NisrUNITED STATES

DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

A111D3 BTflblM

NIST

PUBLICATIONS NIST Technical Note 1336
NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Research Informaticm Center

.Gaithersburg, MD 20899

DATE DUE

i

Demco, Inc. 38-293
Wavelength Measurement System for

Optical Fiber Communications

IQC/

Gregory E. Obarski

Electromagnetic Technology Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

*" JUL. C

/

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director

Issued February 1990
National Institute of Standards and Technology Technical Note 1336

Natl. Inst. Stand. Technol., Tech. Note 1336, 44 pages (Feb. 1990)

CODEN.NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1990

For sale by the Superintendent of Documents, U.S. Government Printing Office, Wasliington, DC 20402-9325
CONTENTS

1

Introduction

2. Background

3. Principle of Lambdameter

4. Accuracy and Resolution

4.1 Path Folding

4.2 Dispersion of Air

4.3 Diffraction

4.4 Colinearity of the Reference and Unknovm Laser Beams

4.5 Phase Uncertainty Between Recombining Beams

4.6 Other Potential Sources of Error

5. System Design

5.1 Optical Design

5.2 Reference Laser

5.3 Photodetectors and Fringe-Signal Frequency

Multipliers

5.4 Instrumentation and Optical Components

5.5 Optical Alignment of the System

5.6 Measured Accuracy

6. Wavelength Measurements on a Single-Mode Diode

Laser Source

6.1 Description of the 1.52 /xm Diode Laser

6.2 Results of Wavelength Measurements

7. Discussion and Conclusions

8

Acknowledgments

9. References

Appendix A. Raw Data From Diode Laser Wavelength Measurements

Appendix B. Optical Designs for Lambdameters

Appendix C. First-Generation System

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39

ILL

WAVELENGTH MEASUREMENT SYSTEM FOR OPTICAL FIBER COMMUNICATIONS

Gregory E. Obarski

Electromagnetic Technology Division

National Institute of Standards and Technology

Boulder, CO 80303

A wavelength measurement system (lambdameter) for singlemode sources used in optical fiber communications is described.

The sources of interest are mainly diode lasers emitting at 1.3

and 1.5 fxm, but the system can be used in the near IR and red

regions of the spectrum. Accuracy in wavelength measurement

is <0. 1 ppm at the 0.63 ^m HeNe line by comparing separately

each of two adjacent modes from a HeNe laser that is frequencystabilized by a polarization technique, with a single mode from

a second similarly frequency-stabilized HeNe laser. Wavelength

instability of a commercially packaged 1.52 ^m distributedfeedback diode laser is in the range ±1 ppm.

Key words: single mode; diode laser; wavelength measurement;

wavelength instability; optical fiber communications;

lambdameter

1. Introduction

The purpose of this research is to build a precision lambdameter for use as a standard for measuring the wavelength of infrared radiation from

single-mode diode laser sources used in optical fiber communication

systems. The sources of interest are primarily distributed- feedback

(DFB) laser diodes emitting at 1.3 and 1.5 /xm, but distributed Bragg

reflector (DBR) laser diodes are becoming increasingly important as well.

Signal transmission at these wavelengths is desirable because certain

classes of fibers exhibit minimum signal attenuation and dispersion at

them. The zero dispersion wavelength of dispersion unshifted single-mode

fibers (EIA class IV a) is 1.3 ^m. Also, dispersion can be made

vanishingly small for optical transmission at 1.55 /xm by suitable choice

of refractive index profile and core radius in single-mode dispersion

shifted fibers (EIA class IV b) in which signal attenuation is

<0.2 dB/km.

Our requirement is to measure wavelength within an uncertainty

approximately equal to source linewidth. This can be achieved using a practical length of carriage motion and a technique that allows counting

zero crossings of the fringe signal frequencies. Thus it is unnecessary

to use one of the more complex fringe fraction counting methods to
approach the desired accuracy [1-4]. A simple calculation gives the

wavelength uncertainty for a 50 MHz linewidth. If c is the speed of

light in vacuum, u the frequency, and A the vacuum wavelength of the

source, then u\ - c , and

c For wavelength measurements at 1.52 /xm in vacuum or air, the condition on spatial linewidth becomes AA ~ 4-10"^ /im. The corresponding uncertainty

in wavelength, AA/A , is —AA AAt/ _ ^ ^c = - -^ ==0.25 ppm,

so with a linewidth of 50 MHz an accuracy A = 0.25 ppm is acceptable.

Our instrument's resolution is 0.1 to 0.2 ppm and corresponds to 20 MHz.

Resolution, which depends on the number of fringes counted, is limited by

the linewidth-dependent phase uncertainty between the interfering beams.

This phase uncertainty can be expressed as the ratio of a fringe fraction

to the total number of fringes counted. It sets limits on the fraction

of a fringe that can be counted and the accuracy to be gained by

increasing the path difference.

The accuracy and resolution of lambdameters reported in the

literature varies over many orders of magnitude, from about 1:10^ to

lilO^-"-. These are given in the background section for general

information, although a reported value may disagree with what the reader

believes attainable for that particular system. Since it is not our purpose to study the limiting boundary conditions on accuracy, arguments

on the validity of a reported accuracy are omitted. In section 5.6 the

accuracy of our system is presented.

2 . Background

The invention of the lambdameter, which is a scanning Michelson

interferometer, arose from the need to rapidly measure the wavelength of

single-mode, continuous -wave (cw) dye lasers with sub-Doppler accuracy.

It was first developed by Hall and Lee [1] , and Kowalski [5] . In each of

these systems an original, independent optical design was employed. Hall

and Lee [1,6] measured laser transitions in neon with an accuracy of

2:10^. The system had a scan distance of 1.22 m and a uniquely folded

path. Interference fringes in the optical signal were divided into 100

levels, and the corresponding output of an oscillator with this multiplied frequency was phase- locked with the optical fringe rate. This

increased accuracy by a factor of 100 beyond that possible for simple

fringe counting.

Kowalski 's original optical design [5] required fewer critical

optical components, but did not have a folded path. Fringe fractions were counted by two successive squaring circuits which quadrupled the

count rate. Measurements were made on hyperfine components of iodine in

the 510 to 570 nm range using a scan distance of 1 m. A dye laser tuned
to coincidence with several lines of atomic sodium confirmed accuracy to

6:10®. This work includes an analysis of the variation of refractive

index of air with wavelength and thermodynamic properties. An improved

system with a novel folded-optical path and phase- locked loop to multiply

fringe counting rate was later developed by Kowalski [7]. Accuracy was tested by measurements on the iodine 514.5 nm line and reported to be

1:108.

For wavelength measurements in the visible spectrum, Branberg and

Nylen [8] developed a system with accuracy of about 1:10^. To reduce the

influence of drift and intensity fluctuations, the interference fringe

signal was digitized by a comparator and the instantaneous value compared

with its mean value. The correction due to the dispersion of air was eliminated by operating the system in a vacuum of 1 mPa.

Bennett and Gill [2] reported an uncertainty of 2:10® for wavelength

measurements of several visible HeNe , Ar and Kr laser lines. To increase

system accuracy, they developed a technique for counting fractional parts

of an interference fringe at the beginning and end of a measurement. The

dispersion correction was calculated from a new and simpler form, giving

a result differing from the Edlen form [9] by only 1.5-10®. The

uncertainty due to dispersion was given as 5:10®.

For wavelength measurements in the visible and infrared, Monchalin

et al. [10] developed a vacuum-operated system. In the 10 /im region,

accuracy was limited by diffraction and reported to be several parts in

10^. In the visible range, accuracy was reported to be several parts in

lO-"-^ . Data were analyzed by a technique in which the unknown wavelength

was sampled for each zero crossing of the reference fringes. Groups of

1000 reference laser fringes were sampled, and the relative phase of the

corresponding unknown laser fringes calculated by a Fourier summation

scheme. The standard deviation was given as 0.003 of a reference HeNe

fringe. The reference laser was an iodine Lamb-dip- stabilized HeNe

calibrated with respect to a basic Kr length standard.

