Jpn. J. Appl. Phys. Vol. 41 (2002) pp. 1369–1373
Part 1, No. 3A, March 2002
#2002 The Japan Society of Applied Physics

Measurements of Third-Order Dispersion Eﬀects for Generation of High-Repetition-Rate,
Sub-Three-Cycle Transform-Limited Pulses from a Glass Fiber
Shinki N AKAMURA*, Liming LI1 , Naoki K ARASAWA{ , Ryuji M ORITA, Hidemi S HIGEKAWA2 and Mikio Y AMASHITA
Department of Applied Physics, Hokkaido University, and CREST, Japan Science and Technology Corporation (JST),Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan1
Department of Photonics Material Science, Chitose Institute of Science and Technology, and CREST,
Japan Science and Technology Corporation (JST), Chitose 066-8655, Japan
2
Institute of Applied Physics and the Center for Tsukuba Advanced Research Alliance (TARA), University of Tsukuba, and CREST,
Japan Science and Technology (JST), 1-1-1 Tennodai, Tsukuba 305-8573, Japan(Received July 30, 2001; accepted for publication November 27, 2001)

An active chirp compensator consisting of a prism pair and a spatial-phase-modulating pulse shaper enables us to accurately
measure the third-order dispersion (TOD) dependence of the interferometric autocorrelation trace while keeping the optimumgroup-delay dispersion constant. As a result, it is shown that even a small change in TOD (þ60 fs3 and 100 fs3 ) greatly
aﬀects the temporal pulse proﬁle in the sub-8-fs region, and 92-fs pulses at a 75-MHz repetition rate from a laser-oscillator
glass-ﬁber system is transform-limitedly compressed to 7.1 fs. [DOI: 10.1143/JJAP.41.1369]
KEYWORDS: active chirp compensation, few-optical-cycle pulse generation, spatial light modulator, glass-fiber nonlinear
propagation, white light continuum

1.

Introduction

Ultrashort pulse generation has advanced considerably inrecent years, and optical pulses in the 4–5 fs regime havebeen generated by external pulse compression1–4) with anampliﬁer at the repetition rate of 1 kHz and directly fromTi:sapphire lasers at the repetition rate of 100 MHz.5,6) For
chirp compensations, combinations of prism pairs, grating
pairs and chirped mirrors have been employed.1–6) However,such techniques have the disadvantages of interdependence
among the group-delay dispersion (GDD), the third-orderdispersion (TOD) and the higher-order dispersion, as well as
bandwidth limitation and the inability to realize in-situ large
phase adjustment without realignment. Therefore, accurate
chirp compensation for the compression of few-optical-cycle
pulses with ultrabroad spectra becomes increasingly diﬃcult
in the generation of shorter transform-limited pulses.
On the other hand, more recently, a novel pulse
compression technique consisting of an Ar-gas-ﬁlled hollow
ﬁber, a prism pair and a pulse shaper with a spatial light
modulator (SLM) has been demonstrated for the generationof sub-5-fs ampliﬁed pulses at a repetition rate of 1 kHz.7–9)
This technique has the ability to overcome the abovementioned problems. Using this technique, we clarify
quantitatively and experimentally the relationship between
the chirped pulse and the applied TOD under the obtained
optimum GDD in the time region less than 10 fs, anddemonstrate the generation of 7.1-fs transform-limited
pulses which are output from a silica ﬁber (2.5 mm length)
at a 75-MHz repetition rate. Single-mode silica optical ﬁbers
are attractive nonlinear media because of their low losses,
small eﬀective areas, low cost, commercial availability andthe capability of broadband spectra generation by low
energy pulses at a high repetition rate. To demonstrateaccurate compensation, it is particularly important to use
high-repetition-rate pulses because their stability is higher
than that of an ampliﬁed pulse output from a hollow ﬁber ata low repetition rate. In addition, we will demonstrate that
the SLM is an excellent device for controlling interindependently the n-th order phase dispersion of chirped
pulses even for the very small change in value of the n-thorder dispersion. The use of nonampliﬁed pulses, whichhave a stable intensity, enables us to demonstrate theseissues for the ﬁrst time.
To investigate the accurate chirp-compensation characteristics, we utilize a high-resolution, large SLM with 256
pixels,10) whose one-pixel size is the same as previously
reported but the total pixel number is doubled, and afrequency-resolved optical gating (FROG) apparatus tocharacterize the frequency-dependent phase of ﬁber output
pulses before the chirp compensation experiment.
2.

