no. 3
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
Keywords: 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 
@article{M2AN_2004__38_3_457_0,
     author = {Castella, Fran\c{c}ois and Chartier, Philippe and Faou, Erwan and Bayart, Dominique and Leplingard, Florence and Martinelli, Catherine},
     title = {Raman laser : mathematical and numerical analysis of a model},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {457--475},
     year = {2004},
     publisher = {EDP Sciences},
     volume = {38},
     number = {3},
     doi = {10.1051/m2an:2004022},
     mrnumber = {2075755},
     zbl = {1078.78012},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an:2004022/}
}
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: Modélisation mathématique et analyse numérique
PY  - 2004
SP  - 457
EP  - 475
VL  - 38
IS  - 3
PB  - EDP Sciences
UR  - https://www.numdam.org/articles/10.1051/m2an:2004022/
DO  - 10.1051/m2an:2004022
LA  - en
ID  - M2AN_2004__38_3_457_0
ER  - 
%0 Journal Article
%A Castella, François
%A Chartier, Philippe
%A Faou, Erwan
%A Bayart, Dominique
%A Leplingard, Florence
%A Martinelli, Catherine
%T Raman laser : mathematical and numerical analysis of a model
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2004
%P 457-475
%V 38
%N 3
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/m2an:2004022/
%R 10.1051/m2an:2004022
%G en
%F M2AN_2004__38_3_457_0
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

[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). | Zbl | MR

[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. | Zbl

[4] G. Golub and C. Van Loan, Matrix Computations. The Johns Hopkins University Press (1989). | Zbl | MR

[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. | Zbl | MR

[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] 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] 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.

Cité par Sources :