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Issue ESAIM: Proc.
Volume 18, 2007
Paris-sud working group on modelling and scientific computing 2006-2007
Page(s) 153 - 162
DOI http://dx.doi.org/10.1051/proc:071813
Published online 12 September 2007

ESAIM: Proc., 2007, Vol. 18, pp. 153-162
DOI: 10.1051/proc:071813

Propagation d'impulsions laser ultracourtes dans un cristal non linéaire.

Olivier Saut1 and Antoine Bourgeade2

1  Institut de Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, CNRS UMR 5251 and INRIA Futurs, 351 cours de la libération, 33405 Talence Cedex, France
2  CEA/CESTA, B.P. 2, 33114 Le Barp, France


(Published online: 12 September 2007)

Abstract
In this paper, we present a mathematical model for ultrashort pulses propagation in nonlinear optical crystals. For ultrashort pulses, classical models based on the slowly varying envelope approximation are no longer relevant. The microscopic model based on the Maxwell-Bloch model, that we present, can accurately describe the wave-propagation while accounting for dispersive nonlinearities. We will describe this model and its numerical discretization in two dimensions of space. Finally, we perform two numerical experiments.


Résumé
Dans cet article, nous présentons un modèle mathématique pour l'étude de la propagation d'impulsions ultra-courtes dans les cristaux non-linèaires. Pour des impulsions ultra-courtes, les modèles classiques basés sur l'approximation de l'enveloppe lentement variable ne sont plus adaptés. Nous décrivons un modèle microscopique basé sur les équations de Maxwell-Bloch qui peut décrire précisément l'interaction lumière-matière en tenant compte de la dispersion de la réponse non-linéaire du milieu à la lumière. Un schéma numérique adapté sera ensuite décrit. Nous finirons par quelques expériences numériques.


Mathematics Subject Classification. 78A60, 81V80

Key words: Impulsions ultra-courtes. Interaction laser-matière. Équations de Maxwell-Bloch.


© EDP Sciences, ESAIM 2007


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