Raman laser: mathematical and numerical analysis of a model

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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 38.3 (2010): 457-475. <http://eudml.org/doc/194223>.

@article{Castella2010,
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. },
author = {Castella, François, Chartier, Philippe, Faou, Erwan, Bayart, Dominique, Leplingard, Florence, Martinelli, Catherine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Optical device; Raman gain; Poisson system; integro-differential equations.; Lotka-Volterra system; Poisson brackets},
language = {eng},
month = {3},
number = {3},
pages = {457-475},
publisher = {EDP Sciences},
title = {Raman laser: mathematical and numerical analysis of a model},
url = {http://eudml.org/doc/194223},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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/194223
ER -

References

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  1. M. Achtenhagen, T. Chang and B. Nyman, Analysis of a multiple-pump Raman amplifiers. Appl. Phys. Lett.78 (2000) 1322–1324.  
  2. U. Ascher, R. Mattheij and R. Russel, Numerical Solution of Boundary Value for Ordinary Differential Equations. Prentice Hall, Englewood Cliffs (1988).  
  3. F. Castella, P. Chartier and E. Faou, Analysis of a Poisson system with boundary conditions. C. R. Acad. Sci. Paris, Sér. I336 (2003) 703–708.  
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  5. E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration Springer-Verlag 31Springer Ser. Comput. Math. Berlin (2002). Structure-preserving algorithms for ordinary differential equations.  
  6. H. Kidorf, K. Rottwitt, M. Nissov, M. Ma and E. Rabarijaona, Pump Interactions in a 100-nm Bandwidth Raman Amplifier. IEEE Photonics Technology Letters11 (1999) 530–532.  
  7. J. Pocholle, M. Papuchon, J. Raffy and E. Desurvire, Non linearities and optical amplification in single mode fibers. Revue Technique Thomson-CSF22 (1990) 187–268.  
  8. M. Rini, I. Christiani and V. Degiorgio, Numerical modeling and optimization of cascaded Raman fiber lasers. IEEE Journal of Quantum Electronics36 (2000) 1117–1122.  

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