Spectral Broadening and Self-compression of Down-chirped
Fs Pulses in Transparent Bulk Kerr Media
Ya. Grudtsyn1, A. Koribut1, S. Mamaev1, L. Mikheev1*, S. Stepanov1, V. Trofimov2, V.
Yalovoy1
1-P.N. Lebedev Physics Institute of Russian Academy of Sciences, Leninsky Prospek, 53, 119991
Moscow, Russia
2- M.V. Lomonosov Moscow State University, Vorob’evy Gory, 119992 Moscow, Russia
*Author e-mail address: mikheev@sci.lebedev.ru
There are two well known schemes for temporal self-compression of
ultrashort pulses without the need for subsequent dispersion
compensation: in filaments and dielectric gas-filled capillaries. We
present a novel self-compression technique relying on spectrum
broadening of down-chirped fs pulses in transparent Kerr media. For the
first time, this phenomenon was observed in our paper [1].
Experimental results.
Fig. 1. Principal scheme of the experiment.
Femtosecond pulses at 475 nm with spectral width of 4.8 nm and pulsewidth of 60 fs were generated by a frequency-doubled Ti:sapphire laser
system (Avesta Project Ltd). After these pulses are down-stretched to
160 fs in a prism pair with negative GVD, the laser beam was spatially
filtrated and focused by a spherical mirror (R=320 cm) onto a 1-mmthick UV fused silica plate mounted on the end of a 45-cm-long vacuum
cell. The window was placed 10 cm before the focal plane located inside
the vacuum cell. The 1/e beam spot width on the plate was ~0.3 mm. At
the incident beam energy of 0.5 mJ, its intensity on the plate reaches 1
TW/cm2. The incoming intensity on the output window of the cell was
one order of magnitude less and did not practically influence the pulse
spectrum. The beam coming out of the vacuum chamber was focused by
a spherical mirror (R=200 cm) onto a 1-mm-diaphragm. Fraction of the
beam passed through the diaphragm was directed into spectrometer,
autocorrelator and beam profiler. Diaphragm location along the beam
propagation axis was chosen so that the pulse width was minimal and
spectrum width was maximal. This position was corresponded to the
plane of the magnified image of the beam cross-section inside the
vacuum cell, in which central part of the incident laser pulse was
focused due to Kerr self-focusing.
Input pulse
 = 4.8 nm
(TL=70 fs)
 = 160 fs
(down-chirped)
Output pulse
 = 8 nm
 = 40 fs
Fig. 2. Experimental results (from left to right): beam profiles, spectra
and autocorrelation functions for input and output beams.
Discussion
I. Spectrum broadening
The observed effect is discussed on the base of combined influence of
self-phase modulation resulting in the formation of a modulated
structure of the spectrum and four-wave mixing leading to parametric
amplification of the side components.
1. Self-phase modulation (modeling)
Experimental results were analysed on the base of Nonlinear
Schrödinger Equation (NSE) in a reference frame moving at the group
velocity vg = c/n0:
A( z , T ) i  2  2 A( z , T )

 i  (| A( z , T ) |2 A( z , T )) 
2
z
2
T
Dispersion
Kerr nonlinearity
A(T , z  0)  A0 Exp[(1  iC )T 2 / T02 ]
The complex valued function A represents the slowly varying pulse
envelope of a linearly polarized optical wave at frequency ω0:
C = - 2 is the chirp parameter, T0 = 160 fs is the input pulse duration, k0
is the wavenumber,
 3 d 2n
2 
2 c 2 d  2
2 n2
 | A |2 
I

= 0.1 ps2/m is the group velocity dispersion parameter,
 = 475 nm, n2= 1.9 cm2/W /2/, I0 = A02 = 1 TW/cm2.
(a)
(b)
Fig. 3. Variation of spectrum with intensity of the incident laser beam
(a) and comparison of calculated and experimental values of spacing
between successive bands in the spectra against intensity of the incident
laser beam (b).
Fig. 3 demonstrates that experimentally measured values of spacing
between successive bands in the spectra and their dependence on the
intensity of the incident laser beam agree well with results of the
numerical modeling. This indicates that structure of the observed spectra
originated from self-phase modulation.
2. Modeling of degenerate four-wave mixing (ωS = ωP + Ω and ωI =
ωP − Ω).
dAP/dz = iPAP2AP + 2iP(AS2 + AI2) AP + 2iP ASAIAP*exp(iΔz)
dAS/dz = iSAS2AS + 2iS(AP2 + AI2) AS + 2iS AP2 AI* exp(-iΔz)
dAI/dz = iIAI2AI + 2iI(AP2 + AS2) AI + 2iI AP2 AS*exp(-iΔz)
Δ = kS + kI – 2kP
If AS(z=0), AI (z=0)<< AP (depletion of pump can be neglected)
parametric gain g  ( P P0 )2  (   2 P P0 )2 = 0. Numerical
modeling at AS(z=0) = AI(z=0) = 0.5AP(z=0) shows that parametric gain
g > 0 and side bands are expected to be parametrically amplified.
II. Temporal self-compression
Temporal profile of the input fs pulse causes Kerr-lens with temporally
variable focus so that different temporal ‘slices’ of the pulse are focused
at different distances from the sample. This allows extracting central
part of the incident laser pulse, experienced strongest nonlinear
interaction in bulk fused silica, by putting diaphragm in a proper crosssection of output beam (Fig. 4) or in the plane of the magnified image of
the cross-section. Self-focusing along with the self-phase modulation
results in the temporal pulse self-compression. On the one hand, selfphase modulation compensates for the initial negative chirp early
introduced into the incoming pulse and, on the other hand, it causes
spectrum broadening.
Fig. 4. Diagram explaining the temporal pulse self-compression.
Spectral broadening of fs pulses was also observed in other Kerr media:
Fig. 5. Spectral broadening of down-chirped fs pulses in bulk MgF2,
LiF, CaF2 и BaF2 at intensity of 1 TW/сm2.
Conclusions
Our results are the first to demonstrate spectral broadening as a result of
nonlinear interaction of down-chirped fs pulses with normally dispersive
transparent Kerr media, that is accompanied by temporal selfcompression of the pulse. Topical problem to be solved in the near
future is the scalability of this technique towards higher energies and
shorter output pulses.
References
1. A.I. Aristov, Ya.V. Grudtsyn, L.D. Mikheev et al. Spectral broadening and selfcompression of negatively chirped visible fs pulses in fused silica. Quantum
Electron. 42, 1097 (2012).
2. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).