Vectorial and random effects in self-focusing and in multiple filamentation

The standard explanation for multiple filamentation of laser beams is that breakup of cylindrical symmetry is initiated by noise in the input beam. In this study we propose an alternative deterministic explanation based on vectorial effects. We derive a scalar equation from the vector Helmholtz equation that describes self-focusing in the presence of vectorial and nonparaxial effects. Numerical simulations of the scalar equation show that when the input beam is sufficiently powerful, vectorial effects lead to multiple filamentation. We compare multiple filamentation due to vectorial effects with the one due to noise, and suggest how to decide which of the two leads to multiple filamentation in experiments. We also show that vectorial effects and nonparaxiality have the same effect on self-focusing of a single filament, leading to the arrest of catastrophic collapse, followed by focusing-defocusing oscillations. The magnitude of vectorial effects is, however, significantly larger than that of nonparaxiality.