TU Darmstadt / ULB / TUbiblio

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

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

Offizielle URL: https://doi.org/10.1007/s10543-014-0521-1

Kurzbeschreibung (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.

Typ des Eintrags: Artikel
Erschienen: 2015
Autor(en): Fliss, Sonia ; Klindworth, Dirk ; Schmidt, Kersten
Titel: Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides
Sprache: Englisch
Kurzbeschreibung (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.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: BIT Numerical Mathematics
Band: 55
(Heft-)Nummer: 1
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:19
DOI: 10.1007/s10543-014-0521-1
Offizielle URL: https://doi.org/10.1007/s10543-014-0521-1
Export:

Optionen (nur für Redakteure)

Eintrag anzeigen Eintrag anzeigen