Raman laser : mathematical and numerical analysis of a model
Castella, François ; Chartier, Philippe ; Faou, Erwan ; Bayart, Dominique1 ; Leplingard, Florence ; Martinelli, Catherine
1 ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 3, pp. 457-475.

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.

DOI : 10.1051/m2an:2004022
Classification : 65L10, 65L20
Mots-clés : optical device, Raman gain, Poisson system, integro-differential equations
Castella, François  ; Chartier, Philippe  ; Faou, Erwan  ; Bayart, Dominique 1 ; Leplingard, Florence  ; Martinelli, Catherine 

1 ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France 
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     title = {Raman laser : mathematical and numerical analysis of a model},
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Castella, François; Chartier, Philippe; Faou, Erwan; Bayart, Dominique; Leplingard, Florence; Martinelli, Catherine. Raman laser : mathematical and numerical analysis of a model. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 3, pp. 457-475. doi : 10.1051/m2an:2004022. http://archive.numdam.org/articles/10.1051/m2an:2004022/

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