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

Please always quote using this URN:urn:nbn:de:0296-matheon-12007
  • 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.

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Metadaten
Author:Dirk Klindworth, Kersten Schmidt, Sonia Fliss
URN:urn:nbn:de:0296-matheon-12007
Referee:Frank Schmidt
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/03/12
Release Date:2013/03/12
Tag:Chebyshev interpolation; Dirichlet-to-Neumann map; Newton method; group velocity; high-order FEM; non-linear eigenvalue problem; photonic crystal wave-guide; super-cell method
Institute:Research Center Matheon
Project:D Optics and Electronics (Electronic and photonic devices) / D26 Asymptotic analysis of the wave-propagation in realistic photonic crystal wave-guides
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Zxx Applications to physics / 65Z05 Applications to physics
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Mxx Basic methods / 78M10 Finite element methods
Preprint Number:1002
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