Bonsch [11] developed a lambdameter to measure the wavelength ratio

of methane-stabilized HeNe at 3.39 fim to iodine-stabilized HeNe at

0.633 /im. The reported uncertainty was 3:10-'-°, with diffraction the

limiting factor. By vibrating the interferometer's reference mirror and

analyzing the fringe signals by phase-sensitive detection, the reported

uncertainty in the determination of fractional interference orders was

10"''. A modification of this interferometer using a single polarization

fiber for coupling light to the interferometer was reported to render

insignificant the error due to optical beam misalignment [12]. With this

modification, a relative uncertainty of 4:10^-'^ (which was smaller than

the reproducibilities of the lasers) was reported by simultaneously

comparing iodine-stabilized laser lines at 515 nm, 633 nm, and 640 nm.

The wavelengths of two HeNe lasers differing by only 1 : 10'' were compared by a system employing a vernier fringe-counting circuit. This

method required coincidence in the phases of the two detected waveform

signals at both the beginning and end of the counting cycle. Using this
system, Kahane et al . [13] report a reproducibility of 5:10^ and an accuracy of 4:10^. The vernierlike coincidence concept is also described

in a wavemeter using a compact spherical interferometer [14].

Kowalski et al. [3] later developed a system which corrected for

interference fringe dropouts caused by transient dye laser instabilities.

Missing fringes were accounted for by comparing numbers counted in an interval with a preceding reference interval. Fractional fringes were monitored by measuring the time separation between the first observed

dye-laser fringe and the first HeNe reference-laser fringe. This was

done with a signal 100 times faster than the fringe signal rate and the

procedure repeated at the end of a scan. The setup was placed in a vacuum chamber and the uncertainty due to dispersion was reported to be

lilO-"-" with instrument precision on the order of 1:10^.

A vacuum-operated system with a new optical design was more recently

developed by Ishikawa et al . [4,15]. It had a multiple folded-path and

specially built rigid structure for improved accuracy. Multicoincidence

fringe counting logic was used to determine coincidence points for the

fringe signals from the reference and unknown lasers. With this technique fringe fractions were reportedly resolved to 1/500 of a fringe.

The wavelength ratio of stabilized HeNe lasers at 612 nm and 633 nm was measured with an uncertainty <4:10-'^°.

Junttila et al . [16] developed a Fourier transform lambdameter for

multimode diode laser measurements and single-mode, long-term frequency

stability measurements. A two-mode, polarization-stabilized, 543 nm HeNe

laser was compared with an iodine-stabilized, 633 nm HeNe laser with an uncertainty <1:10^. Multimode diode laser spectra at 840 nm and 1300 nm were also investigated. To eliminate errors due to misalignment between

the reference and unknown laser beams, the light was f iber-optically

coupled into the interferometer. Shifting and broadening of peaks was observed for diode- laser environmental temperature changes on the order

of 0.1 K.

A high-accuracy lambdameter was reported by Cachenaut et al . [17].

The wavelength of a 612 nm HeNe laser stabilized to a saturated

absorption peak of iodine was measured with an accuracy of 1.6:10^.

Fringes from the unknown and reference lasers were simultaneously

counted, then compared at a phase detector with the output of a voltage

controlled oscillator (VCO) . The VCO frequency was multiplied by a factor of 128 and phase locked by feedback from the output of the phase

comparator. A resolution of 1.4 fm allowed for measurement of the iodine

hyperfine structure with a precision of about 2.5 fm.

To study dye-laser wavelengths, Mulders et al. [18] developed a system employing a phase- locked loop by which the fringe frequency could

be multiplied by a factor of 10. Wavelength measurements were updated

every second with an accuracy of 0.01 nm. Missing fringes due to dyelaser beam interruptions that probably arose from air bubbles in the

lasing area of the dye jet stream were investigated.
In another system, Rowley et al. [19] reported an accuracy of 1:10^,

with the diffraction error estimated to be less than 1:10^. Evans and

Lambert [20] studied lead-salt diode laser wavelengths, reporting an accuracy of a few parts in 10^ with their system. Using Murty's modified

Michelson design [21,22], and with the scanning corner cube mounted on a toy electric train with foam rubber, Hui-Rong et al. [23] report an accuracy of 1:10^. Finally, Milan et al. [24] developed a system with a reported precision between 1:10® and 1:10^. For a review of laser

wavelength meters see references 25 and 26.

3, Principle of Lambdameter

The simplest scheme using a travelling wavemeter to measure the

wavelength of a cw laser source is based on the Michelson interferometer.

One portion of a split beam reflects from a scanning mirror through a fixed distance. The second portion reflects from a stationary mirror and

the interference fringes from the recombining beams are counted at a detector. The most precise way of measuring the scan distance is to

simultaneously count the fringes from a second laser of known wavelength

over the same scan distance. In the lambdameter, instead of plane

mirrors, corner cubes are preferred because they return a beam antiparallel to the direction of its incidence. If the return beam is

precise within a few arcseconds , the interferometer is insensitive to

misalignment, since the reference and unknown laser beams traverse nearly

identical paths through the interferometer. Upon exiting the interferometer, each of the two wavelengths forms a distinct set of interference fringes that is focused onto a separate photodetector . The

signals from each photodetector are simultaneously counted and the ratio

of the two numbers taken. The number of fringes counted for each wave- length is proportional to the distance through which the corner cubes

travel

The common path associated with the scan gives rise to the

relations

Nr^r/^r = N^, A^ /n^

N,A,(n,) = N,A,(n^), (1)

where r is reference and u is unknown; A is vacuum wavelength; A(n) is

dispersion dependent wavelength; n is the corresponding refractive index

of the propagation medium; and N is number of fringes counted. If for

the propagation medium, T = temperature, P = total pressure or sum of

partial pressures, h = partial pressure of water vapor, and C = fractional CO2 concentration, then

n^ = n^(T,P,h,C,AJ

n, = n^(T,P,h,C,AJ. (2)
This allows us to solve for the unknown wavelength given suitable

knowledge of the refractive indices.

Since n^ depends on \^ which is unknown, we solve eq (1) for A^ (n^ )

.

Now for normal atmospheric conditions

n^(T,P,h,C,AJ - n^(T,P,h,C,A^(n^)) < lO'S (3)

as will be shown in section 4.2 on dispersion. Substituting

n^ (T, P,h,C , A^j (n^ ) ) for n^ (T , P ,h, C , A^^ ) we arrive at the vacuum wavelength

as a function of measurable quantities,

K(^) = K/^ = A,/n,(T,P,h,C,AJ

K "= A,(n^)-n,(T,P,h,C,A,(n^)). (4)

Thus determination of the vacuum wavelength of the unknown laser for

accuracies higher than 0.1 ppm requires that we operate the system in

vacuum or have knowledge of the refractive index. For accuracies of

0.1 ppm careful attention must be given to fluctuations in atmospheric

parameters, especially temperature and pressure. The dispersion is

considered in more detail in section 4.2.

4. Accuracy and Resolution

The accuracy of a lambdameter is a measure of its ability to yield

the true wavelength of a single-mode laser source of linewidth narrow

enough not to limit the measurement at that wavelength. If a lambdameter

measures wavelength within one part in lO'^ (where k is an integer) , it

has an accuracy of 1:10^ in our notation. Thus the higher the accuracy,

the smaller the number representing it. The resolution, AA/A , is limited

by the counting error and is described in section 4.1 below. A

frequency-stabilized reference laser with known wavelength and a stability greater than the desired resolution is needed.

Effects that reduce accuracy in a lambdameter can be divided into

wavelength-dependent and nearly wavelength- independent contributions.

All of these can be rendered insignificant for accuracies of the order of

0.1 ppm. The wavelength-dependent contributions are dispersion and

diffraction. The nearly wavelength- independent contributions are the

angular misalignment between the reference and unknown beams, and the

dependence of the refractive indices on atmospheric parameters such as pressure, temperature, humidity, and CO2 content. The remaining

aberrations of the wavefronts and diffraction, although wavelength

dependent, are insignificant, even when we use inexpensive optics.

4. 1 Path Folding

Taking the differential of eq (1) shows that resolution increases

inversely with the number of fringes counted during a scan of the
carriage. (This is done by using the result 5(n^/nj.) ~ 0, derived in

section 4.2 on dispersion.) Path folding results in higher fringe

counts, hence greater resolution. The accuracy can be made equal to the

resolution by eliminating all other sources of error. If p is the degree

of path folding, z the fraction of a fringe counted, and Ax the scan distance of a corner cube, then the resolution is

R® = AA/A - -\-, (5) zpAx

where A is the wavelength of the reference or unknown laser [17],

depending on which laser is used to trigger the counter. In our present

version p == 4 , A = 1.52 /zm. Ax ~ 1.22 m, and z = 2 (zero crossings are counted), so R ~ 1.5-10'^. Some folded-path designs appearing in the

literature are shown in appendix B.

