1742

J. Opt. Soc. Am. B / Vol. 18, No. 11 / November 2001

Karasawa et al.

Optical pulse compression to 5.0 fs by use of only
a spatial light
modulator for phase compensation
Naoki Karasawa
Department of Applied Physics, Hokkaido University, and Core Research for Evolutional Science and Technology,
Japan Science and Technology Corporation, Kita-13, Nishi-8, Kita-Ku, Sapporo, 060-8628 Japan

Liming Li
Department of Photonics Material Science, Chitose Institute of Science and Technology, and Core Research for
Evolutional Science and Technology, Japan Science and Technology Corporation, 758-65 Bibi, Chitose,
066-8655 Japan

Akira Suguro
Citizen Watch Co., Ltd., 840 Shimotomi, Tokorozawa, 359-8511 Japan

Hidemi Shigekawa
Institute of Applied Physics, University of Tsukuba, and Core Research for Evolutional Science and Technology,
Japan Science and Technology Corporation, 1-1-1 Tennodai, Tsukuba, 305-8573 Japan

Ryuji Morita and Mikio Yamashita
Department of Applied Physics, Hokkaido University, and Core Research for Evolutional Science and Technology,
Japan Science and Technology Corporation, Kita-13, Nishi-8, Kita-Ku, Sapporo, 060-8628 Japan
Received March 13, 2001; revised manuscript received May 8, 2001
We experimentally demonstrate the generation of 5.0-fs optical pulses (2.5 ␮J, 1-kHz repetition rate), using
only a spatial light modulator for phase compensation. Pulse compression of the broadband pulse (500–1000nm) from an argon-filled capillary fiber is achieved with a liquid-crystal spatial light modulator without any
prechirp compensation. The output pulse width is found to be 4.1 fs by a fringe-resolved autocorrelator fittedwith a transform-limited pulse and to be 5.0 fs by second-harmonic generation frequency-resolved optical gating with marginal correction. It is to our knowledge the shortest pulse ever generated by use of only a spatial
light modulator for phase compensation. © 2001 Optical Society of America
OCIS codes: 320.7090, 320.5560, 320.7140, 230.6120, 320.5520, 190.7110.

1. INTRODUCTION
Optical pulses of ⬃5 fs have been generated directly froman oscillator1,2 and external compression by use of afused-silica fiber,3–5 a capillary fiber filled with a noble
gas,6,7 or optical parametric amplification8 for spectrum
broadening. All these methods utilize chirped mirrors
for chirp compensation. Chirped mirrors have the advantage of high throughput. However, difficulty in obtaining the large bandwidth, interdependence of different
phase orders, and an inability to fine-tune the phase in
the experimental setup are disadvantages. A pulse shaping technique9 that uses a liquid-crystal spatial light
modulator (SLM) for pulse compression has the advantages of large bandwidth (300–1500 nm) and in situ adaptive phase control. Chirped pulses from an oscillator
have been compressed from 80 to 11 fs by a SLM with a
two-dimensional search algorithm for second- and thirdorder dispersion coefficients.10 Recently the SLM wasused to compress the broadband pulses from an argon0740-3224/2001/111742-05$15.00

filled capillary fiber with prechirp compensation by aprism pair to yield 6-fs pulses11 and sub-6-fs pulses.12
Deformable mirrors were used as phase-only modulators
to compress pulses from 92 to 15 fs.13 In this paper wedemonstrate that a SLM can be used to compress broadband (500–1000-nm) pulses from an argon-filled capillaryfiber, without any prechirp compensation, to generate
5.0-fs pulses. When prechirp compensation optics suchas a prism pair is not used, the optical throughput increases, and alignment becomes easier. To evaluate accurately the pulses that are thus generated, we used not
only a fringe-resolved autocorrelator (FRAC) but also asecond-harmonic generation (SH) frequency-resolved optical gating (FROG) apparatus.4,5,7

2. EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. The output
beam of a Ti:sapphire laser-amplifier system [Femto© 2001 Optical Society of America

Karasawa et al.

