A universal nonparaxial refraction law for spatial solitons

The interaction of self-localizing and self-stabilizing wavepackets with interfaces is a fundamental nonlinear wave phenomenon. Indeed, interfaces play a crucial role as boundary conditions in a wide class of problem, ranging from guided-wave optics in photonic architectures to water waves interacting with coastal structures. We consider scattering of spatial optical solitons at the planar boundary between dissimilar nonlinear materials. Our approach allows arbitrary angles of beam incidence, reflection and refraction (relative to the interface); conventional theories demand these angles (in the laboratory frame) be near-negligibly small. A range of analytical and semi-analytical methods is deployed in both domains, and respecting solution continuity at the boundary allows the derivation of a universal Snell’s law governing beam refraction. Numerical analysis, in combination with fast computational techniques, tests the validity of theoretical predictions. Given the universality of soliton phenomena, we expect the methods developed here to be applicable in other nonlinear-wave based systems.