Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

top
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

top

Mahé, Fabrice. "Computing guided modes for an unbounded stratified medium in integrated optics." ESAIM: Mathematical Modelling and Numerical Analysis 35.4 (2010): 799-824. <http://eudml.org/doc/197582>.

@article{Mahé2010,
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},
keywords = {Finite element method; exact boundary condition; unbounded domain; stratified medium; guided modes; optics; series expansion.; finite element method; series expansion},
language = {eng},
month = {3},
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/197582},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Mahé, Fabrice
TI - Computing guided modes for an unbounded stratified medium in integrated optics
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
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.; finite element method; series expansion
UR - http://eudml.org/doc/197582
ER -

References

top
  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. 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
  3. A.S. Bonnet-BenDhia, G. Caloz and F. Mahé, Guided modes of integrated optical guides. A mathematical study. IMA J. Appl. Math.60 (1998) 225-261.  Zbl0914.35130
  4. A.S. Bonnet-BenDhia and N. Gmati, Spectral approximation of a boundary condition for an eigenvalue problem. SIAM J. Numer. Anal.32 (1995) 1263-1279.  Zbl0834.65104
  5. A.S. Bonnet-BenDhia and P. Joly, Mathematical analysis of guided water waves. SIAM J. Appl. Math.53 (1993) 1507-1550.  Zbl0787.76007
  6. A.S. Bonnet-BenDhia and F. Mahé, A guided mode in the range of the radiation modes for a rib waveguide. J. Optics28 (1997) 41-43.  
  7. N. Gmati, Guidage et diffraction d'ondes en milieu non borné. Ph.D. thesis, University of Paris VI (1992).  
  8. A. Jami and M. Lenoir, A variational formulation for exterior problems in linear hydrodynamics. Comput. Methods. Appl. Mech. Engrg.16 (1978) 314-359.  Zbl0392.76020
  9. M. Koshiba, Optical waveguide theory by the finite element method. KTC Scientific Publishers, Tokyo (1992).  
  10. M. Lenoir and A. Tounsi, The localized finite element method and its applications to the two-dimensional sea-keeping problem. SIAM J. Numer. Anal.25 (1988) 729-752.  Zbl0656.76008
  11. 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).  
  12. D. Martin, Guide d'utilisation du code Mélina, IRMAR, University of Rennes I, France (1997).e-mail: http://www.maths.univ-rennes1.fr/~dmartin  
  13. 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).  
  14. M. Reed and B. Simon, Analysis of Operators. IV: Analysis of operators. Academic Press, New York, San Francisco, London (1978).  Zbl0401.47001
  15. A.W. Snyder and J.D. Love, Optical waveguide theory. Chapman and Hall, London (1983).  
  16. M. Schechter, Spectra of partial differential operators. North-Holland, Amsterdam (1971).  
  17. C. Vassalo, Théorie des guides d'ondes électromagnétiques. Tomes 1 et 2. Eyrolles Éditions and CNET-ENST, Paris (1985).  
  18. J.H. Wilkinson, The Algebraic Eigenvalue Problem. Clarenton Press, Oxford (1965).  Zbl0258.65037

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.