AN EFFECTIVE SEMI-IMPLICIT METHOD FOR CIRCULARLY SYMMETRIC QUENCHING OPTICAL WAVES

Recent electro-optical studies indicate that the spatial profile of a quenching, or collapsing, optical wave evolves to a specific circularly symmetric shape, known as the Townes profile, for elliptically shaped or randomly distorted input beams. Computations of such a Townes profile have been playing an important role in understanding of the wave collapse phenomenon, but the numerical procedures are sensitive due to features of the generalized nonlinear Schr¨odinger equation boundary value problems involved. This paper studies an effective semi-implicit finite difference method equipped with a dynamic shooting strategy for the numerical solution of the quenching optical boundary value problems. The numerical method proposed is simple in structure, easy to use, and weakly asymptotically stable. Simulated circularly symmetric quenching optical waves are given