>, Btrap) broadens

the Rabi-split line shape but does not wash it out. Al- though each group of atoms in the trap corresponds to a

different Rabi splitting, the composite line shape has a

single, well-defined value for the splitting. This single

Rabi splitting represents the weighted average of the in-

(a) /^. ^ • \V. • , Q •

'^ • ^ • •

f-i , • 3 . •. • •. >. :

• V

s •• \» x> • \ m / • x> • %

1

•

0.0 0.5 1.0 1.5 2.0 2.5 V3.0 3.5 Electric Field (units of |E|/Eo)

(b) Fig. 6. (a) Local, small-scale structure of the magnitude of the net trapping laser field lEjaserl for the standard three- dimensional a'*' -a^ MOT configuration. The x and the y axes show the structure over several optical periods for kz fixed at

377-/4. ( b) Composite Monte Carlo distribution of the probability

of finding a certain lEiaserl field averaged over random phases

in units of |Eiaserl/^0-

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iVIarquardt et ai. Vol. 13, No. 7/July 1996/J. Opt. Soc. Am. B 1389

dividual line shapes and can be represented by a single

effective Rabi frequency.

The important parameters in the numerical model are

the decay rates of the cesium levels, the Rabi frequencies for the trapping and the probing laser fields, the de- tuning of the trapping laser, the magnetic field gradient,

and the physical size and shape of the atom cloud. All these parameters are known or measured experimentally.

When the atom density is chosen to be proportional to the local field intensity, the model contains no other free parameters except for the signal size, which is used for normalization. For convenient comparisons the height of the larger peak in the model is set equal to the height of the corresponding peak in the experimental data. The

Rabi frequency for the probe and the trapping lasers can

be calculated from the intensity of the laser beams. At

low intensity the probe beam can be considered nonperturbing, although the model is able to calculate the line shape for any value of the probe's Rabi frequency. We

control the detuning of the trapping laser experimentally

by locking the laser to a saturated absorption signal with

a variable-frequency offset. The magnetic-field gradient

is calculated from the knowledge of the current and the

geometry of the coils. The size of the trap is measured

with a CCD camera, which detects the fluorescence of the

trapped atoms (in the near infrared at 852 nm). The de- cay rates of the coupled states are known experimentally,

and the decay rates of the uncoupled, artificial states can be estimated by use of simple realistic assumptions.

There are many decay paths out of the 9Si/2 state, and the

decay rate depends on which decay path the atom takes. An effective decay rate was estimated with the knowledge of the branching ratios of the possible decay paths.

Table 2 shows the range of the values for the important

trap parameters, an estimation of the uncertainties, and

the qualitative effect of these uncertainties on the line shape.

We turn our attention to the splitting of the levels as a function of various trap parameters. If we first apply a perturbation approach for the probe laser (032 = 0) and assume a single Rabi frequency across the trap, we

can calculate the position of the peaks by solving for the

maxima of the imaginary part of 0-32 {that is, setting

d(lm[cr32])/d832 = and solving for 532}. We get an analytic solution for the special case of 52i = (the solution

for ^21 ^ can be solved numerically). The solution for this case has three values, ^32 = and

83-2 =

4 73

"21(72 + 2^3)

16

72 + 73)

873

"21 + -T 73(72 + 73) 4

V2

(14)

Equation (14) has two values, which represent the Rabisplit peaks; the value 832 = is a local minimum. The

splitting and the widths of the peaks depend only on the

total lifetimes of the coupled levels, not on the artificial levels for this perturbation approach. This is true for all values of 821. However, the amplitude of the absorption

line shape depends on 821- This amplitude dependence

becomes important when one is considering the whole

ensemble of atoms. Therefore the contribution to the to- tal line shape of each Rabi frequency changes as a function of the detuning. At larger detunings the atoms in the larger fields contribute more to the line shape, caus- ing an increase in the effective Rabi frequency compared

with those of the line shapes at smaller detunings. This

makes it impossible to choose a single value of the electric

field to model the splitting dependence on the detuning.

5. COMPARISONS OF THE

MODEL AND EXPERIMENT

Our theoretical model works fairly well in reproducing

the experimental line shapes. Figure 7 shows a comparison of the theoretical model and the experimental

line shape for three different trap detunings d^i. Includ- ing the spatial variations of Eiaser and Btrap and averaging over the phase fluctuations broaden the line shapes

as expected and significantly improve the agreement be- tween theory and experiment. For these spectra the best agreement between the model and the experiment

occurs with an effective Rabi frequency of —15.5 MHz.

The model reproduces the experimental line shape very

accurately at smaller detunings [Fig. 7(a)]. At larger de- tunings the discrepancies between theory and experiment

become more apparent. For most conditions the model

predicts a line shape that exhibits the proper linewidths

and splittings, but the amplitude of the smaller peak

tends to be too small relative to the experimental line shape. The dashed curve in Fig. 7( b) shows the result of the model with a single Rabi frequency under the same

conditions as for the solid curve. One can easily see the

Table 2. Important Parameters, Range of Experimental Values, Their Estimated

Experimental Uncertainties, and the Qualitative Effect on the Theory"

Estimated Relative Effect on Parameter Value Uncertainty Line Shape

Trap diameter (2p) 2.5-4.0 mm ±0.3 mm Small Trap height (22) 1.3-3.0 mm ±0.3 mm Small Magnetic field 12-20 X 10"-* T/cm ±0.5 X 10"* T/cm Small Detumng {\82i/2tt\) 4-16 MHz ±0.1 MHz Very small Rabi frequency

^21 12-19 MHz ±1 MHz Moderate

0132 -0.5 MHz ±0.1 MHz Small ynm Various ±1-10% Moderate

"The decay rates y„m are well known for the lower-lying levels, but the uncertainties increase for the higher-lying states.

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1390 J. Opt. Soc. Am. B/Vol. 13, No. 7/July 1996 Marquardt et al.

20 30 40 50 658.8 nm Tuning (MHz)

(a)

70

20 30 40 50 658.8 nm Tuning (MHz)

(b)

658.8 nm Tuning (MHz)

(C) Fig. 7. Experimental and theoretical line shapes with a field gradient of 16 X 10"'' T/cm, an atom cloud diameter of —3.0 mm,

and tteffective = 15.5 MHz for various trap laser detunings

521. (a) 521/271 = -7 MHz, (b) 52i/27r = -10 MHz, and

(c) S2i/2tt = -13 MHz. The experimental data are represented

by the dots, and the solid curve is the model. The dashed curve

in (b) is the theoretical prediction with the same parameters as the solid curve but for a single Rabi frequency.

importance of the electric-field interference nattern and

the phase fluctuations by comparing the two predicted

Une shapes with the experimental data. The electricfield effects broaden the line shape and improve the rela- tive peak height agreement with the experiment. We

have chosen model parameters that are realistic for our

experiment. (It is possible to change the parameters to unrealistic values to improve the apparent agreement.)

We have investigated the Autler-Townes splitting as a

function of the detuning. Inasmuch as the Zeeman shifts of the atomic energy levels increase the complexity of the

model, we investigated the splitting both with and without the magnetic-field gradient. The line shapes with

the magnetic-field gradient turned off are similar to those

shown in Fig. 7, except that the splitting is slightly larger, as expected, because of the larger effective detuning.

Figure 8 shows the line-shape splitting as a function of detuning with the magnetic field turned off. The solid curve represents the predicted line-shape splitting. Al- though the model does a good job of predicting the splitting, a systematic structure at large detunings is not ac- counted for by the model. It does, however, predict the

dependence of the splitting more accurately than if we

included only a single Rabi frequency. A study of the

splitting with the magnetic field present exhibited similar

results, albeit with slightly larger discrepancies between

theory and experiment at large detunings. This seems

to indicate a need for a more comprehensive treatment of the Zeeman structure. The two peaks in the Autler-Townes line shape can

be interpreted as representing different types of two- photon transition. ^^ In the limit where the pump and

the probe lasers are very weak (a2i == 0, a^2 ~ 0) and

the decay to the artificial levels is negligible (a closed

three-level system), the absorption peaks can be inter- preted in terms of coherent and incoherent transitions. The smaller peak can be represented by a term that is pro- portional to cr22, which requires buildup of a population

in the 6P3/2 state. This represents an incoherent two- photon double-resonance peak. The larger, narrow peak

can be represented as a term proportional to 0-21 and cor- responds to a two-photon transition with no population in the 6P3/2 state. To satisfy the conditions for this second

type of transition, coherence must be preserved. If the

coherence degrades, the transition probability decreases

for the coherent peak but increases for the incoherent

transition. Therefore, if there are excess relative phase

fluctuations, the coherent peak suffers relative to the in- coherent peak (the relative height of the smaller peak in- creases). Most perturbing effects in the laboratory would

destroy coherence, thus increasing the apparent relative

size of the smaller peak. This effect appears to be small

for the laser linewidths (<500 kHz for the trapping laser and < 1 kHz for the probe, as opposed to linewidths of

5.1 MHz for the 6P3/2 state and ~1 MHz for the 9Siy2

state) and the coUisional effects present in our experi25 r

-2 -4 -6 -8 -10 -12 -14 -16

Detuning of 852 nm Laser (MHz)

Fig. 8. Splitting of the line shape versus the detuning of the 852-nm laser with the magnetic-field gradient turned off. The

solid curve is the numerical result of the model. The error bars on the data are roughly equal to the size of the circles.

