The nonlinear Schrodinger equation (NLS) is the model equation for propagation of intense laser beams in a Kerr medium, which has been used to predict that sufficiently intense laser beams would undergo `catastrophic' self-focusing. According to the NLS model, beams with cylindrically-symmetric input profile should remain cylindrically symmetric during propagation. However, self-focusing experiments in solids, liquids, and gases have shown that catastrophic self-focusing is often preceded by multiple filamentation, in which a single input beam breaks-up into several long and narrow filaments. For over thirty years, the standard explanation for multiple filamentation, due to Bespalov and Talanov, has been that it is initiated by random noise in the input-beam profile. In this talk we show that deterministic vectorial effects can also lead to multiple filamentation. We compare the noise and the vectorial effects explanations and suggest a simple experiment for deciding whether multiple filamentation is due to vectorial effects or not.

This is joint work with Boaz Ilan.

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