A paraxial model for optical self-focussing in a nematic liquid crystal

Numerical and asymptotic results are presented for a coupled PDE system that models recent experiments of the selffocussing of laser light in a nematic liquid crystal. This study complements previous asymptotic analyses which, in a narrow-beam limit, describe two essential features observed in nematic self-focussing the undulation and filamentation of a laser beam. These numerical computations represent a direct emulation of the experimental configuration within the context of a paraxial PDE model. In addition to providing numerical corroboration to these earlier asymptotic analyses, these results suggest that initial focussing caustics play a critical rtle in the formation of beam filament pairs.