Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts

In this presentation, we give the first detailed overview of spatial soliton refraction at the planar interface between materials whose nonlinear polarization has contributions from both X(3)and X(5)susceptibilities [1]. 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 [2]. By respecting field continuity conditions at the interface, a universal Snell’s law may be derived for describing the refractive properties of soliton beams. This compact equation contains a supplementary multiplicative factor that captures system nonlinearity, discontinuities in material properties, and finite beam waists. Extensive numerical calculations have tested analytical predictions and provided strong supporting evidence for the validity of our modelling approach across wide regions of a six-dimensional parameter space. Theoretical predictions for critical angles are generally in good agreement with simulations of beams at linear and weakly-nonlinear interfaces, and we have quantified Goos-Hänchen shifts [3,4] in such systems (see Fig. 1). References [1] K. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, Opt. Quantum Electron. 11, 471 (1979). [2] J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, Phys. Rev. A 76, 033833 (2007). [3] F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947). [4] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 36, 3605 (2011)