15 April 1999

Optics Communications 162 Ž1999. 256–260

Experimental generation of an ultra-broad spectrum basedon induced-phase modulation in a single-mode glass fiber
L. Xu a,c,1, N. Karasawa a,c , N. Nakagawa a,c , R. Morita a,c , H. Shigekawa b,c ,M. Yamashita a,cbaDepartment of Applied Physics, Hokkaido UniÕersity, Kita-13, Nishi-8, Kita-Ku, Sapporo 060-8628, Japan
Institute of Materials Science, UniÕersity of Tsukuba and Center for Tsukuba AdÕanced Research Alliance (TARA),
Tsukuba 305-8573, Japanc
CREST, Japan Science and Technology Corporation (JST), Japan

Received 12 January 1999; received in revised form 26 February 1999; accepted 26 February 1999

Abstract
An ultra-broad spectrum over the range from 480 to 900 nm is experimentally generated by induced-phase modulation
ŽIPM. of two 120 fs intense optical pulses copropagating in a 3-mm single-mode fused-silica fiber for the first time to ourknowledge. The center wavelengths of the two pulses are 640 nm and 795 nm, respectively. The Fourier transform of thisspectrum yields a transform limited 4 fs optical pulse. This IPM-induced spectrum broadening method opens the way tomonocycle optical pulse generation in the near future. q 1999 Elsevier Science B.V. All rights reserved.
PACS: 42.65.Re; 42.65.Tg; 42.65.Yj; 42.81.Dp
Keywords: Induced-phase modulation ŽIPM.; Ultra-broad spectrum; Ultra-short pulse; Single-mode glass fiber

Ultra-short light pulses are significant tools for time-resolved spectroscopy. The shorter the duration of the pulse,
the higher the achievable time resolution becomes. The
broad optical spectrum with a well-behaved spectral phaseis one of the main prerequisites for short pulse generation
because the temporal and spectral characteristics of thepulse electric field are related to each other through theFourier transform. Self-phase modulation ŽSPM. in a single-mode glass fiber was demonstrated as the most effective method to generate a broad spectrum. Pulses down to
6 fs were generated in a CPM dye laser-amplifier system
in 1987 w1x and recently sub-5 fs optical pulses weregenerated in a Ti:sapphire cavity-dumped laser systemwith this technique w2x. Meanwhile, the spectrum broadening based on SPM in a gas-filled capillary waveguide was

1

Corresponding author. E-mail: xulin@eng.hokudai.ac.jp

reported w3x and sub-5 fs intense optical pulses were
produced w4,5x. More recently, a diffraction-limited whitelight continuum over the range of 400–1100 nm by SPM
in a hollow waveguide was demonstrated and a pulse
down to 4 fs was generated w6x. However, this performance
was obtained by using very short Ž; 25 fs., mJ-level
optical pulses through a hollow waveguide. For comparatively longer pulses, a novel method for ultra-broad spectrum generation was proposed by using induced-phasemodulation ŽIPM. of two or three different frequency
optical pulses in a glass fiber w7,8x. In this paper, we
experimentally report an ultra-broad spectrum generation
based on IPM of two intense, comparatively longer femtosecond pulses in a glass fiber for the first time to ourknowledge. The induced spectrum which extends from 480
to 900 nm is obtained when two 120 fs, 20 nJ pulses arecoupled into a single-mode fused-silica fiber. The Fouriertransform of this broad spectrum indicates that a transform
limited ; 4 fs pulse could be obtained.

0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 1 0 3 - 0

L. Xu et al.r Optics Communications 162 (1999) 256–260

When two optical pulses copropagate inside a nonlinear
medium, they can interact with each other through thenonlinearity and phase modulation introduced in each pulse
due to the other pulse, which is called IPM. IPM is always
accompanied by SPM because the effective refractive index of a pulse depends not only on its the intensity but
also on the intensity of the other copropagating pulse. The
IPM effect in a picosecond pump-probe configuration was
discussed previously w9–11x and just the weak probe-pulse
spectrum was broadened by the pump pulse. We consider
another case where both optical pulses at different frequencies are the intense pulses. For simplicity, we assume thatboth pulses are linearly polarized along one of the principal axes of the fiber. The electric field for each pulse
Ž j s 1,2. can be written as follows w12,13x:
E j Ž r j ,t . s 12 xˆ Fj Ž x , y . A j Ž z ,t .

