Propagation properties of non-paraxial spatial solitons

We present an analysis and simulation of the non-paraxial nonlinear SchroÈ dinger equation. Exact general relations describing energy ̄ ow conservation and transformation invariance are reported, and then explained on physical grounds. New instabilities of fundamental and higher-order paraxial solitons are discovered in regimes where exact analytical non-paraxial solitons are found to be robust attractors. Inverse-scattering theory and the known form of solutions are shown to enable the prediction of the characteristics of nonparaxial soliton formation. Finally, analysis of higher-order soliton break up due to non-paraxial eå ects reveals features that appear to be of a rather general nature.