TN-260
Marquardt et al. Vol. 13, No. 7/July 1996/J. Opt. Soc. Am. B 1391

ment, and it cannot explain the discrepancies between

theory and experiment. Inasmuch as the model and the experiment agree well at small detunings but less so at

large detunings, the discrepancy between theory and ex- periment is in some way dependent on trap conditions. At large detunings we might expect other effects to begin

to play a larger role, which would increase the effective Rabi frequency, such as atom localization. We made a number of simplifications that need to be

justified. The first assumption is that the atoms are

stationary. In the case of cold trapped cesium atoms

the residual Doppler width is small compared with the natural linewidth of the transition (for a sample of ce- sium atoms cooled to the Doppler limit, the residual

Doppler width is —250 kHz). For Doppler widths in standard cesium traps this effect is small and can be

neglected. Similarly, the movement of atoms across the interference pattern of the electric field can be ne- glected because of the fast cycling frequency and slow

atomic velocities. If the intensities of the six laser beams in the trap are not exactly equal or are not uni- form across the trapping region (because of the spatial mode variation across the laser beam inherent for diode lasers, for example), the electric field distribution differs from that shown in Fig. 6(b). The peak in the distribution changes position slightly, but the effect on the line shape is surprisingly small. Inasmuch as the Zeeman contribution to the total detuning is small

compared with the actual detuning, the effect of other

Zeeman levels is expected to be small. Further, as we

assume maximum mp values in the model, inclusion of lower Zeeman coefficients would increase the effective detuning, which tends to degrade the agreement between

theory and experiment. To validate further the assumption of large mp values, a study was done to investigate the polarization of the three-dimensional electric-field distribution. Although for the standard a* -a~ configuration the electric field is linear ever3rwhere in space

for 4>n = [Eq. (11)], changing the relative phases of the laser beams changed the interference pattern. For most choices of the relative phase, the electric field was

not linear across the trap but was elliptically polarized.

This would tend to optically pump the trapped atoms into the maximum mp states. This is consistent with our assumption of using only the mp = ±F state for each of the coupled states. Other simplifications in the model

involved the assumption of plane waves. Because the diameters of the laser beams are large (-1.5 cm) relative

to the size of the trap and are well collimated, the approx- imation of plane waves seems accurate. The inclusion of

laser beam geometry would be more important for predictions of other phenomena of trap dynamics that are not confined to the very center of the intersecting beams.

The cascaded two-photon probe also proved useful for studying some of the effects of MOT dynamics. We have

used this probe to study some transient properties of the trap following a change in the magnetic field. The

trapped atoms took a surprisingly long time to reach equilibrium. We could easily see these properties by monitoring the splitting of the lines as a function of delay after the magnetic field was changed or shut off. The magnetic field in our trap can be switched off in less than

1 ms, yet the splitting of the lines took much longer to

reach equilibrium (» 10 ms). Long time constants m

MOT dynamics have also been observed in other laboratories but remain largely unexplained. The slow (order

of a few milliseconds) redistribution of atoms between a"

and a~ potential wells has been reported in a four-beam

optical lattice and a longitudinal magnetic field. ^^ In our

six-beam, a* -a' MOT there are no true a* /a~ potential wells, but the long time constants may be due to the

redistribution of atoms in the trap as the result of other

localization or collective effects. We have also used this system to probe a trap configuration consisting of balls and orbiting rings of atoms that are due to the intentional misalignment of the trapping

beams (as seen in other laboratories).^* This configuration consists of the standard a^ -a' MOT with two of the pairs of retroreflected laser beams intentionally misaligned in one plane, creating a racetrack composed of — Ball — Ring

10 20 30 40 50 60 70 80 100

658.8 nm Tuning (MHz)

Fig. 9. 658.8-nm absorption spectra of the ring of atoms and the

ball of atoms. The MOT parameters were d2i/2:r = -8.5 MHz

and aBtrap/fiz = 15 x lO""* T/cm (15 G/cm), The difference between the shapes of the two spectra is due to the large

magnetic field at the location of the ring and the electric field amplitude drop-off of the laser beams. The shift in frequency is due primarily to the Doppler shift of the resonant frequency of the moving atoms. The signal size reflects the smaller number

of atoms in the ring that intersect the probe laser. The additional features at -90 and -25 MHz are sidebands on the probe

laser, which are used as a frequency scale. These signals were

averaged over 20 scans.

150 Frequency (Hz)250

Fig. 10. FFT spectrum of the fluorescence of the MOT showing

the narrow frequency component at 170 Hz corresponding to the

rotational frequency of the orbiting atoms. The horizontal scale

is -19.5 Hz/division, and the resolution bandwidth is 0.5 Hz. The figure was averaged over 20 scans.

TN-261
1392 J. Opt. Soc. Am. B/Vol. 13, No. 7/July 1996 Marquardt et al.

10 20 30 40 50 60 70 80 90 100

658.8 nm Tuning (MHz)

(a)

A

'w' M 1 g J 1 I 3 •* I I ji / 1

1 It

(4 / 1 t »-' ' / 1 e J^ ^ 1 o •7 I

•J3 r \ 1 1 / \ / I S // \J \ ^ ^^^-"^ \

.^-?^, , V Nsta,^.^j<\^ , 10 20 30 40 50 60 70 80 90 100

658.8 nm Tuning (MHz)

(b) Fig. 11. Comparison of the model and the experiment for the 658.8-nm absorption for (a) the z ball and (b) the z ring. The

data and the trap parameters are the same as in Fig. 9. This model contains no width in the velocity distribution of the orbit- ing atoms.

four of the laser beams. This configuration shows col- lective effects of the trapped atoms in which the atoms

orbit in stable rings around the center of the trap (which

may or may not contain a separate ball of atoms). Our

system was aligned to create a ball and ring of atoms

in the vertical plane of the experiment. We studied this configuration by observing the differences in the absorption spectra of the 658.8-nm light as it was sent through

the ball of atoms versus the ring of atoms. We can compare these two absorption spectra to investigate the envi- ronment specific to this particular setup (Fig. 9). Three

main properties of the spectra in this figure merit comment. First, owing to the smaller number of trapped

atoms in the ball and the ring, the signal-to-noise ratio is much lower than that of previous spectra (the fea- tures at —90 and —25 MHz are sidebands on the probe

laser, which are used as a frequency scale). Second, the

Autler-Townes splitting of the line shape of the ball is different from that of the ring. This is expected because

of large magnetic fields at the radial position of the rings, as well as the smaller Rabi frequency, which is due to the

Gaussian nature of the laser beams (the diameter of the

rings was usually —0.6-1 cm, depending on parameters).

Finally, the large frequency shift in the absorption spectra

of the orbiting atoms is due mainly to the Doppler shift (there is a small frequency shift from the magnetic fields, as well). With the knowledge of the magnetic-field shift, the smaller Rabi frequency of the laser beams, and the

diameter of the orbiting rings, the period of the orbit can

be calculated from the Doppler shift. The rotational fre- quency of atoms in our trap was usually between —120

and 200 Hz. We used an independent method for deter- mining the rotational frequency of the rings, as well. The

bandwidth of the optical detection was fast enough that we could observe the time dependence of the absorption

signal as the atoms orbited. This signal was studied in both the time and the frequency domains. A fast Fourier

transform (FFT) was used to display the Fourier spectrum

of the absorption signal and the signal from the photodetector monitoring trap fluorescence. The FFT spectrum

showed a strong and narrow peak at the frequency of the orbiting atoms. Figure 10 shows a tj^pical output of the FFT corresponding to a rotation frequency of 170 Hz. Under most conditions this orbit had a remarkably high

Q of several hundred. Figure 11 shows the experimental and modeled line shapes for the two cases of the ring

of atoms and the ball of atoms. Our model was able to predict accurately the relative splitting and the relative heights of the line shapes, but the widths of the signal

showed poorer agreement.