=exp i Ž b 0 j z y v j t q f 0 j . q c.c. ,4

Ž1.

where xˆ is the polarization unit vector, b 0 j is the corresponding propagation constant at the center angular frequency v j , f 0 j is the initial phase, Fj Ž x, y . represents thetransverse distribution of the fundamental mode, andA j Ž z,t . is the slowly varying amplitude. The propagation
equation for each pulse envelope A j Ž z,t . is derived asfollows w12,13x:

E Aj
Ez

q b1 js

E Aj

in 2 v j
c

Et

i
q
2

b2 j

E 2A j
E t2

q

aj
2

Aj

f j j N A j N 2 q 2 f jk N A k N 2 A j ,Ž2.

where j, k s 1 or 2 and k / j, b 1 j s 1rÕg j , Õg j is thegroup velocity, b 2 j is the group velocity dispersion ŽGVD.
coefficient, a j is the loss coefficient and f jk is a mode
overlap integral between the transverse modes of the pulses
j and k. The first term in the right-hand side of Eq. Ž2.
represents SPM while the second term is responsible for
IPM of the two pulses. It should be pointed out that thegroup velocity difference between the two pulses plays animportant role in IPM because it limits the IPM interaction
length. For a pulse of width T0 Žwhere the intensity
becomes 1re., the walk-off length is defined as:
Lw s

T0
.
y1
N Õg1 y Õy1
g2 N

257

A schematic of our experimental setup is shown in Fig.
1. The first pulse is generated from a Ti:sapphire regenerative amplifier at 1 kHz repetition rate ŽAlpha 1000, BMI..
The pulse duration is about 120 fs Žfull width at half
maximum, FWHM. with bandwidth of 12 nm ŽFWHM.
centered at 795 nm and the output energy is 750 mJŽhenceforth called fundamental pulse.. The main output
energy from Alpha 1000 is used to generate a continuum
wave and pump an optical parametric amplifier ŽOPA.
ŽComet-400, BMI.. The signal–pulse tuning range in OPA
is from 480 to 740 nm with output energy beyond 10 mJ at
1 kHz. The second pulse wavelength is chosen to be 640
nm from OPA and the pulse duration is measured to beabout 120 fs ŽFWHM. with spectral bandwidth of 12 nmŽFWHM. Žhenceforth called signal pulse.. Since the continuum wave is generated by SPM of the fundamental
pulse under the single-filament condition and is selectively
amplified using its second harmonic pulse by optical parametric process with the phase matching condition w14x, thephase of the signal wave should have a relation to thephase of the fundamental wave. This condition is criticalfor generating a stable combined spectrum with IPM in asingle-mode glass fiber, which will be confirmed later.
From Eq. Ž3. the calculated walk-off length between thesignal pulse and the fundamental pulse is about 2.7 mm.
The reason why the second pulse wavelength is selected to
be 640 nm lies in that the walk-off length of these twopulses in a fused silica fiber Ž L w s 2.7 mm. is around thelength that we are able to cut well Ž; 3 mm. and then the
IPM effect between the two pulses could be observed
clearly. The two pulses are combined by a dichroic mirror,
M7, which has high transmission for the fundamental pulse
and high reflection for the signal pulse. The optical path of

Ž3.

It is easy to understandd that IPM occurs only overdistances ; L w irrespective of the actual fiber length L.
L w depends on the relative center-wavelengths and decreases as the center-wavelength difference dl0 increases.
If the fiber length L satisfies the condition of L F L w , theterms on the right-hand side of Eq. Ž2. show that the IPM
effect is two times as large as SPM and a broader spectrumwith both IPM and SPM effects than that with SPM alone
could be generated. Our experiment is based on this effect.