Vol. 18, No. 11 / November 2001 / J. Opt. Soc. Am. B

power Pro; center wavelength, 790 nm; pulse width, 30 fs;
repetition rate, 1 kHz; pulse energy adjusted by a neutraldensity filter (ND), 140 ␮J] was focused into a capillaryfiber with 34-cm length and 0.1-mm inner diameter,
which was positioned in a chamber filled with argon.14
The chamber had two 1-mm-thick sapphire windows.
The output beam from the chamber was collimated by aspherical mirror and was directed to a 4-f system by the
SLM. The 4-f system consisted of two spherical mirrors
with a focal length f ⫽ 20 cm and two silver reflective
gratings (G1 and G2) with a ruling distance d⫽ 1/150 mm. The optical path lengths from the gratings
to the spherical mirrors and those from the spherical mirrors to the SLM were all set to be f. The liquid crystal
SLM (Citizen Company) consisted of 648 97-␮m-wide pixels, with a 5-␮m gap between adjacent pixels. The transmission of the SLM was more than 70% at a 500–700-m
wavelength but decreased at long wavelengths (e.g., 50%
at 1000 nm). The pulse energy after the fiber chamber
was 22 ␮J, and the throughput of the 4-f system was
30%. In the setup we used periscopes (PSs) to change theheight, the polarization direction, or both of the beam,
and a flip mirror (FM) to change the beam direction formeasurements of the FRAC and the SH FROG.

3. DETERMINATION OF THE SLM PHASE
PATTERN
The SLM was used as a phase modulator, which can impose a phase variation of 2␲ for light whose wavelength isless than 1400 nm with a resolution of 192. The Phase␾ SLM(x) from the SLM at position x is given by a polynomial of the form

␾ SLM共 x 兲 ⫽␣2关 ␻共 x 兲 ⫺ ␻0兴2 ⫹

⫹

␥
24

␤
6

关 ␻共 x 兲 ⫺ ␻0兴 ,4

Fig. 2. Calculated group delay of each optical component (solid
curves) at ␭ 0 ⫽ 600 nm at an argon pressure of 2.0 atm. The total group delay (thick solid curve) is compared with the negativeof the experimentally optimized group delay applied by the SLM(dashed curve). Inset, experimental (solid curve) and 4.5-fs fitted transform-limited (dotted curve) FRAC traces at these parameters.

persion (tod), and the fourth-order dispersion (fod), respectively, at ␻ 0 . The group delay t d,SLM(x) imposed by
the SLM wast d,SLM共 x 兲 ⫽⳵ ␾ SLM共 ␻ 兲⳵␻⫽ ␣关 ␻共 x 兲 ⫺ ␻0兴 ⫹⫹关 ␻共 x 兲 ⫺ ␻0兴3(1)

where ␻ 0 is the center angular frequency for a Taylor expansion, ␻ (x) is the angular frequency at position x and isgiven by ␻ (x) ⫽ 2 ␲ c/ 兵 d sin关tan⫺1(x/f ) ⫹ sin⫺1(␭c /d)兴其, cis the speed of light, and ␭ c ⫽ 800 nm is the wavelength
at the central position of the SLM, x ⫽ 0. ␭ c does nothave to be equal to the center wavelength for Taylor expansion ␭ 0 , where ␭ 0 ⫽ 2 ␲ c/ ␻ 0 . ␣, ␤, and ␥ are thegroup-delay dispersion (gdd), the third-order dis-Fig. 1. Experimental setup for generation of 5.0-fs opticalpluses. See text for definitions.

1743

␥
6

␤
2

关 ␻共 x 兲 ⫺ ␻0兴2

关 ␻共 x 兲 ⫺ ␻ 0兴 3.

(2)