Experiment

Our experimental setup is shown in Fig. 1. The 12-fs, 10nJ pulses with the center wavelength of 800 nm weregenerated from a mode-locked Ti:sapphire laser (Femtolaser
GmbH, M-1) at the repetition rate of 75 MHz. The 12-fs

SH-FROG

R1

Main compensator
G1

2.5 mm, 2.7 m
Silica fiber

G2

SLM

M7

M8

R2
M6

12 fs, 10 nJ,
75 MHz,
800 nm

M9

M1
M10

M4
M2

P1

M5

M11

PC
Autocorrelator

Silica prism pair
P2
M3

Precompensator
59 cm

*

Present address: Department of Media and Telecommunications Engineering, Ibaraki University, and CREST, Japan Science and Technology
Corporation (JST), 4-12-1, Nakanarusawa, Hitachi, Ibaraki 316-8511,
Japan. E-mail address: nakamura@dmt.ibaraki.ac.jp{
Present address: Department of Applied Photonics System Technology,
Chitose Institute of Science and Technology, and CREST, Japan Scienceand Technology Corporation (JST), Chitose 066-8655, Japan.

Fig. 1. Layout of the experimental setup. M1-6, M9-11, silver-coatedplane mirrors; M7 and M8, silver-coated spherical mirrors, R ¼
400 mm; P1, P2, Brewster-angle cut silica prisms; G1,G2, gold-coatedgratings d ¼ 300 lines/mm; R1, R2, reﬂective objectives (36); SLM,
spatial light modulator controlled by computer (PC).

1369

where j ¼ 1; 2; . . ., 256 (the pixel number), 00
d2 ð!Þ=d!2 j!0 and ð3Þ d3 ð!Þ=d!3 j!0 at the center
angular frequency !0 ¼ !128 of the pulse spectrum (thecorresponding wavelength 0 ¼ 800 nm at the incidence
angle i ¼ 0) correspond to GDD and TOD, respectively,
and !j  !0 represents the angular frequency diﬀerence
between the jth pixel and the 128th pixel. The angularfrequency !j is given by !j ¼ 2c=j , where c is thevelocity of light in vacuum. The jth pixel wavelength j isexpressed with respect to the spatial position xj as j ¼
½dfsinðtan1 ðxj =f Þ þ sinðc =dÞÞ þ sin i g.7,9,13–16) xj ¼ j x,
and x is the pixel width for the SLM. f denotes the focal
length of the so-called 4-f conﬁguration SLM compensator.
The numerical result of our 4-f SLM chirp compensator is

I(t)

