Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T11:03:32.502Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing guided modes for an unbounded stratified medium in integrated optics

Published online by Cambridge University Press:  15 April 2002

Fabrice Mahé
Fabrice Mahé*
Affiliation:
IRMAR, Campus de Beaulieu, Université de Rennes 1, 35042 Rennes Cedex, France. ([email protected])
Get access

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.

Keywords

Finite element methodexact boundary conditionunbounded domainstratified mediumguided modesopticsseries expansion.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 799 - 824
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A.S. Bonnet, Analyse mathématique de la propagation de modes guidés dans les fibres optiques. Ph.D. thesis, University of Paris VI (1988).
Bonnet-BenDhia, A.S., Caloz, G., Dauge, M. and Mahé, F., Study at high frequencies of a stratified waveguide. IMA J. Appl. Math. 66 (2001) 231-257. CrossRef
Bonnet-BenDhia, A.S., Caloz, G. and Mahé, F., Guided modes of integrated optical guides. A mathematical study. IMA J. Appl. Math. 60 (1998) 225-261. CrossRef
Bonnet-BenDhia, A.S. and Gmati, N., Spectral approximation of a boundary condition for an eigenvalue problem. SIAM J. Numer. Anal. 32 (1995) 1263-1279. CrossRef
Bonnet-BenDhia, A.S. and Joly, P., Mathematical analysis of guided water waves. SIAM J. Appl. Math. 53 (1993) 1507-1550.
Bonnet-BenDhia, A.S. and Mahé, F., A guided mode in the range of the radiation modes for a rib waveguide. J. Optics 28 (1997) 41-43.
N. Gmati, Guidage et diffraction d'ondes en milieu non borné. Ph.D. thesis, University of Paris VI (1992).
Jami, A. and Lenoir, M., A variational formulation for exterior problems in linear hydrodynamics. Comput. Methods. Appl. Mech. Engrg. 16 (1978) 314-359.
M. Koshiba, Optical waveguide theory by the finite element method. KTC Scientific Publishers, Tokyo (1992).
Lenoir, M. and Tounsi, A., The localized finite element method and its applications to the two-dimensional sea-keeping problem. SIAM J. Numer. Anal. 25 (1988) 729-752. CrossRef
F. Mahé, Étude mathématique et numérique de la propagation d'ondes électromagnétiques dans les microguides de l'optique intégrée. Ph.D. thesis, University of Rennes I, France (1993).
D. Martin, Guide d'utilisation du code Mélina, IRMAR, University of Rennes I, France (1997).e-mail: http://www.maths.univ-rennes1.fr/~dmartin
B.M.A. Rahman and J.B. Davies, Finite-element analysis of optical and microwave waveguide problems. IEEE Trans. Microwave Theory Tech. MTT-32(1) (1984).
M. Reed and B. Simon, Analysis of Operators. IV: Analysis of operators. Academic Press, New York, San Francisco, London (1978).
A.W. Snyder and J.D. Love, Optical waveguide theory. Chapman and Hall, London (1983).
M. Schechter, Spectra of partial differential operators. North-Holland, Amsterdam (1971).
C. Vassalo, Théorie des guides d'ondes électromagnétiques. Tomes 1 et 2. Eyrolles Éditions and CNET-ENST, Paris (1985).
J.H. Wilkinson, The Algebraic Eigenvalue Problem. Clarenton Press, Oxford (1965).