Parameters ␣, ␤, and ␥ were initially estimated from thetotal group delay t d ( ␻ ) of the optical components from acapillary fiber (including self-phase modulation) to a nonlinear crystal in the measuring apparatus. t d ( ␻ ) was fitted in the form of Eq. (2), and ␣, ␤, and ␥ were obtained.
Then the negative values of these fitted parameters were
initially imposed by the SLM to satisfy t d,SLM( ␻ )⫹ t d ( ␻ ) ⯝ constant in the whole frequency range.
Theoretically, this condition should produce the shortest
pulses. However, in practice it was necessary to adjust
the phase determined by the SLM to yield the shortest
pulses because of the difference in group delay between
calculations and experiments, which were due mainly tothe approximations used in our calculations. Use of the
Taylor expansion in Eq. (1) was found to be the natural
way to perform fine adjustment of the phase. Parameters ␣, ␤, and ␥ were fine-tuned by a computer to yield
the shortest pulse with the FRAC and later with the SH
FROG apparatus. In Fig. 2 the group delay of each component in the optical path and its negative value obtainedwith the SLM, as well as the totals of these values, areshown for which the shortest FRAC trace (Fig. 2, inset,
the 4.5-fs fitted transform-limited pulse) was obtained for
conditions when ␭ 0 and the argon pressure were set to
600 nm and 2.0 atm, respectively. As shown in Section 5
below, FROG results for 5.0-fs pulses were obtained under1744

J. Opt. Soc. Am. B / Vol. 18, No. 11 / November 2001

Karasawa et al.

these conditions. Here, the effective group delay thatarises from propagation in the capillary fiber was obtained
fromnumerical
nonlinear
propagation
calculations.14 For other optical components, we calculated the group delay by using the Sellmeier equations forfused silica (beam splitters of FRAC–FROG, 0.7 mm),15
BK7 glass (SLM substrates, 1.4 mm),16 sapphire (a chamber window, 1 mm),17 and air (3.7 m).18 As shown in Fig.
2, the agreement between the calculated group delay(thick solid curve) and the negative of the group delay
from the SLM (dashed curve) when the parameters were
optimized is reasonably good.

4. EFFECTS OF FINITE PIXEL SIZE OF THE
SLM
␭ 0 in Eq. (1) was initially set to be 800 nm with values of␣, ␤, and ␥ different from those given in Section 3; the
FRAC trace shown in Fig. 3, which was fitted well for the
4.1-fs transform-limited pulse, was obtained at an argonpressure of 2.8 atm. However, in this case the pulse
width measured by the FROG (⬃6 fs) was longer than thetransform-limited value. This underestimate of thepulse width may be understandable as having resulted
from the poor fit of the pedestals in the autocorrelation
trace19 and the asymmetric temporal intensity profile aswell as the slightly different dispersion optics in the
FRAC and the FROG apparatuses. Thus we were motivated to search for better parameters for the SLM. Because of the finite pixel size, the phase imposed by the
SLM in Eq. (1) was stepwise, and, as the difference inphase between adjacent pixels [which we call ⌬␾(␭)] became larger, phase compensation became more difficult
because of the phase error introduced by the finiteness ofthe pixel width. For our experimental setup the frequency width for each pixel became larger as the wave-

Fig. 4. (a) Applied phase ␾(␭) and (b) phase change per pixel⌬␾(␭) of the SLM for ␭ 0 ⫽ 600 nm (solid curves; parameters usedin Fig. 2) and ␭ 0 ⫽ 800 nm (dotted curves; parameters used inFig. 3).

length became shorter because of the almost-linear relationship between the pixel number and the wavelength of
the SLM. Thus 兩⌬␾(␭)兩 tended to become larger as the
wavelength became shorter than ␭ 0 . In Fig. 4 the applied phase and the phase variation per pixel at the SLM
for ␭ 0 ⫽ 600 nm (Fig. 2) and ␭ 0 ⫽ 800 nm (Fig. 3) are
shown. In both cases the fitted group delays t d,SLM( ␻ )were almost identical. However, the fitted phases werequite different, as shown in this figure. We analyzed兩⌬␾(␭)兩 of the SLM and found that for ␭ 0 ⫽ 800 nm it exceeded ␲ for wavelengths below 672 nm; it was difficult toachieve phase compensation below this wavelength.
This effect was pronounced because the spectrum thatwas generated had a peak at 670 nm owing to the lowtransmission of light in the infrared region at the SLM.
When ␭ 0 ⫽ 600 nm, 兩⌬␾(␭)兩 in the shorter-wavelength
range decreased considerably, and it exceeded ␲ only for
the wavelength below 540 nm, yielding significantly better phase compensation; pulses much closer to the transform limit were obtained with the FROG measurements.