Extensive path folding has limitations due to phase uncertainty (as

discussed in section 4.6) and can present other problems as well.

Vibrations of the moving carriage with corner cubes induce a jitter of

the optical signal at the distant photodetectors of magnitude directly

proportional to the effective scan length. For long distances,

fluctuating power levels may induce false counts. Optical power loss and

wavefront distortion increase due to the additional optical components

needed to fold the paths.

4.2 Dispersion of Air

The dispersion of air can be calculated and its effect on accuracy

can be estimated. Many approximations for the refractive index are scattered throughout the literature [9,27-31]. A useful result for

standard dry air is given by Edlen [9] (he takes T = 15°C, P = 101325 Pa

(760 Torr)),

r IN in8 Qo/o n ^ 2406030 ^ 15997 ,,, (n3-l)-10« = 8342.13 + ^30 . 1/,^ + 38.9 - 1/A^ ' ^^^

where ng is the refractive index and A is the vacuum wavelength in

micrometers. Addition of temperature and atmospheric pressure dependence

yields

^.r ^^^•^^-^^-^ p. 1 (n, - 1)(0.00138823)(133.31556P) .^.

1 + 0.003671T ^^^

where T is in degrees Celsius, P is in pascals, and 133.31556 pascals

= 1 torr. Finally, for visible radiation propagating through moist air,

a correction for water vapor gives

n(T,P,h) = n(T,P) - 133 . 31556 -h • (5 . 722 - . 0457/A2 ) 10" \ (8)

where h is the partial pressure of water vapor in pascals

7
For infrared wavelengths >1 fim, a modified form for the dispersion

[9] is given as

(n3 - D-IO^ = (27261.1 + 154. S/A^). (9)

Since the refractive index as calculated above depends on the

vacuum wavelength, and a lambdameter operating in air measures the

dispersion dependent wavelength, we justify an approximation which

converts from one to the other. We show that in the refractive index for

the unknown wavelength, the vacuum wavelength can be replaced by the

wavelength in the medium, A(n). Thus

n = n(T,P,h,C,A)

A = A(n) •n(T,P,h,C,A)

Using eq (6) above and A^. j^ - 0.632991287 /xm for the vacuum wavelength of our reference HeNe , we find n^. j^ ~ 1.00027652. Thus the dispersiondependent wavelength is Aj.j^(nj.j^) = Aj.j^/nj.j^ ~ 0.63281630 fim. Substituting

into eq (6), we find n'^^ = 1.00027652. Finally,

rl ''rl <

10-s

(10)

The temperature and pressure dependence is found from eq (7) . At

T = 23°C and P = . 82922 . 28 • 10^ Pa (622 Torr) , we have n'(T,P) - n(T,P)

- 0.8-(n',i - n^i) < 10-8.

As an example for the IR region, we use eq (9) and an assumed value

A^ = 1.520 /zm to calculate n^ = 1.00027328. The dispersion-dependent

wavelength is then A^ (n^^ ) = A^/n^ ~ 1.51958473 ^m. Substituting this

value into eq (8) gives n'^ ~ 1.00027328. Finally,

n', - n, < 10-8. m)

Therefore we generalize to the relation,

A^ - A(n,)-n^(T,P,h,C,A(n^)), (12)

which allows us to find the vacuum wavelength of the unknown source for

accuracies on the order of 0.1 ppm. Precise knowledge of the refractive

index of air through optical interferometric displacement measurements

can be no greater than ±8.5:108 [27].

Partial differentiation of eqs (7) and (8) gives the change in temperature, pressure, and humidity required to alter the refractive index

by . 1 ppm and 0.01 ppm. The results are shown in table 1 [27], but with

humidity converted to percent. See reference 27 for the CO2 dependence.
03 Torr) 40 (0,.3 Torr)

-0.01 -0.131

-1 -10

67 _

Table 1 . Change in a thermodynamic variable required to

alter the refractive index by . 1 and 0.01 ppm.

Initial value An ~ 10"^ An ~ 10"

Pressure (Pa) I.OIS-IO^ (760 Torr) 4 (0.03 Torr)

Temperature (°C) 20

Humidity (%) 40

CO2 (ppm) 340

Of greatest importance, however, is the thermodynamic influence on

the ratio of the refractive indices of the reference and unknown lasers

instead of each index separately. We now show that the variation of this

ratio is independent of normal fluctuations in temperature, pressure, and

humidity, and that we need only specify an arbitrary refractive index

corresponding to the reference wavelength. The variation of the ratio of

the fringe counts, R, due to thermodynamic considerations is

5R - const-5[n^(T,P)/n,(T,P)]. (13)

We rewrite eq (7) as

n(T,P) - 1 = ill-^^l^, (14)

where a = 0.00138823, and b = 0.003671. Then

n (T P) - 1 + ^^^"^^^i> ' ^^

aP( n, (A,) - 1)

1 + bT

n,(T,P) = 1 + ""^"^^^^^" '\ (15)

so

n„(T,P) ^ ^ 1 + bT + k,.P

n^(T,P) 1 + bT + k^P' (16)

where k^ = a(n3(A^) - 1), and k^. = a(n3(Aj.) - 1). The variation in L is

then

so for A^ = 1.52 /im, A^ = 0.632 /^m, we have
II

= k, - k, = a(n3(AJ - n^{\,)) - 5•10-^ (17)

where the denominator has been omitted since it is very close to 1. Also

1^ - bP(k, - k,) = 10-8. (18)

The dependence of L on h is even smaller. From eq (8) with L

defined by the ratio of humidity-dependent indices, we have

1^- (5.61n^(T,P) - 5.7n,(T,P))-10-8.

We evaluate this term at T = 23°C, P = 82922.23 Pa (622 Torr) . The

result is ^lO"^. Thus a 50 percent change in humidity, corresponding to

=1466.5 Pa (11 Torr) changes L by only =1:10° and eliminates humidity as a potential source of error. Therefore L, and therefore R, easily

remains constant within 1:10^ for pressure changes <2666.3 Pa (20 Torr)

or temperature changes <10°C. We can specify the unknown wavelength in

the medium as a function of T, P, and the refractive index of the

reference laser. Thus

. . . ^

A. (1 + bT)

^u^^^ R(l + bT + aP(n3(A^) - 1))

(19)

In our system, the time for a set of measurements takes <1 h, so that

dependence of L on these variables does not contribute to loss in

accuracy.

At the NIST Boulder laboratories, average atmospheric pressure is

about 829222.23 Pa (622 Torr) with diurnal cycles of 200 to 300 Pa (a few

Torr) caused by atmospheric tides. This can fluctuate by as much as 2000

Pa (15 Torr) a week due to normal high and low pressure weather systems,

and 2666 to 4000 Pa (20 to 30 Torr) over a season. The fluctuations are greatest in winter and spring [32]. The pressure gradient at the earth's

surface due to gravitation (-13.33 Pa/m (-0.1 Torr/m) ) changes the

refractive index by =3 parts in 10^ per meter of vertical translation.

Also, convection can cause significant horizontal as well as vertical

thermal gradients . Horizontal gradients have been observed as great as several tenths of a kelvin over distances as small as 1 m [27].

4.3 Diffraction

Diffraction is an error source that must be considered because of

the finite waist size of the laser beams. Given a fixed plane outside

the interferometer such as the surface of a photodetector , two beams

recombining at this plane will have traversed different distances. This

difference is directly proportional to the displacement of the scanning

components from the equal path position. Thus the wavefronts of the two

10
beams will have different curvatures; the difference is greatest at the

endpoints and least at the center of motion. In comparison to the time

dependence of the well-behaved phase of the interference fringe signal

from two plane waves, the phase of interfering wavefronts of slightly

different and changing curvature will vary.