Fig. 1. Schematic of the experimental setup. Alpha 1000 is a 1
kHz regenerative amplifier ŽBMI., Comet-400s ŽBMI. is an optical parametric amplifier ŽOPA. pumped by Alpha 1000 Žsee text.,
M1–M6 are aluminum plane mirrors, M7 is a dichroic plane
mirror highly transmitting at 795 nm and highly reflecting at 640
nm; P1 is an aperture, N1, N2 are neutral filters, R1, R2 arereflective objectives.

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L. Xu et al.r Optics Communications 162 (1999) 256–260

the fundamental pulse is varied by an optical delay stage
formed by M2, M3 so that the delay of the two pulses in
the fiber can be adjusted. N1 and N2 are variable neutraldensity filters and the energies of the two pulses can becontrolled independently. The beam size of the signal
pulse is about 1.5 mm with a perfect Gaussian distribution
and an aperture P1 is added in the fundamental pulse beam
to improve beam quality with diameter of around 2.0 mm.
The combined two pulses which have the same linear
polarizations are coupled into a 3-mm single-mode polarization-preserving fused-silica fiber ŽNewport F-SPV, 2.7mm core diameter. by a 36 = reflective objective R1ŽEaling.. The advantage of this kind of reflective objectiveis that no additional GVD is introduced to both pulses
because of its reflective components. The coupling efficiency is measured to be around 35% and 40% for thefundamental and signal pulses, respectively. The output
from the fiber is collimated by the same type of reflective
objective R2 to a wavelength-calibrated spectrometerŽSOLAR TII, Ltd., NP250-2. to monitor the output spectrum.
Fig. 2Ža. shows the spectra of the input fundamentalŽsolid line. and signal Ždashed line. pulses. Fig. 2Žb.
depicts the spectra of the two pulses with SPM alone at theenergy of 20 nJ in the fiber for each pulse. The solid line
represents the SPM induced spectrum of the fundamental
pulse and the dashed line represents the SPM induced
spectrum of the signal pulse. From Fig. 2Žb. we observe
the separated spectra for the two pulses with only the SPM
effect at 20 nJ energy levels. When the two pulses arelaunched simultaneously into the same fiber with an optimum initial delay between the two pulses Žtwo pulses meetat the center of the fiber, to be discussed later., because of
the IPM effect of the two pulses, the two spectra meet eachother. We have observed that the output spectrum issignificantly stable including the overlapping part. Thismeans that the phase of the spectral-broadened fundamental wave and the phase of the spectral-broadened signal
wave have some relation. Accordingly, the output spectrum is constructively synthesized. The optimized spectrum all over the range from 480 to 900 nm is measured
ŽFig. 2Žc... The pulse energy measured after fiber propagation is about 40 nJ. The shortest pulse attainable by phasecorrection of this ultra-broad spectrum is obtained by the
Fourier transform of the spectrum of Fig. 2Žc. assuming a
constant spectral phase. This yields the pulse duration of; 4 fs ŽFig. 2Žc. inset.. It should be noted that a well-behaved spectral phase of the generated broad spectrum issignificant for bandwidth-limited-pulse generation. A
rapidly varying phase over the pulse spectrum means thathigh-orders of spectral phase distortion exist. Even thoughquadratic and cubic spectral phases can be compensatedfor by using a prism pair w15x, a grating pair w16x andchirped mirrors w17,18x, more than forth-order spectralphase compensation becomes very hard using these devices. Fortunately, our calculations by solving Eq. Ž2.

