__Self-focusing
and multiple filamentation of circularly polarized beams__

** Boaz Ilan,** Mark Ablowitz, Gadi Fibich

University of Colorado

The critical nonlinear Schrodinger equation (NLS) is the model
equation for propagation of intense LINEARLY POLARIZED laser beams in Kerr media,
such as air and water. It is well known that NLS solutions can become singular
after a finite propagation distance, which corresponds to a narrowing of the
beam to a point (catastrophic self-focusing).

For over 30 years the studies of propagation of CIRCULARLY
POLARIZED Beams in Kerr media used the model of Close et al. These studies
obtained controversial results regarding the stability of circular
polarization. We show that they used the wrong model to study stability. We
present a systematic study of propagation of circularly polarized beams in a
Kerr medium, which leads to a new system of equations that takes into account
nonparaxiality and the coupling to the axial component. Using the new model we
show that circular polarization is stable during self-focusing. According to
the NLS model, a radially-symmetric input beam remains radially-symmetric
during propagation. However, self-focusing experiments can result in complete
break-up of radial symmetry, which is manifested in MULTIPLE FILAMENTATION,
i.e., break-up of the beam into several long and narrow filaments. In this
study we show that circularly polarized beams are much less likely to undergo
multiple filamentation than linearly polarized beams.