6. CONCLUSION

We have observed and modeled an Autler-Townes-split

optical double-resonance transition for cold atoms in a MOT. The model reproduces the experimental two- photon line shape fairly well under many conditions,

particularly for small detunings of the trapping laser and

large magnetic-field gradients. It also accurately predicts the splitting of the line shape as a function of the

detuning of the trapping laser. The discrepancies be- tween theory and experiment for larger detunings seem

to suggest that, although many of the important aspects

of the trap, such as the three-dimensional properties of the electric and the magnetic fields, are included in the

model, more complexity is needed. We have also used

this system as a useful diagnostic for the investigation

of collective effects of atoms in a magneto-optic trap. In

addition, using the probe laser, we observed transient ef- fects with long time constants that indicate unexplained

optical physics in samples of cold trapped atoms. ACKNOWLEDGMENTS

We acknowledge the helpful comments and discussions of

S. Gilbert, R. Fox, and P. Gould and the support of the

U.S. Air Force Office of Scientific Research.

REFERENCES AND NOTES

1. K. Gibble and S. Chu, "Future slow-atom frequency

standards," Metrologia 29, 201-212 (1992).

2. See, for example, P. S. Julienne, A. M. Smith, and K. Burnett, "Theory of collisions between laser cooled atoms," Adv.

At. Mol. Opt. Phys. 30, 141-198 (1993).

3. See, for example, feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6(11) (1989).

4. J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble,

"Nonlinear spectroscopy of cold atoms in a spontaneousforce optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991); G. Grynberg, B. Lounis, P. Verkerk, J.-Y. Courtis, and C. Salomon, "Quantized motion of cold cesium atoms in two- and three-dimensional optical potentials," Phys. Rev. Lett. 70, 2249-2252 (1993); P. S. Jessen, C. Gerz, P. D. Lett, W. D.

Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook,

TN-262
Marquardt et al. Vol. 13, No. 7/July 1996/J. Opt. Sec. Am. B 1393

"Observation of quantized motion of Rb atoms in an optical

field," Phys. Rev. Lett. 69, 49-52 (1992); A. Hemmench and

T. W. Hansch, "Two-dimensional atomic crystal bound by 10.

light," Phys. Rev. Lett. 70, 410-413 (1993).

5. P. Marte, R. Dum, R. Taieb, and P. Zoller, "Resonance fluo- rescence from one-dimensional molasses," Phys. Rev. A 47, 1378-1390 (1993); J. Guo, "Contribution of energy contm- uum states to probe absorption signal of atoms in one- dimensional optical molasses," Phys. Rev. A 49, 3934-3942

(1994); J.-Y. Courtois and G. Grynberg, "Probe transmis- 11. sion m one-dimensional optical molasses: theory for lin- early crossed polarized cooling beams," Phys. Rev. A 46, 7060-7078 (1992).

6. H. R. Gray and C. R. Stroud, Jr., "Autler-Townes effect in double optical resonance," Opt. Commun. 25, 359-362 12.

( 1978); P. R. Hemmer, B. W. Peuse, F. Y. Wu, J. E. Thomas,

and S. Ezekiel, "Precision atomic-beam studies of atom-field 13. interactions," Opt. Lett. 6, 531-533 (1981).

7. R. W. Fox, S. L. Gilbert, L. Hollberg, J. H. Marquardt, and

H. G. Robinson, "Optical probing of cold trapped atoms," Opt. 14. Lett. 18, 1456-1458 (1993).

8. C. Monroe, W. Swann, H. Robinson, and C. Wieman, "Very

cold trapped atoms in a vapor cell," Phys. Rev. Lett. 65, 1571-1574 (1990).

9. V. M. Fain and Ya. L Khanin, Quantum Electronics (MIT

Press, Cambridge, Mass., 1969); R. M. Whitley and C. R.

Stroud, "Double optical resonance," Phys. Rev. A 14, 1498-1513 (1976).

Initially we assumed that the atom distribution in the atom

cloud was random, but we found that the agreement be- tween theory and experiment improved by assuming that the atom density is proportional to the local field intensity.

The enhancement of the atom density in the higher fields

is expected because of the dipole force that is due to the red-detuned (621 < 0) laser field. We use cylindrical coordinates. The actual shape of the cloud

in our trap is a somewhat irregular, oblate spheroid. The

height of the atom cloud (z direction) is approximately two

thirds of the diameter and is fairly well represented by a

cylindrical volume.

S. Stegholm, Foundations of Laser Spectroscopy (Wiley, New

York, 1984). D, R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtis, K. I. Pestas, and G. Grynberg, "Paramagnetism in a cesium opti- cal lattice," Phys. Rev. Lett. 74, 1958-1961 (1995). D. W. Sesko, T. G. Walker, and C. E. Wieman, "Behavior

of neutral atoms in a spontaneous force trap," J. Opt. Soc. Am. B 8, 946-958 (1991); V, S. Bagnato, L. G. Marcassa, M.

Oria, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, "Spatial

distribution of atoms in a magneto-optical trap," Phys. Rev. A 48, 3771-3775 (1993).

TN-263
Population- and Coherence-Induced Gain and Self-Oscillations in Alkali Vapor

A.S. Zibrov^"', H.G. Robinson*, V.L. Velichansky', V.V. Vasiliev', L. HoUberg', E. Arimondo^ M.D. Lukm^ and M.O. Scully"

" National Institute of Standards and Technology, Boulder. CO. USA

" Texas A&M University, College Station, TX 77843

' Lebedev Institute of Physics. Moscow. 1 17924 Russia

'' Dipartimento di Fisica. Universita di Pisa, Pisa, Italy

Abstract

Gain and oscillations are observed in a 3-level, A configxiration when Rb atoms are driven with a strong, coherent, laser field and a broadband repumping laser. The system

automatically generates an output beam that has a beatnote at the frequency of the ground state hyperfme splitting (6.8 GHz). Gain is due to both population and coherence effects in a Raman

configuration. The experimental system is extremely simple and shows promise of providing a compact, Rb-stabilized microwave oscillator.

Large Raman gain signals are observed in the very simple experimental setup diagrammed in Fig. 1. The beam from a single-mode diode laser DLl (drive laser) is passed

through a Rb cell and is then detected on a fast photodiode. DL2 is a solitary diode-laser that can be spectrally broadened by adding noise to the injection current. These two input beams

propagate through the cell (either in the same or opposite directions) at a small angle that allows separation of the beams and avoids feedback.

Rb CELL POLARIZER AMPLIFIER

ANALYZER

Fig. 1 Experimental setup consists of two diode laser beams, a Rb cell, a fast photodetector,

and a microwave spectrum analyzer used to display the signal. The dotted line indicates the electronic feedback path that is used in some of the experiments.

Raman scattering of the drive laser in the Rb vapor generates a beam that is collinear with the drive but is frequency-shifted by the ground state hyperfme splitting (3.0 and 6.8 GHz for Rb*' and Rb"). The fast photodiode simply detects the beatnote between the drive

laser and the Raman shifted beam. The function of the repumping laser (DL2) is to return the population to the initial ground-state hyperfme level, thus controlling the optical pumping

effects of the drive laser. The tuning of the broadband repumping laser is not critical; any

490

Proc. Fifth Symp. On Frequency Standards and Meterology(i995).

TN-264
491

transition (for example, different P state) that will return population to the initial hyperfine

ground state can be used. In this way the repumping laser serves the same purpose as the buffer gas in the earlier Raman laser experiments. {2}

Figure 2 shows a typical signal that is detected with the fast photodiode. In this example the power of the drive laser was ~13 mW, tuned to resonance on the Dl, F->F' (2->^2') transition; the repumping laser was about 8 mW, broadened to ~500 MHz spectral width and

tuned approximately to the Dl (1-^2') transition. The spot diameters in the center of the 6 cm

long cell were -500 /xm for the drive and ~3 mm for the repump. In this example the beatnote between the self-generated Raman beam and the drive laser has a signal-to-noise

ratio of about 40 dB with a detection bandwidth of 300 kHz.

