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

Authors:
Dirk Klindworth;Kersten Schmidt;Sonia Fliss
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2014

Citing 10
Cited 1

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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 super-cell 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.