Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides

Sonia Fliss 1 Dirk Klindworth 2 Kersten Schmidt 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides.
Type de document :
Article dans une revue
BIT Numerical Mathematics, Springer Verlag, 2014, 55 (1), pp.35
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https://hal.inria.fr/hal-01113869
Contributeur : Sonia Fliss <>
Soumis le : vendredi 6 février 2015 - 14:32:15
Dernière modification le : jeudi 11 janvier 2018 - 06:20:23

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  • HAL Id : hal-01113869, version 1

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Sonia Fliss, Dirk Klindworth, Kersten Schmidt. Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides. BIT Numerical Mathematics, Springer Verlag, 2014, 55 (1), pp.35. 〈hal-01113869〉

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