Appl. Phys. B 74 [Suppl.], S291–S294 (2002)

Applied Physics B

DOI: 10.1007/s00340-002-0895-7

Lasers and Optics

m. shibata1
m. hirasawa1
n. nakagawa1
r. morita1,✉
a. suguro2
h. shigekawa3
m. yamashita1

Experimental demonstrationof phase-dispersion compensation
for ultra-broadband femtosecond optical pulses
generated by induced-phase modulation
1 Department of Applied Physics, Hokkaido University and Core Research for Evolutional Science and Tech-

nology, Japan, Science and Technology Corporation, Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan
2 Display Development, Technical Research Laboratory, Citizen Watch Co. Ltd., 840 Shimotomi, Tokorozawa

359-0001, Japan

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

Received: 19 September 2001/
Revised version: 17 November 2001
Published online: 5 July 2002 • © Springer-Verlag 2002
ABSTRACT Spectrally resolved autocorrelation traces of ultra-

broadband (730 to 1250 nm) pulses generated by dispersive
induced-phase modulation (IPM) and self-phase modulation ina single-mode fused-silica fiber were measured. From thesemeasurements, effective discontinuities in group delay andgroup-delay dispersion in the overlapping spectral region of
two input pulses owing to the IPM effect were found. Not only
conventional nonlinear-chirp compensation, but also frequencyindependent group-delay adjustment, both of which are essential for pulse compression of ultra-broadband femtosecond
pulses generated by IPM, were experimentally demonstratedusing a pulse shaper with a spatial light-phase modulator of
648 pixels.
PACS 42.65.Re; 42.65.Ky; 42.81.Qb

1

broaden the spectrum, the IPM technique has the following
advantages over self-phase modulation (SPM) using a onecolor femtosecond pulse: the phase modulation efficiency is
two times larger, and the output electric fields with different central wavelengths are constructively synthesized in the
spectral region. However, phase-dispersion compensation ofIPM-broadened pulses has not been performed owing to thecomplexity of its spectral phase behavior. In this paper, we experimentally demonstrate that a SLM pulse shaper enables us
to compensate for the complicated phase dispersion due to theIPM effect in a SM fused-silica fiber.
2

Experimental setup and results

2.1

Experimental setup

The experimental setup we used is shown in Fig. 1.
A SM fused-silica fiber (F-SPV, Newport) with a 2.7-µm core
diameter was employed as a medium for dispersive IPM andSPM effects [4]. The two input pulses into the fiber origi-

Introduction

In order to generate extremely ultra-short opticalpulses such as monocycle pulses, intensive spectral broadening of pulses and compensation of complicated phase dispersion are key technologies. In 1996, we proposed the utilization of induced-phase modulation (IPM) based on nonlinear co-propagation of two or more different-color femtosecond pulses with a carrier-phase locking in a singlemode (SM) fiber for spectral broadening exceeding one octave, and the utilization of a 4- f pulse shaper with a spatial light-phase modulator (SLM) for its phase-dispersion
compensation [1–3]. Later, ultra-broadband pulse generation
using the IPM effect for a conventional SM fused-silica fiber(480 to 900 nm) [4] and for a SM gas-filled hollow fiber(300 to 1000 nm) [5] have been experimentally demonstrated.
Moreover, the capability of the SLM pulse shaper for ultrabroadband phase-dispersion compensation has been demonstrated on the basis of the experimental generation of sub-5-fs
pulses for the self-phase-modulated fiber output [6–9]. To✉ Fax: +81-11/706-6706, E-mail: morita@eng.hokudai.ac.jp

FIGURE 1 Experimental setup for spectrally resolved autocorrelation(dashed line) and novel phase-dispersion compensation (solid line) of ultrabroadband femtosecond optical pulses generated by induced- and self-phasemodulations. M1–M7: plane mirrors, DM: dichroic mirror (M2 is rotated by
90◦ when spectrally resolved measurements are performed), F1, F2: flip mirrors, RO1, RO2: reflective objectives, P1, P2: prisms, S: slit, RM: roof mirror,
G1, G2: gratings, CM1, CM2: concave mirrors, SLM: spatial light-phasemodulator

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Applied Physics B – Lasers and Optics