1

100

(t)
80
60
92 fs

0.5

40
20
0

(t) (rad)pulses were coupled into a 2.5-mm silica ﬁber by a 36x
reﬂective objective R1 (Ealing) which was made of gold
mirrors and introduced no additional phase dispersion for the
12-fs pulses. The silica ﬁber was a polarization-preserving
single-mode fused silica ﬁber (Newport, F-SP-V) with a core
diameter of 2.7 m. The coupling eﬃciency was measured
to be 27%. The output from the 2.5-mm ﬁber was collimatedby another objective R2 (Ealing) made of aluminum mirrors
and its spectrum was measured by a spectrometer. In
addition, the output pulse was characterized by our secondharmonic generation FROG (SHG-FROG) apparatus.
With an input pulse power of 120 kW, the ﬁber output
spectrum was broadened due to the dispersive SPM eﬀect,
and the broad-spectral pulse had a duration of 92 fs. The
chirped pulse was ﬁrst precompensated by a pair of fusedsilica Brewster prisms P1 and P2 with a separation length of
59 cm. The output pulse from the prism pair was coupled
into a 4-f pulse-shaping apparatus7–12) which consisted of apair of 300 lines/mm gold-coated gratings G1 and G2(Richardson Grating Laboratory) placed at the focal planesof a pair of 200-mm-focal-length concave-spherical silver
mirrors M7 and M8. A programmable one-dimensional 256pixel SLM (custom-made by BNS Inc.) with a total eﬀective
width of 27 mm and a height of 10 mm was set on the
Fourier plane at the center of the two spherical mirrors
between the two gold-coated gratings. In the SLM, eachpixel had a width of 100 m and an inter-pixel gap of 7 m.
This pulse-shaping apparatus was nondispersive except for
the SLM. The total transmission eﬃciency of the SLM
pulse-shaping system including the losses of many reﬂection
components was about 20%. The chirp-compensated pulses
from the pulse shaper were measured by an interferometricautocorrelator with a 25-m-thick BBO crystal (Femtolaser
GmbH). We were unable to employ the SHG-FROG
technique for the measurement of the pulse shaper output
because the power of the compensated pulse was below thesensitivity of our FROG apparatus.
The main-chirp compensation by the computer-controlled
SLM in the 4-f conﬁguration was carried out by a proceduresimilar to that previously reported.7–9) The spectral phase to
be applied by the SLM, ð!j Þ, is described by the following
equation:1
1
ð!j Þ ¼  00  ð!j  !0 Þ2 þ
2!
3!
ð1Þ
 ð3Þ  ð!j  !0 Þ3 þ    ;S. NAKAMURA et al.

Temporal Phase

Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 3A

Normalized Intensity I(t)

1370

0
100

0

100

200

300

Time (fs)Fig. 2. The FROG-retrieved intensity proﬁle, IðtÞ, and phase,
pulse as a function of time for silica-ﬁber output.

ðtÞ, of the

depicted by the upper and lower horizontal axes in Fig. 3.
3.

Active Chirp Compensation

To ﬁnd the optimum distance between two prisms forprecompensation and the optimum spectral phase retardation
to be applied by the SLM for main compensation, we
measured the temporal intensity and phase proﬁles of theoutput pulses from the silica ﬁber using an SHG-FROG
apparatus (25-m-thick BBO). The pulse was retrieved well,with a FROG error of 0.012 for a 512  512 pixel trace. The
number of delay points was 512 with the delay-time spacingof 2.0 fs, and the number of wavelength points was 512 withthe wavelength spacing of 0.45 nm. Figure 2 shows theretrieved temporal intensity IðtÞ and phase ðtÞ proﬁles ofthe pulse. The pulse width (full width half maximum,
FWHM) of the temporal intensity proﬁle with the large
structures was 92 fs and the FWHM of the intensity
autocorrelation was 135 fs. The change in temporal phase
was nearly 100 radians and the chirp, !ðtÞ ¼ d ðtÞ=dt,
indicated a relatively large nonlinearity as a function of time.
When the retrieved spectral phase ð!Þ was extrapolated at
the center angular frequency !0 using an equation similar toeq. (1), the GDD and TOD values at 0 ¼ 800 nm were
determined to be 00 ¼ þ342 fs2 and ð3Þ ¼ þ187 fs3 ,respectively.
In order to precompensate for the previously obtainedlarge GDD, namely, the linear chirp part of ﬁber output
pulses, the prism distance was set at 59 cm to impart anegative GDD value of 342 fs2 at 800 nm (calculation fromref. 17) with the TOD value of 479 fs3 . Here, the linear
chirp indicates that d =dt is proportional to time t, and it is
known that d =dt ¼ ½1=00 ð!0 Þ  t for the Gaussian pulse
ð3Þand  ð!0 Þ causes nonlinear chirp in the time domain.
Similar calculations indicated that the GDD and TOD values
at 800 nm for the fused-silica SLM substrates of a total
thickness of 4.6 mm were þ165 fs2 and þ125 fs3 , respectively, while dispersion of the 10-m-thick liquid crystal
was neglected.
Based on these considerations (see Table I), the GDD of