If we ignore wavefront aberrations due to imperfections in the

interferometer, a first-order diffraction correction to the wavelength

[11,12] is

AA

A (2nw)- (20)

where w^ is the waist size of the beam. For beams with w^^ =5 mm such as those used in our system, the diffraction correction is =4:10^° at the

HeNe reference wavelength of 0.632 /im, -1.7:10^ at 1.3 /xm, and =2.2:10^

at 1.5 fxm. Since our accuracy is -1:10^, we can neglect diffraction.

Figure 1. Angular misalignment of the reference and unknown lasers. L^

is the equivalent path travelled by the reference laser over

the carriage motion. A hypothetical detector surface is

arbitrarily aligned perpendicular to ^ . L is the equivalent

path of the unknown beam over the carriage motion, shown

misaligned by an angle 9 . Ay is the linear misalignment of

the beams at the surface and 8 is the extra distance travelled

by the misaligned beam.

4.4 Colinearity of the Reference and Unknown Laser Beams

Consider a misalignment of the reference and unknown laser beams [5] as shown in figure 1. Let Lq be the distance traversed by the reference

beam; the beam is incident perpendicular to the detector surface. Let L

be the distance traversed by the unknown beam which is incident upon the

detector surface at an angle 6. Then, if Ay is the linear misalignment

of the beams at the surface, we have

L = Lg + S

Lg = Lcos^ = (Lg + 5)cos^,

11
where tan^ = Ay/L. Now tan^ can be approximated by 6 with the error occurring at 1:10^, which is negligible for our requirements. Thus,

5 = L - Lq = L(l - cos(9)

= L[l - (1 - e^/2 + ...)]

H] . |fAir

= ^ (Ay)2. (21)

For our system, L ~ 4.7 m and Ay < 1.0 mm. Substituting into

eq (21) gives 5 < 1.06 x 10"^ m. In table 2, 5 is expressed as a fraction of a fringe; f = S/X for wavelengths relevant to our system.

Misalignment reduces accuracy by an amount f/(N+f) ~ f/N, where N is the

number of fringes counted. Since (N+f)A = L, accuracy is reduced by 5/L

< 0.02 ppm for all X. To increase system accuracy by employing a fringe

fraction counting technique requires that the alignment be more accurate

than the fraction of a fringe counted. Our system counts signal zero- crossings or half fringes, so that misalignment is insignificant. For

applications requiring accuracy A < 1 : 10^ , small fringe fractions must be

counted. Thus misalignment can limit accuracy.

Of equal importance is angular misalignment between the two interfering beams from the same laser. However, if the reference and unknown

beams are made colinear, this error is negligible. Furthermore, the

symmetry of the optical design, figure 2, shows that if the beams are initially aligned for each wavelength, a misalignment arising from a displacement of the corner cubes perpendicular to their motion retains

equal optical path lengths for the two wavelengths.

Table 2. Path misalignment (in fractions f of a fringe) between

reference and unknown beams for various wavelengths A using

L = 4.7 m and a misalignment of 1 mm. The error due to

misalignment is 5/L < 0.02 ppm for all A.

A(^m) f 5/L(ppm)

0.63 1/6 0.02

1.00 1/10 0.02

1.3 1/12 0.02

1.5 1/14 0.02

12
4.5 Phase Uncertainty Between Recombining Beams

The finite linewidth of the source results in a phase uncertainty

between the recombining beams [7]. The present system is designed such

that the ratio of the phase uncertainty to the total phase from the

fringe counting over the scan distance is approximately equal to instrument resolution, 5 A/A, as we now show. Let $ be the phase, Ax the path

difference, N the number of fringes counted, k the wavenumber, and Ai/ the

linewidth of the unknown source. Then Ax = (N + e)-A, where e is the

fraction of a fringe. For N » e we drop e. Thus we have

, . 27rAx InvA-x.

Sf — itnx —

A c

5$ =

27rAx52^ c

5$

2n

AxSv

c '

5$

27rN

Ax5j/

Nc c 8XA*

(22)

(23)

For our system Ax ~ 4.88 m, A ~ 1.52 fim, and N ~ 3.2-10^ fringes. Now

since the fringes are well defined over the entire scan, we estimate the

linewidth to be <30 MHz. According to eq (22), the phase uncertainty is

<0.488 fringes. This limits the fraction of a fringe we may count to one -half at this linewidth. Equation (23) shows that the phase

uncertainty over the entire scan is equal to the resolution defined by

5A/A. Presently, we count zero crossings, or half fringes, and our resolution is ~ 1.5-10"^.

4.6 Other Potential Sources of Error

Additional potential sources of error are worth mentioning briefly.

Because the carriage traverses a medium of open air, room turbulence can result in local fluctuations of the refractive Indices. This effect is

diminished by making the paths colinear, and retaining a constant optical

path difference for the reference and unknown sources. Retroreflections

from the various surfaces encountered by the beams can re-enter the

lasers and cause destabilization. These are diminished by using optical

isolators. A major source of retroreflections is the detector surface,

and can be minimized by orienting its normal =40 deg to the incident

radiation [10]. Variations in the speed of the scanning retroreflectors

causes fluctuations in fringe signal frequencies, resulting in a relative

phase shift. This may result in an error due to the finite bandwidths of

the detectors. Variations in speed of up to 5 percent, however, bring

about negligible error [10].

13
5. System Design

5.1 Optical Design

In this design, the beam of the unknown wavelength is superimposed

upon the reference beam using a dichroic beamsplitter/joiner, so that

they are colinear as they traverse the interferometer. A displacement of

the corner cubes by a distance x yields a path difference of 4x between

the interfering beams. A dichroic beamsplitter/joiner separates the two

different wavelengths upon exiting. Each fringe signal is sent to its own detector for processing. Figure 2 is a sketch of the basic lambdameter design [1]. Figures 3a and 3b show the path of a light ray through

a corner cube. A ray exits the corner cube antiparallel to the direction

of its incidence, but displaced an equal and opposite distance from the

vertex. Figure 4 is a schematic of the optical components making up the

system. Figure 5 is a photograph of the apparatus.

I(Xu)' \I(Xr,

From entrance

steering mirrors

Figure 2. Optical design of the lambdameter [1] a ' are corner

cubes, Ml, Mj^ are steering mirrors, BS is the Michelson beamsplitter, BSp is dichroic beamsplitter/joiners, and Dj^ , D^ are photodetector devices. l(X^j) and I(Aj^) represent the unknown

and reference beams entering the interferometer. I(t,Au) and

I(t,A[^) represent the time-dependent fringe signals for the

exiting unknown and reference beams.

14
(a)

(b)

Figure 3. (a) Side view showing the path of a beam entering and exiting a corner cube. (b) Front view showing entrance and exit

positions at points x and o.

15
cc cc

Figure 4. Schematic of components making up the optical system. We have

CC ~ corner cubes, M ~ mirrors, BS = essential beamsplitter,

BE ~ beam expanders, ISO ~ optical isolators, L = lenses,

F ~ single-mode fiber, L^ ~ diode laser collimating lens

system, S == shutters, DBS ~ dichroic beamsplitters/joiners, and

Dj^ , D2R ' ^u ~ detectors. (The path of the second reference

laser is parallel but not colinear to the main reference laser

and is only used for system calibration.

)

16
Figure 5. Lambdameter

5.2 Reference Laser

The HeNe reference laser used In this lambdameter Is frequencystabilized by a polarization technique, and can lock onto either the red

or blue side of line center In the Doppler gain profile. These two

adjacent, orthogonally polarized modes oscillate simultaneously In the

laser gain cavity. A polarizing cube beamsplitter separates the modes.

Illuminating a photodlode with one of them. Down the beam path a nonpolarlzlng dielectric beamsplitter diverts about 20 percent of the

remaining mode to a second photodlode. The two photodlode signals are sent to a differential comparator circuit, whose output is converted to a high-current signal and sent to a thermofoll heater in contact with the

laser tube. As the laser cavity tunes by thermal expansion from the

heater element, the Intensities of the two polarization modes vary over

the Doppler gain profile. When one mode is at a maximum, the second mode

is a minimum. The comparator locks in when the two mode intensities

differ by a preset amount. This maintains the heater current at the

preset level and keeps the cavity length tuned to a specified resonance

frequency.

