Fast Petviashvili-Hankel method for vortex solitons in the generalized nonlinear Schrodinger equation

We present a robust numerical procedure for obtaining ring-type spatial optical beams with phase singularities in nonlinear media. This numerical algorithm can be used for fast computing stationary solutions with high topological charge for the case of a generalized nonlinear Schrodinger equation. Remarkably, we find that the method converges to the ring-type solution starting virtually from any initial condition. The method is based in the use of Chebyshev spectral methods for the calculation of a required Hankel transform. We provide the codes for the straightforward use of this algorithm in Matlab.