The critical NLS equation 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.
This is joint work with Gadi Fibich.
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