Nonlinear wave phenomena at optical boundaries: spatial soliton refraction

The behaviour of light at the interface between different materials underpins the entire field of Optics. Arguably the simplest manifestation of this phenomenon – the reflection and refraction characteristics of (infinitely-wide) plane waves at the boundary between two linear dielectric materials – can be found in many standard textbooks on electromagnetism (for instance, see Ref. 1). However, laser sources tend to produce collimated output in the form of a beam (whose transverse cross-section is typically “bell-shaped ” and, hence, finite). When describing light beyond the plane-wave limit, a more involved and sophisticated treatment is generally required. If a beam of light is propagating in a nonlinear planar waveguide, its innate tendency to diffract (spread out) may be compensated by the self-lensing properties of the host medium (whose refractive index is intensity-dependent). Such nonlinear photonic systems are driven and dominated by complex light-medium feedback loops. Under the right conditions (e.g., where the amplitude and phase of the input beam have the correct transverse distribution), the light may evolve with a stationary (invariant) intensity profile. Such self-localizing and self-stabilizing nonlinear waves are known as spatial optical solitons. The seminal analyses of spatial soliton refraction were performed by Aceves, Moloney, and Newell [2,3] more than two decades ago. They reduced the full electromagnetic complexity of the interface problem by