Fig. 2. Ža. The spectra of the input fundamental Žsolid line. andsignal Ždashed line. pulses; Žb. The measured spectra induced by
SPM in a 3-mm single-mode fused-silica fiber. The solid line
represents the fundamental pulse spectrum by SPM and the dashedline represents the signal pulse spectrum by SPM at the pulse
duration of 120 fs, energy of 20 nJ in the fiber for each pulse; Žc.
The measured spectrum induced by IPM of the two pulses, thesame parameters as in Žb., the initial time delay between the twopulses is chosen so that the two pulses meet at the center of thefiber. The Fourier transformed pulse intensity is shown in theinset.

show that a quasi-linear chirp is produced by IPM of thetwo optical pulses copropagating in the fiber if all parameters are optimized w7,8x. On the other hand, a recently-developed adaptive pulse-compression method using a liquid-crystal spatial light modulator ŽSLM. has demonstrated
that it has the potential to compensate for almost-arbitrary
spectral phase distortions w19x. Therefore, it is expect that a
sub-5 fs optical pulse will be generated by applying thisadaptive compressor.
Because of the group velocity difference between thetwo optical pulses propagating in the fiber, they travel at
different speeds and after some distance propagation they
are separated. We measured the IPM-induced spectra withdifferent initial time delays between the two pulses. The
results are shown in Fig. 3. The initial time delay between

L. Xu et al.r Optics Communications 162 (1999) 256–260

Fig. 3. The measured spectra induced by IPM for the two pulses
with different initial time delays under the same parameters as inFig. 2. The thicker solid line represents the spectrum when thetwo pulses meet at the center of the fiber, the dashed line
represents the spectrum when the two pulses meet at the entranceof the fiber and the thinner solid line represents the spectrum
when the two pulses meet at the end of the fiber.

the two pulses t s 0 fs represents that the two pulses
coincide at the fiber entrance Ždashed line., and the delays
t s y40 fs and t s y80 fs represent that the two pulses
meet at the center Žthicker solid line. and the end of thefiber Žthinner solid line., respectively. Our results qualitatively agree with the results reported by Baldeck et al. w20x
in which the induced-frequency shift of one weak pulse
was observed when another strong picosecond pulse wascopropagated with its weak pulse in a 1-m-long singlemode glass fiber. In our case, when the two pulses meet atthe entrance of the fiber Žt s 0 fs., because the fundamental pulse travels faster than the signal pulse in the fusedsilica fiber, the leading edge of the signal pulse interacts
with the trailing edge of the fundamental pulse. As aresult, the signal pulse has IPM-induced positive chirp andthe fundamental pulse has IPM-induced negative chirp.
This leads to larger modulation of the signal pulse spectrum at shorter wavelengths and larger spectral modulationof the fundamental pulse at longer wavelengths. A larger
gap between the two spectra is observed in this case ŽFig.
3, dashed line.. On the contrary, when the two pulses meetat the end of the fiber Žt s y80 fs., the trailing edge ofthe signal pulse mainly interacts with the leading edge ofthe fundamental pulse. As a result, the IPM induced
spectrum of the signal pulse shifts towards its longer
wavelengths and the IPM-induced fundamental pulse spectrum shifts to shorter wavelengths and larger overlap of thetwo pulse spectra is observed Žthinner solid line in Fig. 3..
It is found that when the two pulses meet at the center ofthe fiber, the fundamental pulse passes through the signal
pulse in a symmetric manner. As a result, the spectra are259

broaden by the IPM effect to shorter and longer wavelengths simultaneously for both pulses and the broadest
combined spectrum is generated Žthicker solid line in Fig.
3.. This case is referred to as the optimum initial timedelay which we mentioned above. Note that an evenbroader spectrum could be expected by tuning the second
pulse to shorter wavelength, and utilizing a shorter opticalfiber owing to the walk-off length L w depending on therelative wavelengths and decreasing as the center wavelength difference dl0 increases.
In summary, ultra-broad spectrum generation based on
IPM of two optical pulses copropagating in a single-mode
fused-silica fiber has been experimentally demonstrated. In
the experiment, two 120 fs pulses with wavelengths at 640
and 795 nm, respectively, have been coupled into a 3-mm
single-mode fiber. At pulse energy of 20 nJ coupled into
the fiber for both pulses, an ultra-broad coherent spectrum
induced by IPM which covers the range from 480 to 900
nm has been generated. The Fourier transform of thespectrum can yield a ; 4 fs transform limited pulse. This
IPM technique can also be applied to high energy ultrashort pulse generation using a gas-filled hollow fiber as anonlinear medium w21x. It opens a way to generate asingle-cycle high energy optical pulse in the near future.