17
The manufacturer measured the two frequencies of a random sample of

these HeNe ' s by comparing them with a master laser locked to one of the

known transitions in molecular iodine. These measurements were performed

on several of the lasers at JILA (Joint Institutes for Laboratory Astrophysics) [33] before they were made available commercially. The two

frequencies are reported to be (473 612 298 ± 6) MHz and (473 613 085

± 6) MHz. Taking the speed of light in vacuum to be c = 299 792 458 m/s

,

the corresponding vacuum wavelengths are

A^i - 0.632991287 ± 0.000000008 /im,

A^2 = 0.632990235 ± 0.000000008 /im. (24)

The uncertainty in lambdameter accuracy will be governed by the

uncertainty in the reference wavelengths and the refractive indices. For

our reference laser, the average of the two wavelengths remains stable

within 1:10®. Although the individual modes may drift when locked, they

do so together, toward or away from line center. Therefore we develop a wavelength measurement technique which allows us to make use of this

property (section 6.2).

The relative dispersion of these neighboring wavelengths can be

calculated for dry air using eqs (24) and (6) . The difference vanishes

in the parts per trillion range, so that n^ (red) ~ ng (blue) = 1.000220354. This is in agreement with our intuition.

5.3 Photodetectors and Fringe-Signal Frequency Multipliers

Initially, standard photodetector circuits were assembled for the

reference and unknown fringe signals. The frequency of each signal is

proportional to the speed of the corner cubes and is a constant in the

range 10 to 100 kHz. Several different silicon detectors were tried

successfully for the red HeNe beam. An indium gallium arsenide photodetector was chosen for the 1.52 /xm laser because of its large active area (3 mm diameter) . A germanium detector with an active area of 1 mm^

also worked as well. Since our counter counts pulses in only one direction (positive or negative slope) , system accuracy could be doubled

by adding devices that count the zero crossings for each fringe signal

[34]. These were made using a bidirectional one-shot logic chip. For a sinusoidally varying fringe-signal input, the chip can be made to emit

pulses of selectable width every time the input crosses a preset level,

usually zero. At first, circuits which were distinct from the photodetector circuits were made using separate power supplies as well. These

had a variable resistor which controlled the pulse width. Lambdameter

accuracy was observed in the 0.1 ppm range at the 0.63 ^m HeNe line using

these devices. However, these devices were somewhat unstable because of

lack of a solid ground plane and the finite cable length joining them to

the photodetector boxes. Later, specially designed devices [34] which

were professionally fabricated were purchased. These combined the photodetector and zero-crossing circuitry onto a small printed circuit board

18
(3 cm X 5 cm) , both circuit components receiving power from a single

supply. The unit used for the IR signal had to be simply modified by

addition of a voltage divider to lower the reverse bias voltage across

the IR detector.

False counts in the detector devices were a problem for some time.

Various filtering and shielding techniques had to be applied to the

driver and motor used to power the rail table upon which the carriage

moved. The original driver had a 20 kHz switcher that leaked noise into

the photodetectors along the power lines and through radiation in space.

Filtering the power line input into the driver and shielding the cable

from the driver to the motor significantly reduced noise levels. However, we concluded that the driver should be housed in a Faraday cage

with all inputs and ouputs shielded, including the cable from the indexer

(described below) . It was simpler to find a driver-motor system with

satisfactory noise. False counting due to environmental high-frequency

noise was eliminated by proper grounding of the optical table and removal

of ground loops between it and other equipment such as the counter,

motion control instrumentation, and laser power supplies.

5.4 Instrumentation and Optical Components

The retroreflectors are mounted on the carriage of a precision rail

table having a 1.22 m scan distance. The unit employs a precisionground ball screw instead of a typical rolled screw. Travel limit

switches prevent collision of the carriage with the ball-screw end

mounts. The screw is connected to a rotary step motor driven by a linear

microstep driver. The motion control system is conveniently operated by

a digital indexer with push-button operation that controls carriage

speed, amplitude of oscillation, and acceleration at endpoints . For our measurements carriage speed is ~2 to 3 cm/s . Operation at this speed

gives the least mechanical vibrations of the retroreflectors ; this vibration shows up as jitter in the fringe signals. Figure 6 below is a block

diagram showing the motion control components, interferometer, and other

relevant instrumentation.

The main beamsplitter for the interferometer is coated for 1 . 3 /im

radiation and wedged to eliminate unwanted reflections. At this wavelength, transmittance is about 46 percent for a P-polarization state with

a 45 deg angle of incidence. At 1.52 /im, T for an S-polarization is 29

percent and 73 percent for a P-polarization. For unpolarized light, T is

51 percent. The reflectance and transmittance of the beamsplitter for

0.63 fim HeNe light are about the same as plain glass. This is acceptable

because of sufficient power output from these lasers. Equal beamsplitter/combiners are used at the interferometer entrance and exit to

combine and separate the reference and unknown laser beams. These are coated for 1.55 nm, but without an antiref lection coating. More than 80

percent of the 0.63 /^m reference laser beam is transmitted. More than 98

percent of the 1.5 /im beam is reflected. The first high-reflection

region is 10 percent of line center, which excludes wavelengths =^1 . 3 /im.

Thus additional splitter/combiners will be used for measurements at

1 . 3 /im

.

19
2"dREFX

I (Xr)

KXu)

INTERFEROMETER

MOTOR

^ K

DRIVER

1X1 RAIL TABLE U

IDEXER

COUNTER

Figure 6. Biock diagram showing system components.

Mirrors that had broadband infrared reflector coatings were

purchased. These have high reflectivity at both 0.63 and 1.5 ^m. The

substrate material for the mirrors has negligible thermal expansion and

is only slightly more expensive than standard materials. However, mirror

mounts are made of standard aluminum, because it is very expensive to

fabricate mounts from a material of negligible thermal expansion. Beam

expanders for the reference lasers are standard, uncoated, with lOx

expansion ratios. A Faraday rotator with >30 dB isolation is used to

optically isolate the main reference laser. This works better than a quarter-wave plate and polarizer. Isolation of the 1.52 /xm DFB laser

diode is described in section 6.1.

20
5.5 Optical Alignment of the System

The first part of the alignment procedure is equivalent to that

given in reference 33. The basic idea is similar to that for any

Michelson interferometer using corner cubes. The visible reference beam

is split into two beams which traverse distinct arms of the

interferometer. The reflection from the beamsplitter, BS , is blocked,

and the transmitted portion is reflected off mirror Ml toward the

carriage (with corner cubes) . The beam is aligned parallel to the

direction of motion of the carriage using M^ and the entrance steering

mirrors (fig. 2). The property of a corner cube is such that a beam

entering one of its sextants reemerges antiparallel to the incident

direction, but from the diametrically opposite sextant (fig. 3). When

the carriage is near M^ , the entrance steering mirrors are adjusted so that the beam reflects from the corner cube and exits the system in a desirable direction. A colored circle of slightly smaller diameter than

the beam's is drawn on a screen and placed in front of the photodetector

and the exiting beam positioned so that the spot and beam are concentric.

As the carriage approaches Mj^ , Ml is adjusted to keep the beam concentric

with the reference spot on the screen. In the beginning, concentric

alignment of the spot and beam at one end of the motion results in

misalignment of the two at the opposite end of the motion, so this is an iterative process which terminates when the alignment holds over the

entire path of carriage motion. Then the transmitted beam is blocked and

the beam reflected from BS is aligned as follows: when the carriage is

near Ml, Mj^ is adjusted to give concentricity between spot and beam; when

the carriage is near Mj^ , BS is adjusted.

To speed up the alignment, a small screen with a colored spot can be

taped to the corner-cube mount. Once the beam is incident upon the

corner cube at a desired entry position, the spot is positioned to

intercept the beam concentrically. The beam can be adjusted using the

procedure above by scanning the carriage over the whole motion.

Inaccuracy in wavelength measurement due to optical misalignment of

the lambdameter can be eliminated by superimposing the beams from the

reference and unknown lasers so that they are colinear. The red and IR

laser beams are arranged to be incident upon a dichroic beamsplitter/

combiner from perpendicular directions. This component reflects the IR

light into the same direction as the red light which is transmitted.