6833 6834 6833 6836 6833 6834 6833 6836 MHz MHz

Fig. 2 Signal at 6.8 GHz from the photodetector as displayed on a microwave spectrum

analyzer. Part (a) shows the beatnote between the self-generated Raman beam and the drive

laser with no electronic feedback, while in (h) the spectrum is narrowed when the electronic feedback at 6.8 GHz causes the system to self-oscillate.

Our approach is reminiscent of the previous work of P. Kumar'-^ and P. Hemmer,^

who have demonstrated Raman gain and lasing in Na vapor heat-pipes using optical cavities. Our system is distinguished from previous work in that it does not require an optical cavity, nor a buffer gas. Also, an electronic beatnote signal is generated directly at the hyperfme

difference frequency, which can be use to create a narrow self-oscillation at the hyperfme

frequency. The system is very simple and in its minimum configuration requires only

requires a diode laser, a photodiode and a Rb cell. It does not require a microwave oscillator and it provides a stable oscillation at the frequency defined by the atomic hyperfme splitting. The gain in this system results from both population and coherence effects, and is remarkably high and robust. We have observed gain in both the Stokes and anti-Stokes

configurations, on both the Dl and D2 lines, and within and outside the Doppler profiles. For some configurations the system also shows gain at twice the ground-state hyperfme splitting

(13.6 GHz for Rb) which is most likely due to gain in the double-A configuration.^

Comparison of theoretical and experimental lineshapes is possible for both the microwave spectrum and the optical gain/loss spectrum. A few theoretical models have been

used with an attempt to determine the most important physical effects: hyperfme structure, Zeeman structure, optical coherences, propagation, and Doppler broadening. At least for some range of the experimental parameters, the theory reproduces the experimental lineshapes

reasonably well. This simple system generates a signal with a very good signal-to-noise ratio and with a

TN-265
492

fairly narrow linewidth as a microwave oscillator. An obvious application of the Raman self- oscillator would be as a compact, Rb frequency standard; however a number of questions

remain to be answered before this can be realized. In particular, can the problems associated with AC Stark shifts be minimized to the point that the atomically stabilized microwave

oscillator has useful stability? Stark shifts resulting from the drive laser power are the main

perturbation to the frequency of the Rb self-oscillator. These shifts are complicated by the multilevel nature of Rb, the .variation of intensity across and along the laser beam, and their dependence on the detunings of the lasers from resonance. As a baseline test we set up the Rb self-oscillator without any optimization and let it run without any control on the laser frequencies, cell temperature or laser power levels. Using a frequency counter to record the

oscillation frequency allows a measurement of the Allan variance of the self-oscillator as shown below.

10-6 ^

10-7

100 23 101 23 102 23

Figure 3. Data shows a typical square-root of the Allan variance of the frequency of the free- rurming Rb self-oscillator as a function of averaging time (t) in seconds.

The stability of the frequency is good for a free-running oscillator, but is obviously not of

frequency-standard quality in this free-running state. Active control could easily be

implemented but with some penalty in complexity. Perhaps there are laser tunings and

powers that can be uses to minimize the effects of the AC Stark shift. A potentially

important curiosity of the system is that the oscillation frequency does not appear to have

first-order sensitivity to acceleration. This may be advantageous in some very high

acceleration environments.

We gratefiilly acknowledge numerous helpful comments from D. Gauthier and P. Hemmer, and the support of the Air Force Office of Scientific Research. References

1. P. Kumar and J.H. Shapiro, Opt. Lett. iO, 226 (1985).

2. M. Poelker, P. Kumar, and S.-T. Ho, Opt. Lett. 16, 1853 (1991).

3. J. Donoghue, M. Cronin-Golomb, J. Kane and P. Hemmer, Opt Lett. 17, 1313 (1991).

TN-266
Volume 76, Number 21 PHYSICAL REVIEW LETTERS 20 May 1996

Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb

A.S. Zibrov,i'2-^-5 M.D. Luldn,^'2,3 l Hollberg,^ D.E. Nikonov,'2-3 M.O. Scully,'-2-3 H.G. Robinson,^

and V. L. Velichansky^

^Department of Physics, Texas A&M University, College Station, Texas 77843

^Texas Laser Laboratory, HARC, The Woodlands, Texas 77381

^Max-Planck-lnstitut fUr Quantenoptik, D-85748 Garching, Germany

^National Institute of Standards and Technology, Boulder, Colorado 80303

^Lebedev Institute of Physics, 1 1 7924 Moscow, Russia

(Received 11 December 1995)

We present a proof-of-principle experiment demonstrating a resonant enhancement of the index of

refraction accompanied by vanishing absorption in a cell containing a coherently prepared Rb vapor. The results are in good agreement with detailed theoretical predictions. [80031-9007(96)00142-1]

PACS numbers: 42.50.Ar, 42.55.-f

In the present Letter we report the first demonstration of

a resonant enhancement of the index of refraction without absorption [1]. Surprising and counterintuitive ef- fects involving quantum coherence and interference have

recently become laboratory realities. For example, phe- nomena such as electromagnetically induced transparency

(EIT) [2] and lasing without population inversion (LWI)

[3], predicted theoretically at the end of the 1980s have now been demonstrated experimentally [4-7]. In both of

the above effects quantum coherence dramatically modifies the absorptive properties of the medium. The unusual

behavior of the dispersive part of the susceptibility of coherently prepared medium is no less intriguing. For example, it was shown theoretically that it is possible to have a completely transparent medium with large dispersion (i.e., rapid variation of index of refraction with frequency) or with large index of refraction [ 1 ]. Both of these effects can be achieved using atomic phase coherence in a resonant medium, which is normally optically thick. Coherence effects, however, allow us to prepare an optical medium such

that the medium has vanishing absorption, while the dis- persive part of the susceptibility is enhanced.

The interest in these phenomena is due, on one hand,

to the fundamental nature of coherence effects and, on

the other hand, to possible applications. For example, the dispersive properties of coherently prepared media have

been studied with an eye toward generation of pulses

with very slow group velocity [8], effective control of

nonlinearities [9], high precision magnetometry [10], and

laser acceleration of particles [1]. Several recent experiments [11] have demonstrated the

large dispersion of the index of refraction accompanying

EIT. Index enhancement, however, allows not only for large dispersion, but also for a large refractive index itself, while maintaining a transparent medium.

The conceptual foundation of the present experiment

can be understood by considering the simple A atomic

configuration of Fig. 1, The coherent strong driving field with Rabi frequency (H) and weak coherent probe (Up)

allow us to prepare the atom in a coherent superposition

of states b and c [12]. When the detunings of these two

fields from their respective atomic resonances are equal,

EIT is obtained. The incoherent pumping (represented by

the rate r) alters this coherent superposition by pumping some of the population into other states. Depending upon

the actual parameters of the system this may result in gain,

loss, or complete transparency for the probe field. The linear gain (absorption) coefficient (G) is proportional to the imaginary part of complex susceptibility

ix")- In the case when the driving field is in exact reso- nance with transition a — c it is given for this particular

three-level configuration by [13]

JbcAijcbyab + inP - A^) + L^Bijab + ybc) "

{Jbcjab + inP - A2)2 + A2(y,, + Jbc?

'

(1)

where k — 'ik^Ny'^L/Air, and A and B are given by ^ = [1 + (r^ + ya)nybc^Paa - Pbb , (2)

B = Paa ~ Pbb • (3)

Here p„ is the population of level / calculated to the zeroth order in the probe field, 7,7 is the relaxation rate of the density matrix element pij, N is the density of

atoms, L is the length of the cell, A is the wavelength.

FIG. 1. (a) Simplified three-level model for index enhancement, (b) The actual level scheme of D\ absorption line in Rb*^ and the optical fields used in the present experiment. Energy separation between manifolds 1 and 2 is equivalent to 6.8 GHz.

