Non-paraxial beam propagation methods

Exact analytical results are employed in the testing of split-step and fini te difference approaches to the numerical solution of the non-paraxial non- linear Schrodinger equation. It is shown that conventional split-step schem es can lead to spurious oscillations in the solution and that fully finite difference descriptions may require prohibitive discretisation densities. T wo new non-paraxial beam propagation methods, that overcome these difficult ies, are reported. A modified split-step method and a difference-differenti al equation method are described and their predictions are validated using dispersion relations, an energy flow conservation relation and exact soluti ons. To conclude, results concerning 2D (transverse) beam self-focusing, fo r which no tract analytical solutions exist, are presented. (C) 2001 Publis hed by Elsevier Science B.V.