After the initial phase of the alignment procedure as outlined above, a mirror is placed before the beamsplitter at the entrance to the interferometer. This deflects the reference beam to a screen located at the

opposite end of the room. The IR laser beam is then aligned using its own steering mirrors and the deflecting mirror so that it is concentric

with the visible reference laser beam at a point just passed the combiner

where the two are superimposed, and on the distant screen. This can be

done using an IR-visible converter card. The amount of IR laser beam

power at 1.5 /nm required to observe luminescence using one of these cards

varies among different manufacturers by as much as 50 percent. In our

case, low power output (-1/2 mW) from our 1.52 ^m laser transmitter

requires that we use the most sensitive card available. Once alignment

21
is performed, the deflecting mirror is removed, and the beams traverse

the interferometer almost colinearly. (The error due to misalignment is

described in section 4.4.) Optical power losses in the IR beam may

prevent alignment at the detector surface using a convertor card. In

this case, the small portion of the visible reference beam that is

reflected by the beamsplitter which separates the two beams can be used

to finish the alignment. Also, an IR camera may be used if available.

5 . 6 Measured Accuracy

The accuracy of our system was tested in the visible portion of

the spectrum by a scheme which uses the two adjacent modes on the red and

blue sides of the peak of the Doppler gain profile of a frequencystabilized HeNe laser. The wavelength of a second frequency-stabilized

HeNe laser of wavelength ~ 0.63 fim is measured with the reference laser

locked on the blue side, and then the red side of the peak of the Doppler

gain profile. As we now show, the result is independent of the wave- length of the second laser, as long as its wavelength is stable. If

there is an instability within the measurement accuracy of our lambdameter, it will show up in the ratios.

Let i/(red), j^(blue) be the frequencies; A(red), A(blue) the vacuum

wavelengths; and n(red) , n(blue) the refractive indices of the red and

blue shifted modes from the reference HeNe laser. Let A(S) be the vacuum

wavelength of the second HeNe laser, n(S) its refractive index, and R the

measured ratio of the wavelengths of the reference HeNe laser to the

second HeNe laser in air. Finally, let F be the ratio of frequencies of

the reference HeNe laser, F = i/'(blue)/i/(red) , and Q the ratio of ratios,

Q = R(red)/R(blue) . Then

F H ^C^^^^) ^ 1.000001662 ± 0.000000025 (25)

j/(red)

1.000001637 < F < 1.000001687. (26)

or,

Also,

R(red) =

and

R(blue) =

A(red) n(S)

A(S) n(red)

N(S)

N(red)

A (blue) n(S)

A(S) n(blue)

N(S)

N(blue)

22
Now the quantity n(blue)/n(red) is very nearly 1. Therefore,

R(red) ^ A(red)

^ ~ R(blue) ~ A(blue)

N(blue)

(27)

N(red)

i/(blue)

i/(red)

It is critical that Q be independent of any path difference between the

reference and second HeNe lasers. Since the laser beams are not

colinear, there will be some misalignment. Our result shows that Q is

independent of the number of fringes counted for the second laser, and

hence independent of the path. It is necessary only that the path of the

second laser beam remain constant over the time for corresponding sets of

measurements , and this is the case

.

In table 3 we see a typical set of measurements for both R(red) and

R(blue) . Let <R(red)> and <R(blue)> be the average values for each set.

Then

<R(btuI)> = 1 000001^^ (28)

From the averages shown in the table, Q = 1.00000166. The number of zero crossings counted is = 14-10^, giving an accuracy of -0.7:10^. This

establishes the mechanical stability of the system for measurements at

other wavelengths. Because the value for a ratio measurement is very

nearly equal to unity, a change in the ratio of one part in ten million

corresponds to a fractional uncertainty in the ratio of one part in ten

million.

Table 3. Typical sets of 10 measurements for R(red) and R(blue)

R(red) R(blue)

1.0000004 0.9999987

1.0000004 0.9999988

1.0000004 0.9999988

1.0000004 0.9999988

1.0000004 0.9999987

1.0000004 0.9999987

1.0000004 0.9999987

1.0000004 0.9999987

1.0000004 0.9999988

1.0000004 0.9999987

Avg ± o 1.00000004 ± 0.0 0.99999874 ± 0.52-10"^

23
6. Wavelength Measurements on a Single-Mode Diode Laser Source

Single-mode laser diodes for optical communication systems have

fairly narrow linewidths and low optical output power. But there is an increasing demand for narrower linewidths and higher optical power than

what is presently available commercially, especially when considering

coherent systems. Many laboratories around the world are working to

achieve these goals . Both DBR and DFB diode lasers are finding applications in this field. Some recent advances in this area were presented at

the 1989 CLEO/QELS conference. Koch [35] reported fabrication of DBR

lasers having linewidths as low as 1.9 MHz, with 1.2 MHz possible. These

had 1 to 2 mW optical power and were tunable over 8 nm. Attempts at

wider range tuning increased linewidth. Tohmori et al. [36] fabricated a butt- jointed DBR with a minimum linewidth of 1 MHz and a wavelength of

1.48 ^m. Linewidth increased to 2 to 4 MHz as the wavelength was tuned

over 40 nm. Optical power was 18 mW. A tunable MQW-DBR laser was reported by Hernandez-Gil et al . [37]. The lasing wavelength was 1.5 ^im with a linewidth of 3 MHz. Wang et al. [38] report a DFB laser with 10

MHz linewidth and 6 mW output power at a wavelength of 1.3 /im. DFB

lasers with wavelengths of 1.3 and 1.55 ^m and linewidths less than 10

MHz were reported by Mito and Kitamura [39]. Mihara and Otobe [40]

developed an AlGaAs DFB laser at 0.8 nm with linewidth of 4.2 MHz and

8 mW. A minimum linewidth of 1.5 MHZ was achieved for a multiple quantum

well DFB fabricated by Koj ima et al. [41]. The wavelength was 866.5 nm. Finally, frequency stabilization of a DFB laser module within 0.5 MHz was achieved using the 1.53159 /zm vibrational-rotational absorption line of

acetylene by Sudo et al . [42]. For acetylene gas between -35°C and 70°C,

the temperature dependence of the absorption peak wavelength is

=0.1 MHz/°C. This results in a highly stable source with a small

temperature dependence

.

6.1 Description of the 1.52 ^m Diode Laser

Measurements reported in this paper were made on a high-speed diode

laser transmitter operating in the continuous -wave mode. The source is a GalnAsF DFB diode laser packaged in a plug- in module. Power is supplied

from a mainframe supplied as part of the unit. The laser diode and fiber

are joined through a laser welding process and hermetically sealed to

achieve high stability. The laser beam emerges through a biconic con- nector on the front of the module, but can be harnessed directly using

collimating lenses. Initially, we chose a single-mode fiber with a biconic connector at one end for connection to the transmitter. Because

of instability arising from retroreflections into the laser diode, we switched to a single-mode fiber having an isolator built into it. The

beam emerging from the fiber is collimated with a diode laser collimating

lens that is coated for 1.53 /xm. The transmitter has its own current

supply and temperature stabilization system. A thermistor attached to

the laser and its submount monitors temperature, which is maintained at a preset value by a thermoelectric cooler. Spectral linewidth in the cw,

unmodulated mode is <100 MHz, which is <10"^ fim. Wavelength dependence

with temperature is =0.1 nm/°C. Minimum threshold current is typically

24
=30 mA. Side-mode suppression is >30 dB . Before purchase, emission

wavelength is specified by the manufacturer to be in the range of 1500 to

1570 nm. For our unit the manufacturer specified the wavelength to be

1.5205 ftm. The specifications above are from the manual accompanying

the transmitter. We measured the optical power output to be 0.384 mW

using an optical average-power meter.

6.2 Results of Wavelength Measurements

The average center wavelength of the two independent modes of the

reference HeNe laser is known to 1:10^ (section 5.2). To use this

property of the reference laser we adopt the following scheme: we measure the wavelength of the unknown laser with the reference laser

locked to the blue side of the peak of the Doppler gain profile. This

gives

D/K^„o^ N(LD) A(blue) R(biue) = rrTT-j r = ., , rr—

7

r (29) N(blue) n(blue)A^j (n^ )

•

We then switch the reference laser to the red side and take more measurements. This gives

T>f^^A^ - N(LD) _ A(red) R(red) = ——TT = —7—TTT

7—r- (30) N(red) n(red)A^(n^)

The unknown wavelength is then

A(red)/n(red) + A(blue)/n(blue)

" ~ R(red) + R(blue) " ^ ^

Since n(blue) ~ n(red) = n(ref )

, we write

, ^ A(red) + A(blue) __ n(ref)[R(red) + R(blue)] • ^ ''

The wavelength in air is found from eq (32) above and eqs (6-8) for the

dispersion.