References
w1x R.L. Fork, C.H. Brito Cruz, P.C. Becker, C.V. Shank, Optics
Lett. 12 Ž1987. 483.
w2x A. Baltuska,
ˆ Z. Wei, M.S. Pshenichnikov, D.A. Wiersma,
Optics Lett. 22 Ž1997. 102; A. Baltuska,
Z. Wei, M.S.
ˆ
Pshenichnikov, D.A. Wiersma, R. Szipocs,¨ Appl. Phys. B 65
Ž1997. 175.
w3x M. Nisoli, S. De Silvestri, O. Svelto, Appl. Phys. Lett. 68
Ž1996. 2793.
w4x M. Nisoli, S. Stagiram, S. De Silvestri, O. Svelto, R. Szipocs,¨
Ch. Spielmann, S. Sartania, F. Krausz, Optics Lett. 22 Ž1997.
522.
w5x S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, Optics Lett. 22 Ž1997. 1562.
w6x Z. Cheng, G. Tempea, T. Brabec, K. Ferencz, Ch. Spielmann, F. Krausz, Ultrafast Phenomena XI, T. Elsaesser, J.G.
Fujimoto, D.A. Wiersma, W. Zinth ŽEds.., Springer, Heidelberg, 1998, p. 8.
w7x M. Yamashita, H. Sone, R. Morita, Jpn. J. Appl. Phys. 35
Ž1996. 1194.
w8x M. Yamashita, H. Sone, R. Morita, H. Shigekawa, IEEE J.
Quantum Electron. 34 Ž1998. 2145.
w9x R.R. Alfano, Q. Li, T. Jimbo, J. Manassah, P. Ho, Optics
Lett. 11 Ž1986. 626.
w10x J. Manassah, M. Mustafa, R.R. Alfano, P.P. Ho, Phys. Lett.
A 113 Ž1985. 242.
w11x R.R. Alfano, P.P. Ho, IEEE J. Quantum Electron. 24 Ž1988.
351.
w12x G.P. Agrawal, P.L. Baldeck, R.R. Alfano, Phys. Rev. A 40
Ž1989. 5063.

260

L. Xu et al.r Optics Communications 162 (1999) 256–260

w13x G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, San
Diego, 1989.
w14x A. Shirakawa, I. Sakane, T. Kobayashi, Optics Lett. 23
Ž1998. 1292.
w15x R.L. Fork, O.E. Martinez, J.P. Gordon, Optics Lett. 9 Ž1984.
150.
w16x E.B. Treacy, IEEE J. Quantum Electron. 5 Ž1964. 454.
w17x R. Szipocs,¨ K. Ferencz, Ch. Spielmann, F. Krausz, Optics
Lett. 19 Ž1994. 201.

w18x G. Tempea, F. Krausz, Ch. Spielmann, K. Ferencz, IEEE J.
Sel. Top. Quantum Electron. 4 Ž1998. 193.
w19x D. Yelin, D. Meshulach, Y. Silberberg, Optics Lett. 22
Ž1997. 1793.
w20x P.L. Baldeck, R.R. Alfano, Appl. Phys. Lett. 52 Ž1988. 1939.
w21x N. Karasawa, R. Morita, L. Xu, H. Shigekawa, M. Yamashita, Theory of ultra-broadband optical pulse generation
by induced-phase modulation in a gas-filled hollow waveguide, J. Opt. Soc. Am. B. 19 Ž1999., in press.