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

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Abstract

Two numerical schemes are developed for solutions of the bidimensional Maxwell-Bloch equations in nonlinear optical crystals. The Maxwell-Bloch model was recently extended [C. Besse, B. Bidégaray, A. Bourgeade, P. Degond, O. Saut, A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: An application to KDP, M2AN Math. Model. Numer. Anal. 38 (2) (2004) 321-344] to treat anisotropic materials like nonlinear crystals. This semi-classical model seems to be adequate to describe the wave-matter interaction of ultrashort pulses in nonlinear crystals [A. Bourgeade, O. Saut, Comparison between the Maxwell-Bloch and two nonlinear maxwell models for ultrashort pulses propagation in nonlinear crystals, submitted (2004)] as it is closer to the physics than most macroscopic models. A bidimensional finite-difference-time-domain scheme, adapted from Yee [IEEE Trans. Antennas Propag. AP-14 (1966) 302-307], was already developed in [O. Saut, Bidimensional study of the Maxwell-Bloch model in a nonlinear crystal, submitted (2004)]. This scheme yields very expensive computations. In this paper, we present two numerical schemes much more efficient with their relative advantages and drawbacks. © 2005 Elsevier Inc. All rights reserved.

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Bourgeade, A., & Saut, O. (2006). Numerical methods for the bidimensional Maxwell-Bloch equations in nonlinear crystals. Journal of Computational Physics, 213(2), 823–843. https://doi.org/10.1016/j.jcp.2005.09.003

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