-Ta/? \')a V V Q. ^p// '<\^_

1 : r c

0031 -9007/ 96/76(21)/3935(4)$10.00 © 1996 The American Physical Society

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3935
Volume 76, Number 21 PHYSICAL REVIEW LETTERS 20 May 1996

A is the detuning of the probe laser, and atomic decays

(y'a^y'a) ^^ indicated in Fig. 1(a). For the case A == we see that, in the presence of the coherent driving field, the gain (which is in that case proportional to A) can be

positive even if most population remains in the ground

state b, i.e., even if fi < 0. That is, a weak probe field undergoes amplification without the need of population

inversion [7,14]. If the probe field is detuned from atomic

resonance, the gain coefficient decreases rapidly, and

vanishes when

A = An = ±

Aybci^'^ + Jabybc)

(4)

Ajbc - Biyab + ybc) Let us turn now to the real part of the complex susceptibility ix'), i.e., to the resonant index of refraction. It results, in particular, in the phase shift (</>) for the probe

light transmitted through the resonant vapor, which is proportional to ;^': K Bjycb Tafc + in P - A^) - Aijab + ybc)ybc

"^ 2 {ycbyab + m'^-^^Y + ^Hyab + ybc)'-

'

(5)

The phase shift is equal to zero when the probe field

is tuned precisely to the resonance with the a —* b

transition, but for nonzero probe field detuning it can become quite large. To be more specific, we consider

the system with decay rates and pumping as indicated

in Fig. 1(a) [13]. In this case and if we take r ~ y^ ~

y^^ ^ y> ^yabr, the gain coefficient vanishes at Aq ~

-Vl^rfP "• yabybc- At this point the phase shift is on

the order of

0(Ao)~(k/12)/Ao. (6)

It follows, therefore, that a medium can become transparent at the point where the resonant index of refraction has

a large value. A A-type atomic configuration can be realized within

the D\ absorption line of Rb as shown in Fig. 1(b). Here

right circularly polarized coherent driving and probe fields are tuned close to the 2 —» 2' and 1 — 2' transitions,

respectively [15]. The incoherent pumping out of the

states 1 is accomplished by a broadband right circularly

polarized field which couples the transition 1 —» 2'. All of the fields are copropagating, which allows for the reduction of Doppler broadening.

We note here that optical properties of the real atomic

systems are, in general, different from those of simplified

3- or 4-level models due to the presence of many

hyperfine and Zeeman sublevels. In particular, optical

pumping can play an important role. Indeed, in the case when both driving and pumping fields are present, atoms

can be optically pumped into the state F = 2, Mp = +2

[Fig. 1(b)]. To avoid the trapping of the population in

this state a weak magnetic field (~2 X 10"'* T) is used,

which mixes the populations via Larmor precession.

In order to account for realistic experimental conditions we developed a numerical model, wherein the field polarizations, the presence of hyperfine and Zeeman sublevels

and Doppler broadening are taken into account This is done by numerically solving the density matrix equations

for the 16-level system of Fig. 1(b) and averaging over

a Maxwell velocity distribution. The numerical analysis showed that for parameters typical of our experiment

the effect of index enhancement depends upon the tuning

of the drive laser within the Doppler absorption profile.

This is the case when the intensity of a driving field is relatively low and the ground state relaxation rate is sufficiently high (determined in our case by the incoherent

pump rate). Under these conditions we found the index

enhancement is larger if the driving field is detuned to ei- ther side of the center of the Doppler profile by roughly a

third of the Doppler width.

The results of the calculations are presented in Fig. 2. They clearly show that there is a region (indicated by /) where absorption is canceled and, at the same time, the

real part of susceptibility (i.e., the phase shift) increases

due to the presence of the drive and pump fields. In the experiment we used a 4 cm long cell containing

natural Rb. Drive and probe lasers were extended cavity

diode lasers at 794 nm with linewidths of about 100 kHz.

The powers of these beams in the region of the cell were on the order of 10 mW and 5 /iW, respectively, and the corresponding spot sizes in the same region were 2 mm

and 1(X) /xm. The angle between two beams did not exceed 5 X 10~^ rad. The ^lump laser was a solitary laser diode (794 nm) with output power =5mW. Its linewidth was additionally broadened to about 150 MHz

1.0

0.85

0.7

0.55

(0 *w<' 1 100

1 MHz \

\^k

frequency of the probe frequency of the probe ^ 0.2 !.._ (») i

i 0.2 ^T3t

I 1 100 MHz

Uv1 "

(W)

i.

'—

-t-V

10 MHz

iii

frequency of the protte frequency of the probe

FIG. 2. Calculated absorption coefficient (i,iii) and phase shift

(ii.iv) of the probe field in the Rb vapor. In all figures curve

(a) corresponds to the case without driving and pumping fields, curve (b) corresponds to the case when these two fields are

present. Parameters for numerical modeling are H = 16 MHz,

Doppler width is 500 MHz, incoherent pump corresponds to

r = 0.5 MHz, and magnetic field //, = 2 X 10"" T. Naniral linewidth of the Rb Z>i absorption line is 5.4 MHz.

3936

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Volume 76, Number 21 PHYSICAL REVIEW LETTERS 20 May 1996

by modulating the diode's input current with noise. The

size of the pump beam was on the order of 3 X 5 nmi.

The resonant index of refraction was determined via

phase-shift measurements using a Mach-Zehnder interfer- ometer (see Fig. 3). When the interferometer arms are of

nearly equal length the difference current of photodetectors PDl and PD2 is proportional to

^signal ~ /o exp(G/2) sin(<^ + <f>o)

,

(7)

where /q is the intensity of the probe field and <f>o is a constant phase shift determined by a balance of the interferometer arms. A piezoelectric transducer is used

to vary 0o and thus obtain the scaling of the signal.

The first experiments were carried out with the low

Rb density, such that maximum probe absorption was

on the order of 40%. Under these conditions the signal

given by Eq. (7) is the phase shift of the probe field in the Rb cell, provided that the arms of the interferometer

are appropriately balanced. The absorption of the probe

field was detected simultaneously. Without the drive and

incoherent pump fields, the absorption and the phase shift show the ordinary features of Doppler-broadened twolevel atomic resonance (curve a in Fig. 4). When the drive field is present and tuned within the Doppler profile, the absorption spectrum of the probe laser exhibits a narrow transmission peak at the frequency corresponding

to that of a two-photon resonance condition. When the incoherent pump is added the narrow gain peak appears

(curve b in Fig. 4). If the probe field is detuned slightly

from the two-photon resonance (point / in Fig. 4) the medium is transparent; i.e., it has neither loss nor gain.

The phase shift, which is proportional to the real part

of susceptibility, is shown in Figs. 4(ii) and 4(iv). It can be quite large in the transparency region. In particular, we note that at point / the change in the refractive index

exceeds that found in the same system without the driving

field. That is, the real part of the susceptibility is enhanced

at the point where the absorption vanishes. We note

the good agreement between the theoretical predictions of

Fig. 2 and the experimental observations of Fig. 4. Having observed and analyzed the absorption and

dispersion in an optically thin medium we were also able

to demonstrate the enhancement of refractive index in an optically dense medium. To accomplish this phase

shift and absorption measurements were carried out for

7^\>-?>

FIG. 3. Schematic of experimental setup. ECDLl and

ECDL2 are probe and driving lasers, respectively; LD is an

incoherent pump laser.

a variety of temperatures. Figure 5 shows the value

of the phase shift as a function of atomic density.

For low temperatures the phase shift in the coherently

prepared transparent Rb vapor is somewhat larger than the maximum phase shift in the usual Rb resonant vapor. For

temperatures T > 80°C (A^ > 3 X lO^'cm'^) the Rb

absorbs 100% of the probe light near the resonance, i.e., in the region where the refractive index has its maximum.

When the drive and incoherent pump are present the system is transparent and displays large phase shifts. The

inset in Fig. 5 shows the transmission of the probe laser (curve A) and corresponding output 5sig of the phase

shift measurement (curve B) at a Rb cell temperature

~87 °C. In the presence of coherent drive and incoherent

pumping, the narrow transparency peak appears (curve a) on an otherwise flat, completely absorbing background.

The corresponding phase shift (curve b) measurements

display the oscillations which correspond to large values

of phase shift. Under the present experimental conditions we observed the phase shifts up to —Itt at the point of

complete transparency, which corresponds to the resonant change in the refractive index A/i ~ 10"'*. We note that such a phase shift is not observable in a usual absorber

in the inmiediate vicinity of resonance because of the resonant absorption.

We remark here that quite large phase shifts accompanied by relatively good transparency can be obtained

in a usual nondriven atomic system (e.g., within the Rb

D] line without coherent preparation) at large detunings.

