Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T06:28:18.406Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achtenhagen, M., Chang, T. and Nyman, B., Analysis of a multiple-pump Raman amplifiers. Appl. Phys. Lett. 78 (2000) 1322–1324. CrossRef
U. Ascher, R. Mattheij and R. Russel, Numerical Solution of Boundary Value for Ordinary Differential Equations. Prentice Hall, Englewood Cliffs (1988).
F. Castella, P. Chartier and E. Faou, Analysis of a Poisson system with boundary conditions. C. R. Acad. Sci. Paris, Sér. I 336 (2003) 703–708.
G. Golub and C. Van Loan, Matrix Computations. The Johns Hopkins University Press (1989).
E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration Springer-Verlag 31 Springer Ser. Comput. Math. Berlin (2002). Structure-preserving algorithms for ordinary differential equations.
Kidorf, H., Rottwitt, K., Nissov, M., Ma, M. and Rabarijaona, E., Pump Interactions in a 100-nm Bandwidth Raman Amplifier. IEEE Photonics Technology Letters 11 (1999) 530–532. CrossRef
Pocholle, J., Papuchon, M., Raffy, J. and Desurvire, E., Non linearities and optical amplification in single mode fibers. Revue Technique Thomson-CSF 22 (1990) 187–268.
Rini, M., Christiani, I. and Degiorgio, V., Numerical modeling and optimization of cascaded Raman fiber lasers. IEEE Journal of Quantum Electronics 36 (2000) 1117–1122. CrossRef