1020.1 nm
1.848 rad/fs

0Phase (rad)8

GDD+TODGDD only
TOD only

6

1 (a)

1

Outpu t
Input

0
600

4

Intensity (arb. units)

800.0 nm2.356 rad/fs

Intensity (arb. units)=578.1 nm=3.261 rad/fs

S. NAKAMURA et al.
Intensity (arb. units)

Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 3A

(b)

1371

IFT
7.1 fs

0

700

800

900

Wavelength (nm)0Time (fs)50

Measured2

IFT (7.1 fs)

(c)

0
40

20

0

20

40

Time Delay (fs)Fig. 4. (a) Measured pulse spectrum (solid line) from the 4-f pulse shaper
under optimum GDD and TOD values of 150 fs2 and þ220 fs3 ,respectively. The dashed line shows the measured input spectrum of the
ﬁber. (b) Inverse Fourier transformation (IFT) of the solid line of Fig. 4(a)with 7.1 fs FWHM. (c) The corresponding measured interferometricautocorrelation trace (cross points). The solid line is a ﬁt from the above
IFT.

Phase (rad)

6
4
2
0
1

200

100

256

SLM Pixel Number
Fig. 3. Applied phase distribution as a function of the SLM pixel number
and corresponding folded phase distribution.

Table I. Evaluated dispersion for 800 nm from FROG measurements andvarious optical components, and applied GDD and TOD.
Optical components
Silica ﬁber output
Silica prism pair (59 cm)(2.5 mm, 2.7 m , 12 fs, 120 kW)
SLM substrate(4.6 mm silica)

GDD (fs2 )TOD (fs3 )at 800 nm

at 800 nm

342

187

342

479

165

125

GDD, TOD applied by SLM

150

220

Total

þ15

þ53

150 fs2 and the TOD of þ220 fs3 at 800 nm were appliedby the SLM in the 4-f conﬁguration for main-chirp
compensation, as shown in Fig. 3, where the phase as afunction of the pixel number was folded at each pixel
exceeding 2N radians (N ¼ 1; 2; 3 . . .) as in the previous
reports.11,18) Regarding the GDD value, the optimum result
was not obtained when the GDD of 165 fs2 was applied.
As shown at the top of Fig. 3, the largest angular frequency
through the SLM was 3.261 rad/fs at the 1st pixel and thesmallest angular frequency was 1.848 rad/fs at the 256th
pixel, and the carrier angular frequency !0 was 2.356 rad/fs
located at the 128th pixel. Corresponding wavelengths forthe angular frequencies are also shown at the top of Fig. 3,
and suggest that the use of diﬀraction gratings results in a
spatial dispersion that is nearly proportional to thewavelength.

As a result of applying the phase shown in Fig. 3 to theSLM, the interferometric autocorrelation (IAC) trace asshown in Fig. 4 (cross points) was observed. The power ofthe compensated pulse was below the sensitivity of our
FROG apparatus. We also calculated the IAC trace of the
7.1-fs transform-limited pulse (the solid line in Fig. 4) which
was obtained from the measured spectrum ranging from 670
to 930 nm at the pulse shaper output [the solid line of inset(a) in Fig. 4]. The good agreement between the two IAC
traces suggested that 7.1-fs transform-limited pulses weregenerated. The IAC calculated for small GDD and TOD
values was rather deviated from the best ﬁtting curve which
was calculated from the inverse Fourier transform of themeasured spectrum. To the best of our knowledge, thesewere the shortest pulses generated with the combination of asilica ﬁber and the SLM by non-ampliﬁed pulses. The small
residual phase error shown in Table I might be due to theslight deviation from the dispersion-free distance of thegrating pair forming the 4-f conﬁguration.
It should be noted that this SLM technique for chirp
compensation has two limitations. First, the diﬀerence ofphases imparted on two neighbor-pixels in the SLM,  ¼
i ð!i Þ  iþ1 ð!iþ1 Þ, where i ¼ 1; 2; . . . ; 255, should be lessthan .15,18) Second, the longest tp.in.max to be compensatedfor should be much shorter than the time window tw ¼
0 D=c d cos d ( ¼ 2:0 ps) of the 4-f conﬁguration in order tosatisfy the condition of the Fourier transformation in the
SLM plane (along the x axis).19,20) Here, D and d represent
the incident beam diameter to the ﬁrst grating and the
diﬀraction angle at the central wavelength of 0 , respectively.
4.

