Fliss, Sonia ; Klindworth, Dirk ; Schmidt, Kersten (2015)
Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides.
In: BIT Numerical Mathematics, 55 (1)
doi: 10.1007/s10543-014-0521-1
Artikel, Bibliographie
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 |
| Art des Eintrags: | Bibliographie |
| Titel: | Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides |
| Sprache: | Englisch |
| Publikationsjahr: | 1 März 2015 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | BIT Numerical Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 55 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s10543-014-0521-1 |
| URL / URN: | 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. |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 19 Nov 2018 21:19 |
| Letzte Änderung: | 19 Nov 2018 21:19 |
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