TU Darmstadt / ULB / TUbiblio

Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides

Klindworth, Dirk ; Schmidt, Kersten ; Fliss, Sonia :
Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides.
[Online-Edition: https://www.sciencedirect.com/science/article/pii/S089812211...]
In: Comput. Math. Appl., 67 (4) S. 918-943.
[Artikel] , (2014)

Offizielle URL: 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.

Typ des Eintrags: Artikel
Erschienen: 2014
Autor(en): Klindworth, Dirk ; Schmidt, Kersten ; Fliss, Sonia
Titel: Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides
Sprache: Englisch
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.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: Comput. Math. Appl.
Band: 67
(Heft-)Nummer: 4
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:36
DOI: 10.1016/j.camwa.2013.03.005
Offizielle URL: https://www.sciencedirect.com/science/article/pii/S089812211...
Zusätzliche Informationen:

available as Matheon Preprint 1002

Export:

Optionen (nur für Redakteure)

Eintrag anzeigen Eintrag anzeigen