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

Klindworth, Dirk and Schmidt, Kersten and 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) pp. 918-943.
[Article] , (2014)

Official URL: https://www.sciencedirect.com/science/article/pii/S089812211...

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.

Item Type: Article
Erschienen: 2014
Creators: Klindworth, Dirk and Schmidt, Kersten and Fliss, Sonia
Title: Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides
Language: English
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.

Journal or Publication Title: Comput. Math. Appl.
Volume: 67
Number: 4
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:36
DOI: 10.1016/j.camwa.2013.03.005
Official URL: https://www.sciencedirect.com/science/article/pii/S089812211...
Additional Information:

available as Matheon Preprint 1002

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