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

Fliss, Sonia and Klindworth, Dirk and Schmidt, Kersten (2015):
Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides.
In: BIT Numerical Mathematics, pp. 81-115, 55, (1), DOI: 10.1007/s10543-014-0521-1,
[Online-Edition: https://doi.org/10.1007/s10543-014-0521-1],
[Article]

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.

Item Type: Article
Erschienen: 2015
Creators: Fliss, Sonia and Klindworth, Dirk and Schmidt, Kersten
Title: Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides
Language: English
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.

Journal or Publication Title: BIT Numerical Mathematics
Volume: 55
Number: 1
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:19
DOI: 10.1007/s10543-014-0521-1
Official URL: https://doi.org/10.1007/s10543-014-0521-1
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