5. SH FROG RESULTS

Fig. 3. Experimental (circles) and fitted transform-limited(FTL, solid curve) interferometric autocorrelation traces obtained at ␭ 0 ⫽ 800 nm at an argon pressure of 2.8 atm. Inset,
the pulse spectrum.

In Fig. 5 the results of pulse measurements with the SH
FROG at ␭ 0 ⫽ 600 nm are shown. Owing to the slightdifference in the optics used in the FRAC and in the
FROG apparatuses, we readjusted the SLM parametersslightly for the FROG measurements. In the SH FROG
apparatus (Fig. 1) a 0.5-mm-thick broadband (400–1300nm) dielectric beam splitter (BS) was used to separate thebeam that was directed to the silver-coated retroreflector(RR) in a balanced configuration. Beam separation d b at
the parabolic mirror (PM) was 2 mm; beam diameter w m
was 1 mm.
The time smearing4 was ␶ d⫽ 冑2 ln 2␭db /(␲cwm) ⫽ 1.6 fs
atwavelength␭⫽ 650 nm, with Gaussian space and time profiles as-

Karasawa et al.

Vol. 18, No. 11 / November 2001 / J. Opt. Soc. Am. B

1745

frequency marginal of a 5.0-fs SH FROG is to our knowledge the shortest pulse width ever generated by use of a
SLM as the only phase compensator.

ACKNOWLEDGMENT
The authors thank K. Oka for accurate determination of
the phase-change characteristics of the SLM.

Fig. 5. Results of the corrected frequency marginal corrected
FROG measurements with SLM parameters. (a) Margin calculated from the experimental spectrum M Th( ␻ ) (solid curve) andthat obtained from the FROG trace M Ex( ␻ ) (dotted curve). (b)Spectrum intensity I(␭) and phase ␾(␭). Dotted curves experimental spectrum. (c) Temporal intensity I(t) and phase ␾ (t).

N. Karasawa’s e-mail address is n-karasa@
photon.chitose.ac.jp. Present address, Department ofApplied Photonics System Technology, Chitose Instituteof Science and Technology, 758-65 Bibi, Chitose 066-8655
Japan.

REFERENCES
1.

sumed. The 10-␮m-thick ␤-barium borate crystal (BBO;
Fig. 1) at a cutting angle of 40° was used in type 1 geometry. Owing to the limited bandwidth of the crystal, thefrequency marginal20 calculated from the FROG trace
M Ex( ␻ ) and that from the spectrum intensity autoconvolution M Th( ␻ ) did not match, as can be seen from in Fig.
5(a). To correct for this effect we multiplied each value inthe FROG trace by a frequency-dependent factor suchthat the marginal calculated from the FROG trace became identical to that obtained from the spectrum.20 After correction of the marginal we used commercial FROG
software (Femtosoft) to retrieve the pulse intensity andphase. In the measurements, a 1024-channel opticalmultichannel analyzer with an intensified CCD was used.
The step number was 256 and the delay time was 1.34 fs.
The time required for the measurement was ⬃1 min, andthe stability of the pulses was excellent during that time.
Also, we could usually reproduce the pulse width measured by FROG within 10% by using the same parameters several hours after they had been optimized. In
Figs. 5(b) and 5(c) the spectrum and the temporal waveforms, respectively, of the pulse are shown. The FROG
error was 0.0038. The measured and the calculated spectra agree quite well because of the correction of the marginals. However, the temporal width was not changed bythat correction. The 5.0-fs pulse obtained had 2.4 cycles
at the center wavelength (633 nm), and its width was 14%
longer than the transform-limited pulse width (4.4 fs for
the FROG measurement). If the geometrical smearing
effect is taken into account, we estimate that the pulse
width will be 4.7 fs. The residual phase was within ␲/2
in the wavelength range (550–800 nm), where the spectral intensity is significantly large.

6. CONCLUSION
SLM-only phase compensation to generate a 5.0-fs pulse
has been experimentally demonstrated. It has beenshown that the choice of the center wavelength for a Taylor expansion of the phase obtained from a SLM is important for obtaining pulses that are near the transform
limit. The pulse width evaluated by correction of the

2.

3.
4.

5.

6.

7.

8.

9.

10.
11.

12.

13.

