The Snell law is a fundamental optical principle that describes the behavior of an optical wave passing through the interface between two media with different refractive indices. The reflection and refraction of wave are derived from the discontinuous of linear susceptibilities. The Snell law has been generalized for metasurfaces where a linear phase shift is introduced artificially.

By analyzing the nonlinear processes on the nonlinear interface, we find that the nonlinear harmonic waves are not collinear with the fundamental wave. We demonstrate that the angles at which second-harmonic waves are generated at ferroelectric domain walls satisfy the Snell law for nonlinear media. Nonlinear reflection and refraction are observed experimentally and the relation is found to be in good agreement with theoretical predictions. In the periodic domain structure, the coherent superposition of second-harmonic waves has been observed, on the basis of which we have proposed a comprehensive theory to explain nonlinear effects in multilayered structures.

See also: PHYSICAL REVIEW A 95, 043841 (2017)