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 ve ctorial effects. We derive a scalar equation from the vector Helmholtz equa tion that describes self-focusing in the presence of vectorial and nonparax ial effects. Numerical simulations of the scalar equation show that when th e input beam is sufficiently powerful, vectorial effects lead to multiple f ilamentation. We compare multiple filamentation due to vectorial effects wi th the one due to noise, and suggest how to decide which of the two leads t o multiple filamentation in experiments. We also show that vectorial effect s and nonparaxiality have the same effect on self-focusing of a single fila ment, leading to the arrest of catastrophic collapse, followed by focusing- defocusing oscillations. The magnitude of vectorial effects is, however, si gnificantly larger than that of nonparaxiality. (C) 2001 Elsevier Science B .V. All rights reserved.