U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus,
J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T.
Tschudi, ‘‘Sub-two-cycle pulses from a Kerr-lens modelocked Ti:sapphire laser,’’ Opt. Lett. 24, 411–413 (1999).
D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F.
Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T.
Tschudi, ‘‘Semiconductor saturable-absorber mirrorassisted Kerr-lens mode-locked Ti:sapphire laser producing
pulses in the two-cycle regime,’’ Opt. Lett. 24, 631–633(1999).
A. Baltuška, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma,
and R. Szipöcs, ‘‘All-solid-state cavity-dumped sub-5-fs laser,’’ Appl. Phys. B 65, 175–188 (1997).
A. Baltuška, M. S. Pshenichinikov, and D. A. Wiersma,‘‘Amplitude and phase characterization of 4.5-fs pulses byfrequency-resolved optical gating,’’ Opt. Lett. 23, 1474–
1476 (1998).
A. Baltuška, M. S. Pshenichinikov, and D. A. Wiersma,‘‘Second-harmonic generation frequency-resolved opticalgating in the single-cycle regime,’’ IEEE J. Quantum Electron. 35, 459–478 (1999).
M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania,
Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, ‘‘Anovel high-energy pulse compression system: generationof multigigawatt sub-5-fs pulses,’’ Appl. Phys. B 65, 189–
196 (1997).
Z. Cheng, A. Fürbach, S. Sartania, M. Lenzner, Ch. Spielmann, and F. Krausz, ‘‘Amplitude and chirp characterization of high-power laser pulses in the 5-fs regime,’’ Opt.
Lett. 24, 247–249 (1999).
A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi,‘‘Sub-5-fs visible pulse generation by pulse-front-matchednoncollinear optical parametric amplification,’’ Appl. Phys.
Lett. 74, 2268–2270 (1999).
A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II,‘‘Programmable shaping of femtosecond optical pulses byuse of 128-element liquid crystal phase modulator,’’ IEEE J.
Quantum Electron. 28, 908–919 (1992).
D. Yelin, D. Meshulach, and Y. Silberberg, ‘‘Adaptive femtosecond pulse compression,’’ Opt. Lett. 22, 1793–1795(1997).
L. Xu, N. Nakagawa, R. Morita, H. Shigekawa, and M. Yamashita, ‘‘Programmable chirp compensation for 6-fs pulse
generation with a prism-pair-formed pulse shaper,’’ IEEE J.
Quantum Electron. 36, 893–899 (2000).
L. Xu, L. Li, N. Nakagawa, R. Morita, and M. Yamashita,‘‘Application of a spatial light modulator for programmableoptical pulse compression to the sub-6-fs regime,’’ IEEE
Photonics Technol. Lett. 12, 1540–1542 (2000).
E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane,
G. Mourou, H. Kapteyn, and G. Vdovin, ‘‘Pulse compression
by use of deformable mirrors,’’ Opt. Lett. 24, 493–495(1999).

1746

J. Opt. Soc. Am. B / Vol. 18, No. 11 / November 2001

14.

N. Karasawa, R. Morita, H. Shigekawa, and M. Yamashita,‘‘Generation of intense ultrabroadband optical pulses by induced phase modulation in an argon-filled single-mode hollow waveguide,’’ Opt. Lett. 25, 183–185 (2000).
I. H. Malitson, ‘‘Interspecimen comparison of the refractive
index of fused silica,’’ J. Opt. Soc. Am. 55, 1205–1209(1965).
Schott Glaswerke, Schott optical glass catalog (Schott
Glaswerke, Mainz, Germany, 1992).
I. H. Malitson, ‘‘Refraction and dispersion of synthetic sapphire,’’ J. Opt. Soc. Am. 52, 1377–1379 (1962).

15.
16.
17.

Karasawa et al.
18.
19.

20.

D. E. Gray, ed., American Institute of Physics Handbook,
3rd ed. (McGraw-Hill, New York, 1972).
L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer,and U. Keller, ‘‘Techniques for the characterization of sub10-fs optical pulses: a comparison,’’ Appl. Phys. B 70, S67–
S75 (2000).
G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C.
Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, ‘‘Measurement of 10-fs
laser pulses,’’ IEEE J. Sel. Top. Quantum Electron. 2, 575–
585 (1996).