Wait time to stochastic self-focusing

Abstract

The first passage time extended to stochastic nonlinear beam dynamics emerges as a natural time scale and a meaningful estimator for the expected wait time to the first self-focusing event within a large sample of stochastic laser pulses. We show that the ratio P/Pcr of the laser peak power P to the critical power of self-focusing Pcr, which plays a central role in deterministic self-focusing, keeps its status as a key governing parameter in stochastic self-focusing. However, in contrast to its deterministic counterpart, the Pcr/P ratio of a stochastic laser beam is no longer an indicator of whether self-focusing will occur, but is, rather, a predictor of when the self-focusing is expected, in the sense of the first passage time, given the statistics of the laser field.