Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics: angles and interfaces, solitons and Snell’s law

The interaction of self-localized waves with an abrupt interface is a problem of fundamental importance in many branches of physics, engineering, and applied mathematics. Waveguide optics, for instance, is dominated in an essential way by such considerations. There, the full complexity of electromagnetic propagation is conveniently reduced to an equation of the nonlinear Schrödinger (NLS) class. These simplified models are physically intuitive, mathematically tractable, and hold a certain universal appeal. All their desirable features notwithstanding, theories based on paraxial diffraction are seldom appropriate when angular considerations are of principal interest. Here, we report on our recent analyses of nonlinear optical wave refraction using more general Helmholtz equations, and introduce (for the first time in this single-interface context) a cubic-quintic system response. A Snell law is derived for beams, and its predictions tested by exhaustive computations. New Goos-Hänchen (GH) shift calculations are also detailed for this material regime of nonlinear-interface problem.