The fractional uncertainty in the wavelength can be found from the

measurements by simply calculating the fractional uncertainty in the

ratio, 5R/R. The counter error, which we approximate by 1/N for the

reference laser, is <10"^ and can be neglected in comparison with the

observed physical fluctuations due to temperature, injection current, and

possibly optical feedback. Thus the fractional uncertainty in the diode

laser's wavelength reduces to 5R/R.

To test the wavemeter's precision at various points of the scan, but

excluding the endpoints, two sets of twelve ratio measurements were taken

with a 4 s gate time. This is approximately one- tenth of the time for a complete scan and resulted in a counter display of six digits. This

25
corresponded to a wavelength accuracy in the parts-per-million range.

(The reference laser was set on the blue side.) Table 4 below shows that

wavelength stability of the laser diode may exceed 1 ppm and that

instrument resolution is at least this high.

Table 4. Ratio measurements for a 1.52 /xm DFB diode laser relative to a stabilized HeNe . The 4 s gate time resulted in an accuracy of

1 ppm. The numbers show that source stability and instrument

resolution are at least this high.

Set 1 Set 2

0.416103 0.416104

0.416103 0.416104

0.416103 0.416103

0.416103 0.416104

0.416103 0.416103

0.416104 0.416107

0.416104 0.416104

0.416103 0.416104

0.416104 0.416105

0.416104 0.416103

0.416104 0.416103

0.416104 0.416104

To insure that retroreflections did not destabilize the laser diode

during the time of a measurement, a single fringe of the interference

signal was observed on an oscilloscope. The pulse width was =30 ns . If

the pulse flickered, presumably due to a stray reflection, data were

discarded. This was justified because it was possible to orient the

Faraday isolator so as to eliminate all flickers for periods of several

hours. Eventually the isolator was positioned off the optical table to

isolate it from mechanical vibrations caused by the motion control system

for the scanning corner cubes. Also, merely touching the fiber or isolator resulted in severe signal instability. Thus we assume that the

diode laser's wavelength was affected by the intensity and phase of the

optical feedback that it received at any given time. The primary source

of optical feedback most likely resides at the biconic connector output

on the transmitter.

Four sets of measurements were taken with a 40 s gate time

corresponding to an accuracy of =2:10^. Table 5 shows two sets of data

with the reference laser locked to the red side of the Doppler gain

profile; for the other two sets it is locked to the blue side.

Wavelength instability is <±1 ppm.

26
Table 5. Ratio measurements (day 1) for the 1.52 /xm laser using a 40 s gate time. In sets 1 and 3 the reference laser is locked to

the red side of the peak of the Doppler gain profile. In sets

2 and 4 it is locked to the blue side. Laser diode instability

is <±1:10^

Set 1 (Red side) Set 2 (Blue side)

0.4161053 0.4161044

0.4161053 0.4161045

0.4161052 0.4161044

0.4161050 0.4161042

0.4161051 0.4161049

0.4161051 0.4161046

0.4161049 0.4161048

0.4161055 0.4161043

0.4161048 0.4161045

0.4161051 0.4161046

<R>=0. 4161052 <R>=0. 4161045

Set 3 (Red side) Set 4 (Blue side)

0.4161050 0.4161044

0.4161053 0.4161045

0.4161050 0.4161045

0.4161055 0.4161045

0.4161049 0.4161043

0.4161054 0.4161048

0.4161052 0.4161048

0.4161052 0.4161048

0.4161054 0.4161047

0.4161049 0.4161045

<R>=0. 4161052 <R>=0. 4161046

Using eq (31) and the averages for <R> above, we estimate the

average wavelength of the diode laser at T = 23°C, P = 82922.28 Pa

(622 Torr), to be

A = 1.521089 ± e /im. (32)

where e is the uncertainty due to instrumental error, wavelength

instability arising from fluctuations in physical parameters such as temperature and injection current, and optical feedback. Instrumental

error has been estimated to be <±2 : 10'' . Since e is not a random

variable, we cannot define a standard deviation of the mean. From these

data we conclude that the short-term instability of our DFB diode laser

is <1 ppm.

27
More measurements were taken (day 2) with the room lights off. The

results are shown in table 6. The ratios obtained for both the blue and

red sides are higher than for the previous day. This corresponds to a slightly smaller average value for the unknown wavelength and probably

arises from differences in room temperature or injection current from day

to day. Although approximate room temperature was recorded and found to

vary by a few degrees Celsius from day to day, an accurate record is

useless because the manufacturer cannot provide data on temperature

changes of their laser for small changes in ambient temperature. (They

specify laser temperature stability, resulting from their temperature

control system, to be AT = ±1°C over the full operating range of -15°C

< T < +65°C.) Finally, table 7 shows ratio measurements taken on yet

another day. These are in agreement with the values shown in table 5. Additional ratio measurements are given in appendix A.

Table 6. Ratio measurements whose values are greater than for the

previous set taken on a different day. These correspond to a slightly smaller average value for the DFB laser diode

wavelength.

Set 1 (blue side) Set 2 (blue side)

0.4161052 0.4161053

0.4161050 0.4161055

0.4161049 0.4161054

0.4161048 0.4161051

0.4161050 0.4161052

0.4161051 0.4161049

0.4161056 0.4161055

0.4161050 0.4161046

0.4161049 0.4161047

0.4161051 0.4161049

<R>=0. 4161051 <R>=0. 4161051

Set 3 (red side) Set 4 (blue side)

0.4161058 0.4161050

0.4161057 0.4161046

0.4161056 0.4161057

0.4161056 0.4161049

0.4161065 0.4161054

0.4161059 0.4161053

0.4161055 0.4161048

0.4161059 0.4161052

0.4161057 0.4161058

0.4161061 0.4161051

<R>=0. 4161058 <R>=0. 4161052

28
Set 5 (red side) Set 6 (red side)

0.4161056

0.4161057

0.4161057

0.4161062

0.4161053

0.4161058

0.4161056

0.4161055

0.4161069

0.4161054

0.4161054

0.4161055

0.4161052

0.4161059

0.4161063

0.4161060

0.4161057

0.4161058

0.4161056

0.4161055

<R>=0. 4161056 <R>=0. 4161057

Set 7 (blue side)

0.4161047

0.4161052

0.4161053

0.4161054

0.4161050

0.4161051

0.4161051

0.4161056

0.4161054

<R>=0. 4161052

29
Table 7. Ratio measurements taken on day 3 agree with those in table 5. Note that Set 6 has only seven measurements. This is because

the DFB laser destabilized at that time and the measurement was

stopped.

Set 1 (blue side) Set 2 (red side)

0.4161045 0.4161051

0.4161041 0.4161054

0.4161044 0.4161052

0.4161049 0.4161048

0.4161046 0.4161054

0.4161043 0.4161049

0.4161044 0.4161050

0.4161041 0.4161052

0.4161042 0.4161051

0.4161042 0.4161058

<R>=0. 4161044 <R>-0. 4161052

Set 3 (red side) Set 4 (blue side)

0.4161057 0.4161048

0.4161053 0.4161049

0.4161054 0.4161051

0.4161057 0.4161048

0.4161056 0.4161043

0.4161060 0.4161046

0.4161052 0.4161047

0.4161058 0.4161045

0.4161057 0.4161050

0.4161062 0.4161049

<R>=0. 4161056 <R>=0. 4161048

Set 5 (red side) Set 6 (blue side)

0.4161056 0.4161048

0.4161058 0.4161046

0.4161057 0.4161044

0.4161056 0.4161049

0.4161057 0.4161048

0.4161056 0.4161050

0.4161057 0.4161050

0.4161055

0.4161059 <R>=0. 4161048

0.4161060

<R>=0. 4161057

30
7. Discussion and Conclusions

A lambdameter which measures the wavelength of sources used in

optical fiber communications has been built. An accuracy of <0 . 1 ppm

has been observed at the 0.63 /im HeNe line. From this we deduce an accuracy of -0.2 ppm in the near infrared. Averaging could increase

accuracy further for highly stable sources. Instability of the 1.52 /um

DFB diode laser source was in the range ±1 ppm. This is likely to be a result of fluctuations in temperature or injection current. However,

optical feedback into the diode laser from the biconic connector-fiber

output interface intermittantly caused significant signal instability.

