Raman laser : mathematical and numerical analysis of a model

François Castella; Philippe Chartier; Erwan Faou; Dominique Bayart[1]; Florence Leplingard; Catherine Martinelli

  • [1] ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 3, page 457-475
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Castella, François, et al. "Raman laser : mathematical and numerical analysis of a model." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.3 (2004): 457-475. <http://eudml.org/doc/246007>.

@article{Castella2004,
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.},
affiliation = {ALCATEL Research & Innovation, Unité Transmissions Photoniques, Route de Nozay, 91460 Marcoussis, France},
author = {Castella, François, Chartier, Philippe, Faou, Erwan, Bayart, Dominique, Leplingard, Florence, Martinelli, Catherine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {optical device; Raman gain; Poisson system; integro-differential equations; Lotka-Volterra system; Poisson brackets},
language = {eng},
number = {3},
pages = {457-475},
publisher = {EDP-Sciences},
title = {Raman laser : mathematical and numerical analysis of a model},
url = {http://eudml.org/doc/246007},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Castella, François
AU - Chartier, Philippe
AU - Faou, Erwan
AU - Bayart, Dominique
AU - Leplingard, Florence
AU - Martinelli, Catherine
TI - Raman laser : mathematical and numerical analysis of a model
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 3
SP - 457
EP - 475
AB - 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.
LA - eng
KW - optical device; Raman gain; Poisson system; integro-differential equations; Lotka-Volterra system; Poisson brackets
UR - http://eudml.org/doc/246007
ER -

References

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  1. [1] M. Achtenhagen, T. Chang and B. Nyman, Analysis of a multiple-pump Raman amplifiers. Appl. Phys. Lett. 78 (2000) 1322–1324. 
  2. [2] U. Ascher, R. Mattheij and R. Russel, Numerical Solution of Boundary Value for Ordinary Differential Equations. Prentice Hall, Englewood Cliffs (1988). Zbl0671.65063MR1000177
  3. [3] 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. Zbl1030.45006
  4. [4] G. Golub and C. Van Loan, Matrix Computations. The Johns Hopkins University Press (1989). Zbl0733.65016MR1002570
  5. [5] 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. Zbl0994.65135MR1904823
  6. [6] H. Kidorf, K. Rottwitt, M. Nissov, M. Ma and E. Rabarijaona, Pump Interactions in a 100-nm Bandwidth Raman Amplifier. IEEE Photonics Technology Letters 11 (1999) 530–532. 
  7. [7] J. Pocholle, M. Papuchon, J. Raffy and E. Desurvire, Non linearities and optical amplification in single mode fibers. Revue Technique Thomson-CSF 22 (1990) 187–268. 
  8. [8] M. Rini, I. Christiani and V. Degiorgio, Numerical modeling and optimization of cascaded Raman fiber lasers. IEEE Journal of Quantum Electronics 36 (2000) 1117–1122. 

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