NUMERICAL-SOLUTION FOR THE PROPAGATION OF AN ELLIPTIC GAUSSIAN-BEAM IN A KERR MEDIUM

A numerical algorithm combining the fast Fourier 2D transform and Runge-Kutta techniques is applied to the problem of the propagation of a cw elliptical Gaussian beam in a nonlinear Kerr medium. The numerical solution is compared to those of the aberrationless paraxial approximation and of the variational method. We find that the deviations from either approximations can be substantial. Furthermore, we show that novel qualitative features, such as hole formation in the beam center and the transformation of an elliptic beam into a cylindrical beam immediately prior to self-focusing, which are not predicted by either approximation are present in the numerical treatment.