Klindworth, Dirk ; Schmidt, Kersten (2014)
Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides.
In: IEEE Trans. Magn., 50 (2)
doi: 10.1109/TMAG.2013.2285412
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
In this work we present a complete algorithm for the exact computation of the guided mode band structure in photonic crystal (PhC) wave-guides. In contrast to the supercell method, the used approach does not introduce any modelling error and is hence independent of the confinement of the modes. The approach is based on Dirichlet-to-Neumann (DtN) transparent boundary conditions that yield a nonlinear eigenvalue problem. For the solution of this nonlinear eigenvalue problem we present a direct technique using Chebyshev interpolation that requires a band gap calculation of the PhC in advance. For this band gap calculation we introduce as a very efficient tool a Taylor expansion of the PhC band structure. We show that our algorithm like the supercell method converges exponentially, however, its computational costs in comparison to the supercell method only increase moderately since the size of the matrix to be inverted remains constant.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2014 |
| Autor(en): | Klindworth, Dirk ; Schmidt, Kersten |
| Art des Eintrags: | Bibliographie |
| Titel: | Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides |
| Sprache: | Englisch |
| Publikationsjahr: | Februar 2014 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | IEEE Trans. Magn. |
| Jahrgang/Volume einer Zeitschrift: | 50 |
| (Heft-)Nummer: | 2 |
| DOI: | 10.1109/TMAG.2013.2285412 |
| Kurzbeschreibung (Abstract): | In this work we present a complete algorithm for the exact computation of the guided mode band structure in photonic crystal (PhC) wave-guides. In contrast to the supercell method, the used approach does not introduce any modelling error and is hence independent of the confinement of the modes. The approach is based on Dirichlet-to-Neumann (DtN) transparent boundary conditions that yield a nonlinear eigenvalue problem. For the solution of this nonlinear eigenvalue problem we present a direct technique using Chebyshev interpolation that requires a band gap calculation of the PhC in advance. For this band gap calculation we introduce as a very efficient tool a Taylor expansion of the PhC band structure. We show that our algorithm like the supercell method converges exponentially, however, its computational costs in comparison to the supercell method only increase moderately since the size of the matrix to be inverted remains constant. |
| Freie Schlagworte: | Chebyshev approximation;convergence of numerical methods;eigenvalues and eigenfunctions;interpolation;optical waveguides;photonic band gap;photonic crystals;Chebyshev interpolation;Dirichlet-to-Neumann transparent boundary conditions;PhC band structure;Taylor expansion;bandgap calculation;convergence;guided mode band structure;nonlinear eigenvalue problem;photonic crystal waveguides;Boundary conditions;Chebyshev approximation;Eigenvalues and eigenfunctions;Interpolation;Photonic band gap;Taylor series;Boundary conditions;eigenvalues and eigenfunctions;finite-element methods;nonlinear equations;photonic crystals (PhCs) |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 19 Nov 2018 21:32 |
| Letzte Änderung: | 19 Nov 2018 21:32 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum