Bidimensional study of the Maxwell-Bloch model in a nonlinear crystal

Olivier Saut (1)

1 IMB - Institut de Mathématiques de Bordeaux

This article presents a numerical scheme for a model ([5]) of electro- magnetic wave propagation in a nonlinear optical crystal in two dimensions in space. It uses Maxwell's equations to describe the wave field and Bloch's equations for the medium at the quantum-mechanical level. We have al- ready described the discretization of the model in the unidimensional case in [14]. In this paper, we discretize the model in the bidimensional case, while ensuring a scheme of order 2. Finally, several numerical simulations are performed. We insist on physical effects that could not be observed with an unidimensional model.

Mots clés: Optique non linéaire; Géneration d'harmonique

Domaines: Analyse numérique [math.NA]; Optique [physics.optics]; Equations aux dérivées partielles [math.AP]

Olivier Saut. Bidimensional study of the Maxwell-Bloch model in a nonlinear crystal. 2007. ⟨hal-00131950⟩