Abstract
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.
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References
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).
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).
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.
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.
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Vol. 15 (Springer, New York, 1983).
H. Brezis, Analyse fonctionnelle. Théorie et applications (Masson, Paris, 1983).
G. Dahlquist and A. Björck, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974).
D. Givoli and J.B. Keller, Exact nonreflecting boundary conditions, J. Comput. Phys. 82 (1989) 172-192.
D. Gómez Pedreira, A numerical method for the computation of guided waves in integrated optics, Ph.D. thesis, Universidad de Santiago de Compostela (1999).
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).
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).
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).
P. Joly and C. Poirier, Mathematical analysis of electromagnetic open waveguides, RAIRO Modél. Math. Anal. Numér. 29 (1995) 505-575.
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).
D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).
R. Piessens and E. Donckert-Kapenga, QUADPACK, A Subroutine Package for Automatic Integration, Springer Series in Computational Mathematics, Vol. 1 (Springer, New York, 1980).
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.
A.W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
C. Vassallo, Optical Waveguide Concepts (Elsevier Science/North Holland, Amsterdam, 1991).
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Bermúdez, A., Gómez Pedreira, D. & Joly, P. A Hybrid Approach for the Computation of Guided Modes in Integrated Optics. Advances in Computational Mathematics 16, 229–261 (2002). https://doi.org/10.1023/A:1014454317209
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DOI: https://doi.org/10.1023/A:1014454317209