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.
@article{M2AN_2004__38_2_321_0, author = {Besse, Christophe and Bid\'egaray-Fesquet, Brigitte and Bourgeade, Antoine and Degond, Pierre and Saut, Olivier}, title = {A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {38}, year = {2004}, pages = {321-344}, doi = {10.1051/m2an:2004015}, mrnumber = {2069149}, zbl = {1081.81127}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2004__38_2_321_0} }
Besse, Christophe; Bidégaray-Fesquet, Brigitte; Bourgeade, Antoine; Degond, Pierre; Saut, Olivier. A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 321-344. doi : 10.1051/m2an:2004015. http://gdmltest.u-ga.fr/item/M2AN_2004__38_2_321_0/