Volume 38, Number 3, May-June 2004
|Page(s)||457 - 475|
|Published online||15 June 2004|
Raman laser: mathematical and numerical analysis of a model
IRMAR, Université de Rennes 1, Campus Beaulieu, 35042 Rennes Cedex, France. Francois.Castella@univ-rennes1.fr.
2 INRIA Rennes, Campus Beaulieu, 35042 Rennes Cedex, France. Philippe.Chartier@irisa.fr.; Erwan.Faou@irisa.fr.
3 ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France. Dominique.Bayart@alcatel.fr.; Florence.Leplingard@alcatel.fr.; Catherine.Martinelli@alcatel.fr.
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Mathematics Subject Classification: 65L10 / 65L20
Key words: Optical device / Raman gain / Poisson system / integro-differential equations.
© EDP Sciences, SMAI, 2004
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