Klindworth, Dirk ; Schmidt, Kersten ; Fliss, Sonia (2014)
Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides.
In: Comput. Math. Appl., 67 (4)
doi: 10.1016/j.camwa.2013.03.005
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
The computation of guided modes in photonic crystal wave-guides is a key issue in the process of designing devices in photonic communications. Existing methods, such as the super-cell method, provide an efficient computation of well-confined modes. However, if the modes are not well-confined, the modelling error of the super-cell method becomes prohibitive and advanced methods applying transparent boundary conditions for periodic media are needed. In this work we demonstrate the numerical realization of a recently proposed Dirichlet-to-Neumann approach and compare the results with those of the supercell method. For the resulting non-linear eigenvalue problem we propose an iterative solution based on Newton's method and a direct solution using Chebyshev interpolation of the non-linear operator. Based on the Dirichlet-to-Neumann approach, we present a formula for the group velocity of guided modes that can serve as an objective function in the optimization of photonic crystal wave-guides.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2014 |
| Autor(en): | Klindworth, Dirk ; Schmidt, Kersten ; Fliss, Sonia |
| Art des Eintrags: | Bibliographie |
| Titel: | Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides |
| Sprache: | Englisch |
| Publikationsjahr: | März 2014 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Comput. Math. Appl. |
| Jahrgang/Volume einer Zeitschrift: | 67 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1016/j.camwa.2013.03.005 |
| URL / URN: | https://www.sciencedirect.com/science/article/pii/S089812211... |
| Kurzbeschreibung (Abstract): | The computation of guided modes in photonic crystal wave-guides is a key issue in the process of designing devices in photonic communications. Existing methods, such as the super-cell method, provide an efficient computation of well-confined modes. However, if the modes are not well-confined, the modelling error of the super-cell method becomes prohibitive and advanced methods applying transparent boundary conditions for periodic media are needed. In this work we demonstrate the numerical realization of a recently proposed Dirichlet-to-Neumann approach and compare the results with those of the supercell method. For the resulting non-linear eigenvalue problem we propose an iterative solution based on Newton's method and a direct solution using Chebyshev interpolation of the non-linear operator. Based on the Dirichlet-to-Neumann approach, we present a formula for the group velocity of guided modes that can serve as an objective function in the optimization of photonic crystal wave-guides. |
| Zusätzliche Informationen: | available as Matheon Preprint 1002 |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 19 Nov 2018 21:36 |
| Letzte Änderung: | 19 Nov 2018 21:36 |
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