An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber

Alain Bamberger; François Coron; Jean-Michel Ghidaglia

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 3, page 405-424
  • ISSN: 0764-583X

How to cite

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Bamberger, Alain, Coron, François, and Ghidaglia, Jean-Michel. "An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.3 (1987): 405-424. <http://eudml.org/doc/193507>.

@article{Bamberger1987,
author = {Bamberger, Alain, Coron, François, Ghidaglia, Jean-Michel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Helmholtz equation; convolution product; order of convergence; electric field; optical fiber; Beam Propagation Method; wave propagating},
language = {eng},
number = {3},
pages = {405-424},
publisher = {Dunod},
title = {An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber},
url = {http://eudml.org/doc/193507},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Bamberger, Alain
AU - Coron, François
AU - Ghidaglia, Jean-Michel
TI - An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 3
SP - 405
EP - 424
LA - eng
KW - Helmholtz equation; convolution product; order of convergence; electric field; optical fiber; Beam Propagation Method; wave propagating
UR - http://eudml.org/doc/193507
ER -

References

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  1. [1] A. BAMBERGER, F. CORON and J. M. GHIDAGLIA, Analyse de la B.P.M.,méthode de résolution approchée de l'équation d'Helmholtz dans une fibreoptique, modélisation, convergence et stabilité. Rapport interne de l'ÉcolePolytechnique 151, Palaiseau, France, 1986. 
  2. [2] J. T. BEALE and A. MAJDA, Rates of convergence for viscous splitting of the Navier-Stokes équations. Math. Comput. 37, 243-260 (1981). Zbl0518.76027MR628693
  3. [3] M. D. FEIT and J. A. FLECK, Light propagation in graded-index optical fibers, AppL Opt. 17, 3990-3998 (1978). 
  4. [4] R. A. FISCHER and W. K. BISCHEL, Numerical studies of the interplay betweenself phase modulation and dispersion for intense plane wave laser puises, J.Appl. Phys. 46, 4921-4934 (1975). 
  5. [5] A. FRIEDMAN, Partial differential équations, Holt Rinehart and Winston Inc., New York, 1969. Zbl0224.35002MR445088
  6. [6] J. L. LIONS, Quelques méthodes de résolution desproblèmes aux limites nonlinéaires, Dunod, Paris, 1969. Zbl0189.40603
  7. [7] J. L. LIONS and E. MAGENES, Nonhomogeneous boundary value problems andapplications, Springer, Berlin, 1972 (and Dunod, Paris 1968). Zbl0223.35039
  8. [8] L. SCHWARTZ, Théorie des distributions, Hermann, Paris, 1966. Zbl0149.09501MR209834
  9. [9] E. STEIN and G. WEISS, Fourier analysis in euclidian spaces, Princeton, 1971. 
  10. [10] R. TEMAM, Sur la stabilité et la convergence de la méthode des pas fractionnaires, Ann. Math. Pura. AppL LXXIV, 1968, p.191-380. Zbl0174.45804MR241838

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