Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 4, page 799-824
  • ISSN: 0764-583X

Abstract

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We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem is scalar and 2-dimensional.

How to cite

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Mahé, Fabrice. "Computing guided modes for an unbounded stratified medium in integrated optics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 799-824. <http://eudml.org/doc/194074>.

@article{Mahé2001,
abstract = {We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem is scalar and 2-dimensional.},
author = {Mahé, Fabrice},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element method; exact boundary condition; unbounded domain; stratified medium; guided modes; optics; series expansion},
language = {eng},
number = {4},
pages = {799-824},
publisher = {EDP-Sciences},
title = {Computing guided modes for an unbounded stratified medium in integrated optics},
url = {http://eudml.org/doc/194074},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Mahé, Fabrice
TI - Computing guided modes for an unbounded stratified medium in integrated optics
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 4
SP - 799
EP - 824
AB - We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem is scalar and 2-dimensional.
LA - eng
KW - finite element method; exact boundary condition; unbounded domain; stratified medium; guided modes; optics; series expansion
UR - http://eudml.org/doc/194074
ER -

References

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  1. [1] A.S. Bonnet, Analyse mathématique de la propagation de modes guidés dans les fibres optiques. Ph.D. thesis, University of Paris VI (1988). 
  2. [2] A.S. Bonnet-BenDhia, G. Caloz, M. Dauge and F. Mahé, Study at high frequencies of a stratified waveguide. IMA J. Appl. Math. 66 (2001) 231–257. Zbl0986.78014
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