This happens because the real part of the susceptibility x' decreases slower than x" with detuning. However,

for large detunings, x' of a usual absorber increases with

density much slower than the resonant x'- I" particular, for A^ ~ 10'^ cm"^ we observed that the absorption of the

8 80 E

•)

40

If)

b \

b

fraqucncy of th« probt traqiNficy of ttto probo

FIG. 4. Transmitted intensity (i,iii) of the probe light in the Rb cell and the difference current of photodetectors, converted

into the phase shift (ii,iv). In all figures curve (a) was observed

without driving and pumping fields, curve (b) was observed

when those two fields were present.

3937

TN-269

M\
Volume 76, Number 21 PHYSICAL REVIEW LETTERS 20 May 1996

0.0 0.2 0.4 0.6 0.8 1.0 atomic density ( xl O'^ cni-3

FIG. 5. (i) The phase shifts in Rb vapor as a function of a vapor density. D is the phase shift in coherently prepared Rb

at the point of complete transparency; A is the maximum value of phase shift in the same system without coherent preparation,

(ii) Transmission of the probe (curve a) and corresponding

quadrature component of interferometer signal (curve b) in an

optically dense Rb vapor with driving and incoherent pumping

fields present, (iii) The enlarged central part of (ii).

probe field in the nondriven Rb vapor is essentially zero

at detuning —15 GHz. In this region the measured phase

shift was approximately 1 .5 rad. In conclusion, we have presented an experimental

demonstration of an enhancement of the refractive index

in a coherently prepared atomic medium accompanied

by vanishing absorption. The experimental results were

predicted by and are in good agreement with a detailed

theoretical analysis.

The authors gratefully acknowledge discussions with

E. Arimondo, H. Briegel, M. Fleischhauer, E. Fry, and

T. Hansch, valuable assistance of T. Zibrova, and the support from the Office of Naval Research, the Welch Foundation, the Texas Advanced Research and Technology

Program, and the Air Force Office of Scientific Research.

[1] M.O. Scully, Phys. Rev. Lett. 67, 1855 (1991); M.O.

Scully and S.-Y. Zhu, Opt. Commun. 87, 134 (1992);

M. Heischhauer et ai, ibid. 87, 109 (1992); A.D.

Wilson-Gordon and H. Friedman, ibid. 94, 238 (1992);

M. Fleischhauer et ai, Phys. Rev. A 46, 1468 (1992); U. Rathe et ai, ibid. 47, 4994 (1993); J. Dowling and

C. Bowden, Phys. Rev. Lett. 70, 1421 (1993); A. Manka et ai, ibid. 73, 1789 (1994); O. Kocharvoskaya,

P. Mandel, and M.O. Scully, ibid. 74, 2451 (1995).

[2] S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107(1990).

[3] O. Kocharovskaya and Y. Khanin, JETP Lett. 48, 630

(1988); S.E. Harris, Phys. Rev. Lett. 62, 1033 (1989);

M.O. Scully, S.-Y. Zhu, and A. Gavrielides, ibid 62,

2813 (1989).

[4] K.-J. Boiler, A. Imamoglu, and S.E. Harris, Phys. Rev.

Lett. 66, 2593 (1991).

[5] A. Nottelmann, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1933); E.S. Fry et al., ibid. 70, 3235 (1993);

W. E. van der Veer et ai, ibid. 70, 3243 (1993).

[6] A. S. Zibrov et ai. Phys. Rev. Lett. 75, 1499 (1995).

[7] G.G. Padmabandu et ai, Phys. Rev. Lett. 76, 2053 (1996).

[8] S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46,

R29 (1992).

[9] S.E. Harris, Opt. Lett. 19, 2018 (1994).

[10] M.O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69,

1360(1992).

[11] M. Xiao et ai, Phys. Rev. Lett. 74, 666 (1995); R. Moseley et ai, ibid. 74, 670 (1995); D. Meschede

et ai, in Proceedings of CLEO/QELS '95 Boston 1995.

[12] G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo

Cimento Soc Ital. Fis. 36B, 5 (1976); E. Arimondo and

G. Orriols, Nuovo Cimento Lett. 17, 333 (1976); H.R.

Gray, R. M. Whitley, and C. R. Stroud, Jr., Opt. Lett. 3, 218 (1978).

[13] We note here that the results for x' ^i^d x" depend upon

the particular choice of the model, e.g., upon the particular incoherent pump mechanism. In the present three-level model, which we use to illustrate the physics, we assume

an indirect pump mechanism which populates level c via

a "one way" pumping from level b. [14] A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154(1991).

[15] In such a configuration probe and driving fields form three effective A systems with the Rb Di manifold [Fig. 1(b)]. Note that the situation would be different if we used

fields with linear polarizations: In that case fields form

only two effective A systems (since the transition 2, m/r = —» I'nif = is forbidden) which impUes a large

absorption of the probe field on the transition \, mp =

-» 2'm/r = 0.

3938 TN-270
Volume 79, Number 16 PHYSICAL REVIEW LETTERS 20 October 1997

Spectroscopy in Dense Coherent Media: Line Narrowing and Interference Effects

M.D. Lukin,'-'* M. Fleischhauer,'-^ A.S. Zibrov,'^-^ H.G. Robinson,^ V.L. Velichansky,'-^

L. Hollberg,2 and M.O. Scully'-^

^Department of Physics, Texas A & M University, College Station, Texas 77843

^National Institute for Standards and Technology, Boulder, Colorado 80303

^Sektion Physik, Universitdt MUnchen, D-80333 MUnchen, Germany

'''Max-Planck Institut fiir Quantenoptik, D-85748 Garching, Germany

^Lebedev Institute of Physics, Moscow, Russia

(Received 18 April 1997)

Spectroscopic properties of coherently prepared, optically dense atomic media are studied experimentally and analyzed theoretically. It is shown that in such media the power broadening of the resonances can be substantially reduced. A density-dependent spectral narrowing of the electromagnetically induced transparency (EIT) window and novel, even narrower, resonances superimposed on the EIT line are observed in dense Rb vapor. A nonlinear two-photon spectroscopic technique based on

coherent atomic media and combining high resolution with a large signal-to-noise ratio seems feasible. [50031-9007(97)04278-6]

PACS numbers: 42.50. -p, 42.62.Fi

In conventional methods of resonant spectroscopy, optically thin ensembles of atoms or molecules are probed with

lasers of limited intensity [1]. Low intensities are used in order to avoid power broadening and frequency shifts. In general, as the Rabi frequency of the resonant electromagnetic field exceeds the natural width of the transition under

consideration, the width of the resonance increases, result- ing in a rapid loss of resolution. This effect is especially

profound when transitions between long-lived states are considered, in which case the necessity of low-intensity

light fields results in an unfavorably low signal-to-noise

ratio [2]. An example of such a resonance is a two-photon

transition in a A-type atomic configuration [3]. In the present Letter we study experimentally and describe theoretically the spectroscopic properties of dense

ensembles of atoms coherently prepared and probed by

strong optical fields. We observe and discuss the nar- rowing of power-broadened dark resonances [4,5] associ- ated with electromagnetically induced transparency (EIT).

Moreover, when the atomic density becomes sufficiently

large, we observe novel, even narrower structures super- imposed on the EIT line. We find that these resonances

are due to interference induced by a new field component

arising from resonantly enhanced coherent Raman scatter- ing [6]. We show that, in contrast to simple transmission

measurements, the characteristics of these novel spectral features are determined by the dispersive properties of

the dense phase-coherent medium [7]. In particular, their width can be orders of magnitude smaller than the usual

power-broadened limit; that is, power broadening can be

compensated to a large extent. This makes feasible a new

regime of two-photon spectroscopy, in which high resolution can be achieved with higher intensities and therefore with lower noise than in conventional methods.

Before proceeding we note that it has already been rec- ognized that sometimes it is advantageous to do spectroscopy in optically thick samples [8]. As will be seen, the

essential new features of the present system are twofold:

the absorption cancellation due to quantum interference [5] and the importance of the dispersive and nonlinear optical

properties of a coherently prepared medium. The present

technique is also related to a coherent anti-Stokes Raman

spectroscopy (CARS) [6]. Our method, however, differs qualitatively from the latter since in our case it is essential

to operate near the single photon resonance. As a result the spectral resolution is determined mostly by the linear susceptibility rather than the ;^'^^ nonlinearity. We further note that the advantage of using the dispersion of EIT reso- nances for spectroscopic measurements has been pointed

out in a recent group delay experiment [9]. Our approach

is conceptually different in that it utilizes a combination of

linear and nonlinear response on cw fields. The conceptual foundations of the present work can be understood by considering a simple 3-level A system

as shown in Fig. 1(a). A resonant driving field on the a —* c transition with complex amplitude E = Eoe~"^''' and Rabi frequency H = PacEo/lh produces symmetric

Autler-Townes dressed states with a frequency separation

phase lock |J-[mq] e*) pdO

ECDLl

ECDL2

yMS SA

(^PA/4 RbceU PD

FIG. 1. (a) Simplified 3-level model for EIT.

