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Raman laser: mathematical and numerical analysis of a model

Published online by Cambridge University Press:  15 June 2004

François Castella ,
Philippe Chartier ,
Erwan Faou ,
Dominique Bayart ,
Florence Leplingard  and
Catherine Martinelli
François Castella
Affiliation:
IRMAR, Université de Rennes 1, Campus Beaulieu, 35042 Rennes Cedex, France. Francois.Castella@univ-rennes1.fr.
Philippe Chartier
Affiliation:
INRIA Rennes, Campus Beaulieu, 35042 Rennes Cedex, France. Philippe.Chartier@irisa.fr.; Erwan.Faou@irisa.fr.
Erwan Faou
Affiliation:
INRIA Rennes, Campus Beaulieu, 35042 Rennes Cedex, France. Philippe.Chartier@irisa.fr.; Erwan.Faou@irisa.fr.
Dominique Bayart
Affiliation:
ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France. Dominique.Bayart@alcatel.fr.; Florence.Leplingard@alcatel.fr.; Catherine.Martinelli@alcatel.fr.
Florence Leplingard
Affiliation:
ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France. Dominique.Bayart@alcatel.fr.; Florence.Leplingard@alcatel.fr.; Catherine.Martinelli@alcatel.fr.
Catherine Martinelli
Affiliation:
ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France. Dominique.Bayart@alcatel.fr.; Florence.Leplingard@alcatel.fr.; Catherine.Martinelli@alcatel.fr.
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Abstract

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.

Keywords

Optical deviceRaman gainPoisson systemintegro-differential equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 3 , May 2004 , pp. 457 - 475
Copyright
© EDP Sciences, SMAI, 2004

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References

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