A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP

Abstract

Abstract. This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material.Mathematics Subject Classification. 78A60, 81V80.

Numerical methods for the bidimensional Maxwell–Bloch equations in nonlinear crystals

“…The dipolar matrix for a KDP crystal is given in [1]. We believe that the method exposed in [1] could be extended to treat a large class of crystals.…”

“…We believe that the method exposed in [1] could be extended to treat a large class of crystals. For instance, in [2], we perform several computations with an AgGaS 2 crystal.…”

“…Adding a quadratic dispersive nonlinearity is a complex task [8,2]. As shown in [1], the Maxwell-Bloch renders any order of the nonlinearity with its dispersive relation.…”

“…In [1], we have derived a semiclassical model based on the Maxwell-Bloch equations, adapted to describe the wave-matter interaction in nonlinear crystals. The propagation of an electromagnetic wave is classically described by the full-vector time-dependent Maxwell equations.…”

“…In the last Section, we perform several numerical experiments to underline some numerical considerations and to study the validity of our model [1].…”