nated from the same light source. One pulse (the fundamental
pulse) was generated by a Ti:sapphire regenerative amplifier (Alpha-1000S, B. M. Industries) at a 1-kHz repetition
rate and had a duration of 80 fs, 12-nJ energy per pulse anda spectrum centered at 800 nm. The other pulse (the idler
pulse), being centered at 1100 nm with an 80-fs duration and
48-nJ energy per pulse, was converted from the fundamental pulse by an optical parametric amplifier (COMET-400S,
B. M. Industries). That is, the idler pulse was generated by thetwo-stage parametric amplification of white-light continuum
based on a single-filament SPM of the fundamental pulse.
Therefore, the carrier phase difference between them waslocked [10–12].
The length of the fiber was 3 mm, which almost equals
the walk-off length (5 mm) between the two pulses. The delay
time of the fundamental pulse with respect to the idler pulse
was adjusted by a delay stage with a sub-µm accuracy, andwas calibrated by the observation of the sum-frequency lightusing a 10-µm β -barium borate (BBO) crystal. To focus these
two input pulses into the fiber and collimate its output, a pairof nondispersive reflective objectives (×36) coated with goldand silver, respectively, was used. The typical fiber output efficiency was 20%. The output pulse from the fiber was directed
to a pair of prisms with a slit for spectrally resolved measurements of autocorrelation traces, or to a SLM pulse shaper forphase-dispersion compensation. The distance between two
fused-silica, 60-degree prisms with double paths was 610 mm.
The 4- f pulse shaper consisted of a pair of gratings (withgrating constant d = (1/150) mm), a pair of concave mirrors(focal length f = 350 mm) and a novel SLM, which was fabricated by one of the authors (A. S.). It has 648 pixels andan 8-bit resolution (a pixel width of 97 µm and a pixel gapof 5 µm). The throughput of the 4- f system was about 30%.
After passing the prism pair or the 4- f pulse shaper, the output
pulse was characterized by a noncollinear autocorrelator witha 10-µm-thick BBO crystal.
2.2

FIGURE 2 a Spectrum of the output pulse from the fiber broadened bydispersive induced- and self-phase modulations. The corresponding calculated transform-limited pulse is shown in the inset. b The corresponding
autocorrelation trace of the fiber output pulse without any compensation

Effective discontinuities in group delay andgroup-delay dispersion

In our experiment, the fundamental and idler pulses
were simultaneously focused into the fiber (with a null delaytime). In this case, both dispersive IPM and SPM effects occurred in the fiber, with the spectral broadening from 730 to1250 nm, as shown in Fig. 2a. First, the corresponding autocorrelation trace (without any chirp compensation) was measured, as depicted in Fig. 2b. The full width at half maximum(FWHM) of the trace is 150 fs.
Second, the autocorrelation trace of the pulse with bestphase-dispersion compensation by only a pair of silica prisms
was measured, as shown in Fig. 3a. This trace with FWHM
of 52 fs was composed of three peaks, which indicated double pulses. To clarify the spectral phase behavior of the pulse,
we measured the spectrally resolved autocorrelation traces
under prism phase-dispersion compensation [13], as depicted
in Fig. 3b,c and d. They correspond to wavelength regions of
730–850, 850–1010 and 1010– 1250 nm, and have FWHMs
of 55, 40 and 41 fs, respectively. The autocorrelation FWHMs
derived from the transform-limited pulse durations of 22 fs
are 34 fs for all spectrally resolved regions, on the assump-

FIGURE 3 Spectrally resolved autocorrelation traces of the pulse whose
phase dispersion was compensated for by a prism pair. a Whole wavelength region (730–1250 nm), b shorter-wavelength region (730–850 nm),c middle-wavelength region (850–1010 nm) and d longer-wavelength region(1010–1250 nm)

SHIBATA et al.

Phase compensation for ultra-broadband pulses generated by IPM

dφ(ω) /d ωpressed by
tdSLM (ω) = dφSLM(ω)/dω
C2(1) (ω − ω01 ) + C3(1) (ω − ω01 )2 /2,

=
0

ω
ω dc

Schematic drawing of the pulse group delay dφ(ω)/dω. Although, in the strict sense, the spectral phase of the pulse φ(ω) may be shownby the dashed line, it can be approximately expressed by a combination of
two cubic spectral phase functions with respect to ω, as the solid line. Group
delay as well as group-delay dispersion can be considered to have an effective
discontinuity at the frequency ωdc in the middle-wavelength region

FIGURE 4

tion of sech2 pulse shapes. The deviations of the measured
FWHMs from the transform-limited FWHMs are due to fluctuation in pulse intensity and phase during the accumulation
time of 16 s, which is required for low-signal detection. Particularly, the larger deviation in the shorter-wavelength region suggests stronger IPM, which is difficult to compensate
for by only a prism pair, originating from higher intensityof idler. In the shorter-wavelength region (b) and the longerwavelength region (d), phase-dispersion compensation withdifferent prism insertions from each other results in a singlepeak autocorrelation trace. In good contrast to this, in the
middle-wavelength region (c) the autocorrelation trace has
three peaks. In the strict sense, the spectral phase inducedand self-modulation may vary continuously as the dashed line
shown in Fig. 4. However, it can be approximately expressedby a combination of cubic spectral phase functions with respect to ω, as the solid line shown in Fig. 4. It is supportedby the calculated result from equations describing IPM andSPM nonlinear propagation [2]. Thus the experimental resultin the middle-wavelength region suggests the effective discontinuity in group delay (GD) dφ(ω)/dω and the effective
discontinuity in group-delay dispersion (GDD) d2 φ(ω)/dω2
expressed by a combination of two functions as the solid line
shown in Fig. 4.
2.3

