E. A. McCoy

Nonparaxial soliton refraction at optical interfaces with χ (3) and χ (5) susceptibilities

Summary form only given. 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 de focusing τ materials, respectively.In this presentation, we give the first detailed overview of beam refraction at the interface between materials whose nonlinear polarization has contributions from both χ(3) and χ(5) susceptibilities [5]. The governing equation is of the inhomogeneous Helmholtz class with a cubic-quintic nonlinearity, and analysis is facilitated through the exact bright soliton solutions of the corresponding homogeneous problem [6]. By respecting field continuity conditions at the interface, a universal Snells law may be derived for describing the refractive properties of soliton beams. This compact nonparaxial law contains a supplementary multiplicative factor that captures the interplay between system nonlinearity, discontinuities in material properties, and finite beam waists. Extensive numerical calculations have tested analytical predictions, providing strong supporting evidence for the validity of our modelling approach across wide regions of a six-dimensional parameter space. Our Snells law also provides theoretical predictions for critical angles that are in generally good agreement with full simulations of beams at linear and weakly-nonlinear interfaces. We have quantified Goos-Hänchen shifts [7] at such interfaces (see Fig. 1). Of particular interest are regimes involving external linear refraction [8], since these physical contexts have no counterpart in conventional (Schrödinger-based) theory [1]. For strongly nonlinear interfaces, new and potentially exploitable qualitative phenomena can emerge.

Refraction and Goos-Hänchen Shifts of Spatial Solitons at Cubic-Quintic Interfaces

We present the first analysis of spatial solitons refracting at the planar interface between dissimilar materials with both χ(3) and χ(5) optical susceptibilities. A nonparaxial Snell’s law is derived and giant Goos-Hanchen shifts are predicted.

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-Hanchen 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.

Refraction of power-law spatial solitons — The Helmholtz-Snell law

The behaviour of a scalar optical beam at the boundary between two dissimilar nonlinear media is of fundamental interest in photonics. Here, we report the first systematic generalization of our Kerr analyses to a wider class of power-law materials. Universal refraction laws will be given, and theory-simulation agreement demonstrated.