Advances in Computational Mathematics

, Volume 16, Issue 2–3, pp 229–261 | Cite as

A Hybrid Approach for the Computation of Guided Modes in Integrated Optics

  • A. Bermúdez
  • D. Gómez Pedreira
  • P. Joly


In this work, we are interested in the numerical approximation of an eigenvalue problem arising from the computation of guided modes in integrated optics waveguides which are particular cases of open waveguides.

integrated optics guided modes open electromagnetic waveguides numerical methods mixed elements hybrid methods 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).Google Scholar
  2. [2]
    A.S. Bonnet-Ben Dhia, Analyse mathématique de la propagation de modes guidés dans les fibres optiques, Technical Report 229, Ecole Nationale Supérieure de Techniques Avancées (1989).Google Scholar
  3. [3]
    A.S. Bonnet-Ben Dhia, G. Caloz and F. Mahé, Guided modes of integrated optical guides. A mathematical study, IMA J. Appl. Math. 60 (1998) 225-261.Google Scholar
  4. [4]
    A. S. Bonnet-Ben Dhia and F. Mahé, A guided mode in the range of the radiation modes for a rib waveguide, J. Opt. 28 (1997) 41-43.Google Scholar
  5. [5]
    F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Vol. 15 (Springer, New York, 1983).Google Scholar
  6. [6]
    H. Brezis, Analyse fonctionnelle. Théorie et applications (Masson, Paris, 1983).Google Scholar
  7. [7]
    G. Dahlquist and A. Björck, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974).Google Scholar
  8. [8]
    D. Givoli and J.B. Keller, Exact nonreflecting boundary conditions, J. Comput. Phys. 82 (1989) 172-192.Google Scholar
  9. [9]
    D. Gómez Pedreira, A numerical method for the computation of guided waves in integrated optics, Ph.D. thesis, Universidad de Santiago de Compostela (1999).Google Scholar
  10. [10]
    D. Gómez Pedreira and P. Joly, Mathematical analysis of a method to compute guided waves in integrated optics, Technical Report 3933, Institut National de Recherche en Informatique et Automatique (I.N.R.I.A) (2000).Google Scholar
  11. [11]
    D. Gómez Pedreira and P. Joly, A method for computing guided waves in integrated optics. Part 1: Mathematical analysis, SIAM J. Numer. Anal. 39(2) (2002).Google Scholar
  12. [12]
    D. Gómez Pedreira and P. Joly, A method for computing guided waves in integrated optics. Part 2: Numerical approximation and error analysis, to appear in SIAM J. Numer. Anal. 39(5) (2002).Google Scholar
  13. [13]
    P. Joly and C. Poirier, Mathematical analysis of electromagnetic open waveguides, RAIRO Modél. Math. Anal. Numér. 29 (1995) 505-575.Google Scholar
  14. [14]
    F. Mahé, Etude mathématique et numérique de la propagation d'ondes electromagnétiques dans les microguides de l'optique intégrée, Ph.D. thesis, Université de Rennes I (1993).Google Scholar
  15. [15]
    D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).Google Scholar
  16. [16]
    R. Piessens and E. Donckert-Kapenga, QUADPACK, A Subroutine Package for Automatic Integration, Springer Series in Computational Mathematics, Vol. 1 (Springer, New York, 1980).Google Scholar
  17. [17]
    J.E. Roberts and J.M. Thomas, Mixed and hybrid finite element methods, in: Handbook of Numerical Analysis, eds. P.G. Ciarlet and J.L. Lions (Elsevier Science/North-Holland, Amsterdam, 1991) pp. 523-639.Google Scholar
  18. [18]
    A.W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).Google Scholar
  19. [19]
    C. Vassallo, Optical Waveguide Concepts (Elsevier Science/North Holland, Amsterdam, 1991).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • A. Bermúdez
    • 1
  • D. Gómez Pedreira
    • 1
  • P. Joly
    • 2
  1. 1.Departamento de Matemática AplicadaUniversidad de Santiago de CompostelaSpain
  2. 2.INRIA-RocquencourtFrance

Personalised recommendations