An index-matching gel which should eliminate this feedback reflection is

being ordered. Also, one or more additional optical isolators will be

added to reduce fiber and other component sources of feedback from the

interferometer to ~60 dB. Introduction of radiation from the unknown

source into the interferometer without the fiber is under consideration.

8 . Acknowledgments

I thank Bob Drullinger for illuminating discussions on lambdameters

,

and for supplying fine photodetector devices having zero-crossing signal

frequency multipliers built into them. I am grateful to Doug Franzen for

suggesting the HeNe reference laser that oscillates in either one of two

adjacent cavity modes, and for other useful discussions. Also, thanks to

Leo Holberg for some interesting conversations related to this research

and to Edie DeWeese for preparing the final manuscript.

References

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L.W.G. Electronic Improvement of Interferometric Measurement of

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19] Rowley, W.R.C., Shotton, K.C., and Woods , P.T. A Simple MovingCarriage Interferometer for 1 in 10^ Wavelength Intercomparison,

and a Servocontrolled Fabry-Perot System For 3 in 10^ -"^ Accuracy.

Hall, J.L., and Carlsten, J.L., eds . Laser Spectroscopy III,

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only One Cube-Corner Prism. J. Opt. Soc. Am. 50(1): 83-84; 1960

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33] Barger, R. Private communications, Joint Institute for Laboratory

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Capability and Long Coherence Length of AlGaAs Distributed Feedback

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41] Kojima, K. , Hara, K. , and Kyuma, K. Narrow Linewidth AlGaAs/GaAs

Multiple Quantum Well Distributed Feedback Lasers. CLEO 89, 1989

April 24-28; Baltimore, Maryland, Paper WL 4: 238-239; 1989.

42] Sudo, S., Sakai, Y. , Yasaka, H., and Ikegami , T., FrequencyStabilized DFB Laser Module Using 1.53159 /im Absorption Line of

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34
Appendix A. Raw Data From Diode Laser Wavelength Measurements

The ratio measurements below were taken with a 40 s gate time.

Signal instability, presumably due to retroreflections , was observed

about every tenth measurement as pulse flicker on an oscilloscope. The

corresponding wild readings were discarded. Typical values were -0.4161000. As can be seen from the data, the other values are consistent with those given in the tables of section 6.2.

Blue side Red side

0.4161045 0.4161054

0.4161044 0.4161051

0.4161045 0.4161055

0.4161044 0.4161055

0.4161044 0.4161054

0.4161047 0.4161050

0.4161044 0.4161052

0.4161047 0.4161053

0.4161038 0.4161052

0.4161048 0.4161053

0.4161048 0.4161053

0.4161046 0.4161044

0.4161044 0.4161052

0.4161046 0.4161055

0.4161037 0.4161049

0.4161047 0.4161052

0.4161046 0.4161046

0.4161043 0.4161052

0.4161045 0.4161056

0.4161043 0.4161051

0.4161046 0.4161053

0.4161046 0.4161051

0.4161032 0.4161053

0.4161044 0.4161052

0.4161045 0.4161052

0.4161046 0.4161054

0.4161045 0.4161045

0.4161046 0.4161054

0.4161044 0.4161055

0.4161044 0.4161054

35
Appendix B. Optical Designs for Lambdame ters

The simplest design is a standard Michelson interferometer in which

the beams are split at right angles to each other and only one corner

cube is scanned. A displacement of the corner cube by some increment Ax

alters the path difference that light travels through the two arms of the

interferometer by 2Ax. The number of interference fringes occurring for

light of wavelength A is N = 2Ax/A . Figure B-1 shows an equivalent

design [5]. A clever folded path design is shown in figure B-2 [7].

Here a displacement of the carriage by a distance Ax yields an effective

path difference of 4Ax, so that the number of fringes available for

counting is N = 4Ax/A . In figure B-3 a folded path is shown in which

each beam is reflected to return upon an identical path to recombine

[23]. This can result in unwanted retroreflections into the lasers. A

higher order folded-path design is shown in figure B-4. Because very

long path differences can impose limits on accuracy, this design is good

for decreasing the size of a lambdameter while keeping the resolution

constant. A similar design uses mirrors instead of the prism [4].

36
'

. '

* /

^ \'

'

I

Figure B-1. Kowalski's original wavemeter design [5]

/ ^-

/ ^

1 /\'' \

I

1

1

j ^ 1 u

\

1

\ ^;

1 *

1

f

j h." V

/ ,r / % . \

, */ / K

'

1

1 ,

;

i

Figure B-2. Kowalski's modified design having a four- fold pach [7

37
Figure B-3. Wavemeter design showing four-fold path using only one moving corner cube [22,23].

X

Figure B-4. A modified Hall design with an eight-fold path using a right angle prism and mirror opposite each corner cube.

Only the left beam and components are shown.

38
Appendix C. First-Generation System

A first-generation wavemeter was built using a linear stepping-motor

system with an air bearing for the scanning component. It was rented on

a trial basis and tested to determine whether noise and vibration would

be low enough to count the fringes from the interferometer. The system

consisted of a driver, a 0.66 m platen, and a forcer that ran on an air

bearing requiring a flow of 14.1 i/min. Air was supplied from the com- pressor used to float the optical table. The same indexer was used for

the final system described in this paper.

The optical arrangement was that of a simple Michelson interferometer that had having two perpendicular arms. The scan distance was =0.51 m, and the length of the forcer was -0.15 m. System accuracy was

=1 ppm. Fringe signal noise due to vibrations arising from the motion of

the forcer over the platen was surprisingly high in spite of the air

bearing. Qualitatively, noise was often observed beginning at the third

fringe on an oscilloscope screen, but was a function of forcer position

along the platen. A different model driver from the same manufacturer

was tested, but vibration noise remained high. We decided to look for a system with less noise and greater probability for success at higher

accuracies. Although platens of longer length were available for use with air bearing components and which might have increased system

accuracy, these were never considered.

The time for a single measurement was ==1 min. The output from the

reference HeNe (A ~ 0.63 /im) laser was split and sent into the interferometer along parallel but noncolinear paths. Upon emerging from the

interferometer, each fringe signal was sent to its own detector, and the

ratio of the numbers of fringes counted during a single scan. A value of

1.000000 was obtained without significant variation. The error was estimated to be 1/N ~ 1:10^. The output from the DFB laser diode transmitter (A ~ 1.52 ij.m) was compared with the HeNe reference laser. The

ratio was found to vary over several parts per million.

A second wavemeter was built using a standard rail table that had

==0.76 m carriage motion and a Hall optical design. An unstabilized HeNe

laser (A = 0.63 /zm) was measured using the same reference laser. Ratio

measurements were limited to a few parts per million due to the

instability of the test laser. But noise levels were lower than with the

previously described linear stepping-motor system. Based on this observation we purchased a precision-grade rail table having a 1.22 m carriage

motion. This was used in the final system, as described in this paper.

39
NIST-114A

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BIBLIOGRAPHIC DATASHEET

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2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBUCATION DATE February 1990

4. TITLE AND SUBTITLE Wavelength Standard for Optical Fiber ComTnunications

5. AUTHOR(S)

Gregory E. Obarski

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

8«¥t*eftS¥e(fta^»tt5^iS89S Boulder, Colorado 80303-3328

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1 1 . ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBUOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

A wavelength standard in the form of a lambdameter for measurement of single-mode sources

used in optical fiber communications is described. The sources of interest are mainly

diode laser emitting at 1.3 and 1.5 ym, but the system can be used in the near IR and red

regions of the spectrum. Accuracy in wavelength measurement is verified to be <0.1 ppm

at the 0.63 ym HeNe line by comparing separately each of two adjacent modes from a HeNe

laser that is frequency-stabilized by a polarization technique, with a single mode from a second similarly frequency-stabilized HeNe laser. Wavelength instability of a commercially packaged 1.52 ym distributed-f eedback diode laser was measured to be in the range

±1 ppm.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

diode laser; optical fiber communications; single mode; wavelength instability;

wavelength standard

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