Une méthode spectrale pour les équations de Maxwell-Bloch bidimensionnelles dans les cristaux non-linéaires

To study the propagation of ultrashort laser pulses in a nonlinear optical crystal, it has become necessary to develop new models. Classical models from nonlinear optics are no longer relevant for such pulses. In Besse et al. [Math. Model. Numer. Anal. 38 (2) (2004) 321-344], we have developed a model adequate to study such a propagation. A bidimensional numerical study based on the Yee scheme [IEEE Trans. Antennas Propag. 14 (1966) 302-307] was performed elsewhere. To shorten computation times, we present here a new discretization method adapted from Liu [Microwave Opt. Techn. Lett. 15 (1997) 158-165]. To cite this article: O. Saut, C. R. Acad. Sci. Paris, Ser. I 340 (2005).