Optical scattering by a nonlinear medium, II: induced photonic crystal in a nonlinear slab of BBO

TL;DR

This paper investigates the complex scattering phenomena in a nonlinear BBO crystal slab illuminated by multiple plane waves, leading to the formation of a photonic crystal structure, using advanced finite element methods without simplifying approximations.

Contribution

It introduces a novel approach to model nonlinear scattering in a thin slab without the slowly varying envelope approximation, incorporating retroactions and virtual sources for accurate FEM simulation.

Findings

Formation of induced photonic crystal in nonlinear slab

Effective modeling of nonlinear scattering with FEM and virtual sources

Insights into wave interactions in sub-wavelength nonlinear media

Abstract

The purpose of this paper is to investigate the scattering by a nonlinear crystal whose depth is about the wavelength of the impinging field. More precisely, an infinite nonlinear slab is illuminated by an incident field which is the sum of three plane waves of the same frequency, but with different propagation vectors and amplitudes, in such a way that the resulting incident field is periodic. Moreover, the height of the slab is of the same order of the wavelength, and therefore the so-called slowly varying envelope approximation cannot be used. In our approach we take into account some retroactions of the scattered fields between them (for instance, we do not use the nondepletion of the pump beam). As a result, a system of coupled nonlinear partial differential equations has to be solved. To do this, the finite element method (FEM) associated with perfectly matched layers is well suited. Nevertheless, when using the FEM, the sources have to be located in the meshed area, which is of course impossible when dealing with plane waves. To get round this difficulty, the real incident field is simulated by a virtual field emitted by an appropriate antenna located in the meshed domain and lying above the obstacle (here the slab).