Skip to Main content Skip to Navigation
Journal articles

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
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/hal-01113869
Contributor : Sonia Fliss <>
Submitted on : Friday, February 6, 2015 - 2:32:15 PM
Last modification on : Monday, June 15, 2020 - 12:00:33 PM

Identifiers

  • HAL Id : hal-01113869, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

371