(b) Experimental setup (schematic). ECDLl and ECDL2

are extended-cavity diode lasers (probe and driving lasers, respectively). PD: photodetector, P: polarizer, MG: microwave

synthesizer, and SA: spectrum analyzer. The Rb cell is inside magnetic shields.

0031-9007/97/79(I6)/2959(4)$I0.00 © 1997 The American Physical Society

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Volume 79. Number 16 PHYSICAL REVIEW LETTERS 20 October 1997

of 20,. ^ac is the dipole moment of the a —+ c transition and coij the drive-field frequency. Interference of tran- sitions from the ground state to the two dressed states causes a reduction of absorption of a probe field Ep tuned

to the center of the b —> a transition. This is the essence

of dark resonances [4] and EIT [5]. The EIT window in the single-atom response is power broadened and its spectral width approaches 2fl. As we will now demonstrate,

this conclusion is not valid in the case of transmission

through a thick atomic ensemble [10]. The spectroscopic properties of a dense vapor of

coherent A-type Rb atoms were studied in the experiment

indicated in Fig. 1(b). Two extended-cavity diode lasers, a drive laser and a probe laser, were phase locked with

a frequency offset (coq ~ o^hfs = 6.83 GHz) determined

by a tunable microwave-frequency synthesizer. Two

collinear laser beams were passed through a 5 cm long

cell containing natural Rb, and the transmitted power was

detected by a fast photodetector (PD). Both beams were

of identical circular polarization. The powers of the drive

and probe beams in the cell ranged from 5 to 10 mW

and 0.05 to 0.1 mW with spot sizes of 5 and 3 mm,

respectively. The frequency of the drive laser was tuned

to the center of the S 1/2, F = 2 — P\/2,F = 2 transition of the Rb D\ line, while the frequency of the probe

laser was scanned across the S\/i,F = I — P[/2, F = 2

transition by tuning the synthesizer frequency. In such

a configuration probe and drive fields create a A-type

system [Fig. l(a)J within the Rb D| manifold.

In the present experiment the signal was recorded by

monitoring the amplitude of the time-dependent component of the detector current at frequency a>o = cop — ajd

corresponding to the difference frequency between probe

and drive fields. In the case of a dilute medium the heterodyne signal at the photo detector is proportional to the transmitted probe-field amplitude.

At relatively low values of the atomic density the observed signal shows the usual absorptive features corresponding to EIT [Fig. 2(a)]. When the beat-note

frequency of the lasers matches the resonant frequency

of the /? — c transition, the medium becomes transparent

displaying an EIT-type resonance [curve / in Fig. 2(a)]

with a nearly symmetric line shape. The peculiar feature of this resonance is that its width decreases with the atomic density. At higher densities the transparency

window becomes substantially asymmetric. Within

this window, additional few kilohertz-wide resonances

[Fig. 2(b)] were clearly resolved. Their characteristics such as position, width, and amplitude depend on the strength of the drive field and on the atomic density.

Furthermore their position was found to be very sensitive

to atomic level shifts, induced, for example, by weak

magnetic fields. Under the conditions of dense media, resonances as narrow as 3 kHz were observed with a high

signal-to-noise ratio. For the data presented here, the estimated Rabi frequencies of drive and probe fields were

correspondingly on the order of 10 and 2 MHz.

2960

probe detuning probe detuning

FIG. 2. Measured signal as a function of a relative laser de- tuning for various atomic densities, (a) Curves /-;v correspond

to atomic densities N ~ 6 X 10'°, 1 X 10", 2 X 10", and

6 X 10" cm"\ respectively. Estimated Rabi frequencies are 10 and 2 MHz for drive and probe, (b) Extra resonances in optically dense Rb vapor. Dnve-field Rabi frequency is 13 MHz

and atomic density is —10'- cm"-'. Scan time was a few sec- onds. The estimated time-of-flight broadening in the probe and

drive beams is —15 and —8 kHz, respectively. There is no external magnetic field. Natural linewidth of the Rb Di line is 5.4 MHz. Doppler broadening is —500 MHz.

The narrowing of the dark resonances with increasing

density has a nature similar to that of Ref. [8] and can easily be understood from an idealized 3-level model in which

probe and drive interact solely with the respective transi- tions a —* b and a —» c. For simplicity let us assume, in addition, a spatially homogeneous Rabi frequency of the drive field. The intensity transmission of a monochromatic

probe of wavelength A through a vapor cell of length L is described by T = exp{-;^"A:L}. Here k = 2tt / X and x"

is the imaginary part of the susceptibility x^ which for the

idealized, homogeneously broadened 3-Ievel h. system and

a weak {Vlp < Cl) field is given by [5] _ / iybc - (A - A^) ^ "^^"[yat + /A][r,, + /(A - Arf)] + a2'

where 17 = 3A^AV47r-, A^ is the atomic density, A is the detuning of the probe laser, and A^ is the detuning of the drive laser, y'a-y'a ^^e the radiative decay rates as per

Fig. 1(a), and y^^ are the decay rates of the respective

coherences.

In the low density limit (rjkL <3C 1) the spectral fea- tures of the transmission coincide exactly with those of x" Iri the high density limit, however, only spectral components which are very close to the center of

the transparency are transmitted. In order to estimate

the effective width of the EIT window, we expand x"

around the point of maximum transmission [A = ( 1 -

ybc/yab)^d] assuming the usual EIT conditions: O" »

yabybc-i^dybc^^lybc/yab^ and yab » Jbc- The result- ing transmission spectrum is a Gaussian function of the detuning. Its characteristic half width

n^ 1 \a)i (2)

scales inversely with the square root of the density-length

product and can become substantially smaller than the single-atom power-broadened width.

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Volume 79, Number 16 PHYSICAL REVIEW LETTERS 20 October 1997

Let us now turn to the additional resonances. We show

that these resonances are due to a new field generated

by resonantly enhanced coherent Raman scattering [see

Fig. 3(a) and Ref. [11]] and that they reflect the dispersive properties of the medium. The mechanism of this process can be understood if we note that the strong

driving field couples the excited state to both ground

state hyperfine levels. The interaction of the drive and

probe fields with the resonant transitions generates co- herence between the ground states. In the presence of

this coherence, the interaction of the drive with the off- resonant transition S\/2,F = 1 — P\/2,F = 2 leads to a nonlinear generation of a new field £„ with frequency

co„ = 2(0(1 ~ ^p- This process is very similar to the re- cently observed frequency conversion in coherent atomic

media in Ref. [12]. For a large density-length product, the output amplitude of the new field E„ can be of the same

order as that of the probe field, Ep . At the photodetector,

the new field gives rise to an additional component to the beat note at frequency coq. Taking this contribution into account we find that the signal power at a>o in the present

heterodyne detection scheme is given by

Sl^ oc \EaEl + E*Ep\\ (3)

To understand the nature of the additional resonances,

in particular, their relatively narrow width, let us consider

again the simplified 3-level model discussed before. We

now, however, take the nonresonant couplings and the associated parametric process into account. Let us further assume that the probe and "new" field are much weaker

than the drive field, and that the drive field (A^ = 0) is undepleted. These assumptions (which will not be used

in the later numerical simulations) allow for a simplified

discussion of the relevant physics. In this case we arrive

at the system of equations

ail a\2

ail

(4)

The coefficient a\\ is proportional to the linear susceptibility of the resonant field Ep and an to that of the off-resonant field £„. The cross-coupling coefficients a 12 and 021 describe the resonantly enhanced ;^*-^'-type nonlinearity. Under near-resonance conditions and in the absence of Doppler broadening they are given by an =

Pl/2

0.75

0.5 E

1 0.25

•3 0. \-. -0.25

-0.5 F=l

FIG. 3. (a) 3-wave mixing leading to parametric generation of

field En within the Rb D\ line, (b) Illustration of the difference between absorption and dispersion spectroscopy based on EIT

in optically dense medium. Solid curve (characteristic width

I^va) illustrates typical absorption signal, while dashed curve

(width A I'd) shows the dispersion signal.

ix - -ivy'a^^ - 0.^/m)/^^ - vy'ayhc/^\^ «22 -

-ir)y'^/2(oo, and ai2 = a^i = -iiqyjm) X e]/\EA'^.

