Helmholtz Bright Spatial Solitons and Surface Waves at Power-Law Optical Interfaces

We consider arbitrary angle interactions between spatial solitons and the planar boundary between two optical materials with a single power-law nonlinear refractive index. Extensive analysis has uncovered a wide range of new qualitative phenomena in non-Kerr regimes. A universal Helmholtz-Snell law describing soliton refraction is derived using exact solutions to the governing equation as a nonlinear basis. New predictions are tested through exhaustive computations, which have uncovered substantially enhanced Goos-H？nchen shifts at some non-Kerr interfaces. Helmholtz nonlinear surface waves are analyzed theoretically, and their stability properties are investigated numerically for the first time. Interactions between surface waves and obliquely incident solitons are also considered. Novel solution behaviours have been uncovered, which depend upon a complex interplay between incidence angle, medium mismatch parameters, and the power-law nonlinearity exponent. 1. Introduction A light beam impinging on the interface between two dissimilar dielectric materials is a fundamental optical geometry [1–12]. After all, the single-interface configuration is an elemental structure that facilitates more sophisticated device designs and architectures for a diverse range of photonic applications. The seminal work of Aceves et al. [6, 7] some two decades ago considered perhaps the simplest scenario, where a spatial soliton (i.e., a self-trapped and self-stabilizing optical beam) is incident on the boundary between two different Kerr-type materials. Their intuitive approach reduced the full complexity of the electromagnetic interface problem to something far more tractable, namely, the solution a scalar equation of the inhomogeneous nonlinear Schr？dinger (NLS) type. The development of an equivalent-particle theory [3–6] provided an enormous level of insight into the behaviour of scalar solitons at material boundaries. The adiabatic perturbation technique developed by Aliev et al. [13, 14] provides another toolbox for analyzing interface phenomena (e.g., light incident on the boundary between a linear and a nonlinear medium). Photorefractive [15] and quadratic [16] materials have also been considered. A recurrent feature of the waves at interfaces literature is the appearance of the paraxial approximation, which combines the assumptions of broad (predominantly transverse-polarized) beams and slowly varying envelopes [1–16]. The adoption of this ubiquitous mathematical device can impose some strong physical constraints that should be borne in mind when modelling precisely