Self-focusing of chirped optical pulses in media with normal dispersion

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Abstract
The self-focusing of ultrashort optical pulses in a nonlinear medium with normal dispersion is examined. We demonstrate that chirping the pulse initially can strongly increase the achievable peak intensity by competing with the splitting of the pulse in the time domain. On the one 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 pulse, it is shown by means of exact analytical estimates that a transverse collapse can never occur. In the opposite situation, i.e., when the chirp forces the pulse to expand temporally while it shrinks in the transverse diffraction plane, we display numerical evidence that chirping can generate highly spiky electric fields. We further describe the splitting process that takes place near the self-focusing finite distance of propagation and discuss the question of the ultimate occurrence of a collapse-type singularity.