S293

tg + C2(2) (ω − ω02 ) + C3(2) (ω − ω02 )2 /2,

ω < ωdc ,ω ≥ ωdc ,(3)

where ω01 and ω02 are the center angular frequencies of the
Taylor expansion corresponding to 1100 and 800 nm, respectively, and ωdc is the angular frequency where the total groupdelay tdSLM (ω) is discontinuous. The value of ωdc is determined to be 930 nm from the calculation describing IPM
and SPM nonlinear propagation [2, 14]. Parameters C2(i) andC3(i) (i = 1, 2) are the GDD and the third-order dispersion(TOD) in the region of ω < ωdc or ω ≥ ωdc , respectively.
The constant group delay tg is determined so that the discontinuity φ (ωdc + 0) − φ (ωdc − 0) of the group delay vanishes. Figure 5a shows the autocorrelation trace in the casewhere C2(1) = −500 fs2 , C3(1) = −200 fs3 , C2(2) = −700 fs2 andC3(2) = −700 fs3 with tg = 0 fs were applied by a SLM in thesame manner as in [6–8]. They were determined based on
the fact that these values resulted in best chirp compensation
when only the fundamental pulse or the idler pulse propagated in the fiber with only the SPM effect. The three-peaktrace of Fig. 5a is very similar to that of Fig. 3a, suggesting theeffective group-delay discontinuity. To cancel this frequencyindependent group-delay effect, we applied the value of tg
to be −120 fs together with the same C2(i) and C3(i) (i = 1, 2)
values and obtained a single-peak autocorrelation trace, as
shown in Fig. 5b. The correlation FWHM was 75 fs, which
was the same as that of the main peak of Fig. 5a, and the duration of the compensated pulse was evaluated to be 49 fs on theassumption of a sech2 pulse shape. The corresponding duration of the transform-limited pulse is 8 fs, as shown in the inset
of Fig. 2a. The reason for this disagreement is considered to
be as follows. In the present experiment, the applied GDD and
TOD dispersion parameters using a SLM were determined

Phase-dispersion compensation by a SLM

The chirp compensation implies, in general, thatd[φ(ω) + φSLM(ω)]/dω = const., where φ(ω) and φSLM (ω)
are the spectral phase of pulses and the phase to be applied
by a SLM, respectively. However, in the present case of theinduced- and self-phase-modulated pulse, unlike the conventional case of the self-phase-modulated pulse, dφ(ω)/dω includes the effective group-delay discontinuity of φ (ωdc +0) − φ(ωdc − 0) at ωdc , whereφ (ωdc + 0) ≡φ (ωdc − 0) ≡lim

dφ(ω)/dω,

(1)

lim

dφ(ω)/dω,(2)

ω→ωdc +0
ω→ωdc −0

as shown by the solid line in Fig. 4. Therefore, from the experimental result mentioned above, for perfect compensationof the phase dispersion to generate the shortest pulse, the totalgroup delay tdSLM (ω) to be applied by a SLM should be ex-(1)(1)
FIGURE 5 Autocorrelation traces of pulses a with C2 = −500 fs2 , C3 =−200 fs3 , C2(2) = −700 fs2 , C3(2) = −700 fs3 and tg = 0 fs (no frequencyindependent group-delay adjustment), and b with the same parameters as
in a except that tg = −120 fs (with the frequency-independent group-delay
adjustment)

S294

Applied Physics B – Lasers and Optics

based on the experimental results where only SPM occurred.
That is, either the idler or the fundamental pulse propagatedin a fiber. Moreover, fluctuation in pulse intensity and phaseduring a comparable long accumulation time to improve thesignal to noise ratio for a low-intensity output from a fiber
restricts the resolvable correlation FWHM to be ∼ 35 fs.
The optimum value of tg = −120 fs was determined on thebasis of the time difference between the main peak and the
sub-peak in the autocorrelation trace of Fig. 5a. This group delay is significantly different from the 48-fs propagation timedifference of the idler pulse with respect to the fundamental
pulse due to the group-velocity difference. Therefore, this result also suggests that the effective group-delay discontinuity
originates from the dispersive IPM and SPM effects.
Thus, it should be noted that pulse compression using IPM
with two phase-locked optical pulses requires not only conventional nonlinear-chirp compensation but also frequencyindependent group-delay adjustment. Both compensations
are simultaneously performed by a 4- f system with a SLM.
Accurate characterization of the spectral phase using ourmodified SPIDER technique [15] and better phase-dispersion
compensation based on it will enable us to generate much
shorter optical pulses such as few-cycle or monocycle pulses.
3

Conclusion

In conclusion, we measured spectrally resolved autocorrelation traces of the ultra-broadband pulse generated
by dispersive IPM and SPM. From these measurements, wefound effective discontinuities in group delay and groupdelay dispersion in the overlapping spectral region of thetwo input pulses, which were caused by IPM. Moreover, we
experimentally demonstrated novel phase-dispersion compensation for the ultra-broadband femtosecond optical pulse

generated by dispersive IPM and SPM, using a 4- f optical pulse shaper with a spatial light-phase modulator. In
compression of the ultra-broadband optical pulses utilizing
the IPM effect with two phase-locked pulses, not only conventional nonlinear-chirp compensation but also frequencyindependent group-delay adjustment are essential.
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