L. Berge et al., SELF-FOCUSING OF CHIRPED OPTICAL PULSES IN MEDIA WITH NORMAL DISPERSION, Journal of the Optical Society of America. B, Optical physics, 13(9), 1996, pp. 1879-1891
The self-focusing of ultrashort optical pulses in a nonlinear medium w
ith normal dispersion is examined. We demonstrate that chirping the pu
lse initially can strongly increase the achievable peak intensity by c
ompeting with the splitting of the pulse in the time domain. On the on
e hand, we apply a variational procedure to Gaussian beams, leading to
a reduced system of ordinary differential equations that describe the
characteristic spatiotemporal evolutions of the chirped pulse. On the
other hand, when the chirp induces a temporal compression of the puls
e, it is shown by means of exact analytical estimates that a transvers
e collapse can never occur. In the opposite situation, i.e., when the
chirp forces the pulse to expand temporally while it shrinks in the tr
ansverse diffraction plane, we display numerical evidence that chirpin
g can generate highly spiky electric fields. We further describe the s
plitting process that takes place near the self-focusing finite distan
ce of propagation and discuss the question of the ultimate occurrence
of a collapse-type singularity. (C) 1996 Optical Society of America.