Solving this linear propagation problem and substituting

the solution into Eq. (3) we find that the beat note at the photodetector contains an interference term with an amplitude depending on the probe laser detuning via the phase shift A0 = ;^;''/:L/2, which modulates the usual transmission profile and gives rise to extra resonances. Hence the characteristics of the new resonances are deter- mined by the dispersive properties of the EIT medium [7]. Since the index of refraction close to the point of

maximum transmission is a linear function of the probe

detuning [7], the phase shift of the transmitted field is also linear in A. For a large density-length product

the phase shift accumulated over the cell length can

easily surpass 27r already for a very small detuning

from the two-photon resonance. Hence the interference term (~exp{— ;^"/cL/2}sin A</>) in the beat note at the photodetector rapidly oscillates with A as indicated in Fig. 3(b). We define a characteristic width Awjis

Awdis = '"—;

TT > (5)

as the detuning from the line center at which the phase

of a probe laser shifts by 7r/2. This expression scales inversely with the density-length product itself instead

of its square root as in Eq. (2). Thus we conclude

that in dense media the width of interferometric fringes

("dispersive" width Awdis) can be considerably smaller

than the characteristic width of the EIT transmission

Eq. (2). Because of the parametric generation and the homodyne detection technique both "absorptive" and

"dispersive" widths are observed in our experiment.

To make a detailed comparison with the experiment we

consider a theoretical model in which the 3-wave mixing

process is included together with Doppler broadening and

the full (hyperfine) level structure of Rb^^. The propagation equations for the three fields were solved numerically. The atomic polarization was calculated from the density matrix equations with a Floquet ansatz. To trun- cate the resulting hierarchy, the beat note frequency coq was

assumed to be large compared to the relevant decay rates and Rabi frequencies. As shown in Fig. 4 the result of

this calculation is in good agreement with the experimental data. In particular, the additional narrow resonances indeed have a width close to the "dispersive" width in a dense medium, Eq. (5). Finally, the observation of the extra resonances coincided with the appearance of a new field component E„ as was verified by making a beat note be- tween the output field and an independent laser. Before concluding we remark on the possible implications of the compensation of power broadening in dense

media. To this end we estimate the theoretical limit of

this compensation by considering an ideal 3-level Atype medium with a large density-length product, such

that the probe-field intensity is attenuated at line center by \/e. In this case, which corresponds to a maximum

2961

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Volume 79. Number 16 PHYSICAL REVIEW LETTERS 20 October 1997

probe detuning probe detuning

FIG. 4. Calculated signal [Eq. (3)] as a function of probe

detuning, (a) Curves i-iv correspond to atomic densities of the Fig. 3(a). (b) Extra resonances under the conditions corresponding to those of Fig. 3(b). All parameters correspond

to Fig. 3. Relaxation rate of ground state coherences is taken

to be 15 kHz, and relaxation rate of ground state populations

is 8 kHz. Signal is normalized such that unity corresponds to undepleted probe and drive fields.

signal-to-noise ratio at the output, the "absorptive" and

"dispersive" widths approach

a

ybc

A&>dis Trybe (6)

which implies that under idealized conditions the effect of power broadening can be completely compensated in a dispersive measurement [13]. For a realistic experimental

situation this conclusion is certainly too optimistic due to

light shifts from off-resonant levels and/or due to effects of collisional broadening of the ground state transition

(e.g., for the maximal laser power used in our experiments

residual power broadening of the resonances became

observable at about ~20 kHz). In general these effects

limit the "useful" laser intensity [14]. We further note

that the particular heterodyne detection scheme used here

yields a rather complicated, asymmetric line shape and

is therefore not ideal for the determination of the atomic

line center. It is, however, likely that modification of the detection scheme [15] can lead to more symmetric line shape and therefore to improved precision for the line center determination.

In conclusion, we have shown that a spectroscopic

technique based on dense ensembles of coherent atoms

can be much less sensitive to power broadening, and

thus may combine high resolution with large intensities resulting in an enhanced signal-to-noise ratio. The authors gratefully acknowledge useful discussions

with E. Arimondo, Yu. Rostovtsev, and G. Welch, the valuable assistance of T. Zibrova, and the support from

the Office of Naval Research, the Welch Foundation,

the Texas Advanced Research and Technology Program,

and the Air Force Office of Scientific Research. M. F. thanks the Alexander-von-Humboldt foundation for financial support.

[1] W. Demtroder, Laser Spectroscopy: Basic Concepts and

Instrumentation (Springer, Berlin, 1996).

[2] J, Vanier and C. Audoin, The Quantum Physics of Atomic

Frequency Standards (A. Hilger, Bristol, 1989).

[3] The narrow features of two-photon transitions were exploited in many experiments for optically thin samples

and weak fields: M.S. Feld and A. Javan, Phys. Rev.

177, 177 (1964); W. Gawlik et at., Phys. Lett. 48A, 283

(1974); R.P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979); J. E. Thomas et al.. Phys. Rev. Lett. 48, 867

(1982); M. Kailova et al.. Phys. Rev. A 32, 207 (1985); A. Akulshin, A. Celikov, and V. Velichansky, Opt. Commun. 84, 139(1991).

[4] G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo

Cimento 36B, 5 (1976); E. Arimondo and G. Orriols, Nuovo Cimento Lett. 17, 333 (1976); H. R. Gray,

R.M. Whitley, and C.R. Stroud, Jr., Opt. Lett. 3, 218

(1978).

[5] K.-J. Boiler, A. Imamoglu, and S.E. Harris, Phys. Rev.

Lett. 66, 2593 (1991); for review see S.E. Harris, Phys.

Today 50, No. 7, 36(1997).

[6] Y. R. Shen, The Principles of Nonlinear Optics (John

Wiley & Sons, New York, 1984).

[7] Dispersive properties of coherent media have been studied

in M.O. Scully, Phys. Rev. Lett. 67, 1855 (1991); S.E.

Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46,

R29 (1992); M. Xiao et al., Phys. Rev. Lett. 74, 666

(1995); R. Moseley et al., Phys. Rev. Lett. 74, 670 (1995); O. Schmidt et al., Phys. Rev. A 53, R27 (1996); A.S.

Zibrov etal.. Phys. Rev. Lett. 76, 3935 (1996).

[8] S. Svanberg etal.. Opt. Lett. 11, 138 (1986); S. Svanberg

et al., J. Opt. Soc. Am. B 4, 462 (1987); O. Di LorenzoFilho et al.. Opt. Lett. 16, 1768 (1991).

[9] A. Kasapi et al., Phys. Rev. A 53, 4547 (1996).

[10] Various aspects of propagation in dense EIT media were

studied in S.E. Harris, Phys. Rev. Lett. 72, 52 (1994);

M. Reischhauer, Phys. Rev. Lett. 72, 989 (1994); M. Jain

et al., Phys. Rev. Lett. 75, 4385 (1995); A. Kasapi et al.. Phys. Rev. Lett. 74, 2447 (1995); S.E. Harris and ZhenFei Luo, Phys. Rev. A 52, R928 (1995); M.B. Gomy,

B.G. Matisov, and Yu. V. Rozhdestvenskii, Sov. Phys.

JETP68, 728 (1989).

[11] Y. Li and M. Xiao, Opt. Lett. 21, 1064 (1996).

[12] M. Jain et al., Phys. Rev. Lett. 77, 4326 (1996); we also point out the relevant studies of P. Hemmer et al.. Opt.

Lett. 20,982(1995).

[13] M.O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360(1992).

[14] We note here that our results indicate that the ac-stark

shift and accompanying power broadening due the off- resonant (Ahfs ~ 800 MHz) states of the f = 1, Pi/2 hyperiine manifold is substantially reduced for the present choice of polarizations, since the dark states associ- ated with two different upper levels P\/2,F = 1 and

F = 2 are identical. For example, for parameters of

Fig. 2 a naive estimate yields for shifts and broadening values H^/Ahfs ~ 200 kHz, which is more than an order of magnitude larger than the experimentally

observed .value. [15] For example, detecting the generated field itself can combine a symmetric line shape with a resolution given

by the dispersive width.

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