Abstract

In their most general form, wave-interface problems are inherently angular in nature. For instance, the interaction between light waves and material boundaries essentially defines the entire field of optics. The seminal works of Aceves et al. [1,2] considered scalar bright spatial solitons impinging on the planar interface between two Kerr-type media with different χ⁽³⁾ susceptibilities. While these classic nonlinear Schrödinger models undeniably paved the way toward understanding how self-collimated light beams behave at material discontinuities, they suffer from a fundamental limitation: the assumption of slowly-varying wave envelopes means that, in the laboratory frame, angles of incidence, reflection and refraction (relative to the interface) must be near-negligibly small. This intrinsic angular restriction may be eliminated by adopting a mathematical and computational framework based on the solution of nonlinear Helmholtz equations. To date, we have considered bright [3] and dark [4] soliton refraction in dissimilar focusing and defocusing χ⁽³⁾ materials, respectively.

© 2013 IEEE