Helmholtz non-paraxial beam propagation method: An assessment

Abstract

We present a performance evaluation of a non-paraxial beam propagation method suitable for the study of Helmholtz solitons. The analysis aims to determine the accuracy limits of the numerical scheme in terms of the maximum propagation angle addressable. Our investigation is based on the spectral representation of the exact soliton solutions and the study of their evolution at extreme propagation angles, together with the analysis of the propagation invariants. Based on these results, a simple heuristic criterion for the boundaries of the validity domain of the algorithm is provided.