Third-Order Dispersion Eﬀect

We investigated the TOD dependence of the IAC trace
while keeping the GDD (150 fs2 ) constant (Fig. 5). First,
we measured the shortest IAC trace of Fig. 4 [and Fig. 5(d)]under the best chirp compensation by the SLM. This trace
indicated the expected ratio of 8 : 1 : 0 (the ratio among the1372

Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 3A

S. NAKAMURA et al.

Fig. 5. Measured interferometric autocorrelation traces: (a) with no dispersion applied by the spatial light modulator; (b)–(f) as afunction of diﬀerent TOD values while keeping the GDD value constant at 150 fs2 .

absolute maximum, the background and the absolute
minimum of the IAC trace), and agreed with the transform-limited pulse obtained from the measured spectrum.
Therefore, we concluded that the alignment and theoperation of our IAC apparatus were correct for thismeasurement. Next, we measured the remainder of the
traces [Figs. 2(a) to 2(c) and 2(e) to 2(f)] without any
realignment of our IAC apparatus by changing only the TOD
values and keeping the GDD value [except for (a) where wewere oﬀ the applied electric ﬁeld of the SLM], using thecomputer-controlled SLM. This is one of the advantages of
the SLM method, and implies that the measurements of (a)to (c) and (e) to (f) were also correct and these traces havethe expected ratio of 8 : 1 : 0 for a long delay time.
When the applied GDD and TOD were both zero [Fig.
5(a)], the large substructure appeared in the IAC trace,
where the background in the far time region from the peak
was appropriately low. However, when only the GDD was
set at 150 fs2 [Fig. 5(b)], the relative amplitude of the oﬀcenter features decreased. With increasing only the TODfrom þ120 to þ220 fs3 , a good peak-to-background ratio of
8 : 1 was observed and the small wing corresponding to thetransform-limited pulse proﬁle [the inset (b) in Fig. 4]
appeared. A further increase of the TOD from þ280 toþ360 fs3 again yielded oﬀ-center features which slightly
diﬀered from earlier observations. These results suggest thateven a small change in TOD (þ60 fs3 and 100 fs3 ) greatly
aﬀects the temporal intensity proﬁle of the pulse in the 7-fs
regime. The diﬀerence between the cases of the TOD
increase and decrease may be due to the yielding of therelative diﬀerence between the GDD phase distribution andthe TOD phase distribution in the high-frequency region (seeFig. 3), where the frequency width per pixel becomes larger
and hence the phase diﬀerence between one pixel and its

neighbor exceeds the critical value of .15,18)
5.

Conclusions

We experimentally and quantitatively demonstrated thatthe change in the small value of the TOD of þ60 fs3 and100 fs3 at 800 nm was highly sensitive to the generation of
7.1-fs transform-limited pulses of sub-three optical cycles.
The 92-fs pulses at a 75-MHz repetition rate from the shortglass ﬁber were compressed for the ﬁrst time to become 7.1fs transform-limited pulses using a fused-silica prism pair
and a 256-pixel-SLM pulse shaper that in-situ adjusts
independently and accurately any order dispersions without
physically realigning any optics. This extremely accurate
and ﬂexible SLM chirp compensator can be applied to theclariﬁcation of the compensation mechanism of the complicated phase when this method is combined with the adaptive
feedback system.11) It should be noted that this nonlinear
chirp compensator with the ultrabroad bandwidth (from480 nm to 1250 nm whose wavelength range is based on ourprevious experiments7–9,14,16)) can be applied for complete
chirp compensation of the one-octave-exceeding bandwidth
pulse from the recently developed photonic crystal ﬁbers21)
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