Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides
Please always quote using this URN:urn:nbn:de:0296-matheon-12525
- In this work we present a complete algorithm for the exact computation of the guided mode band structure in photonic crystal (PhC) wave-guides. In contrast to the supercell method, the used approach does not introduce any modelling error and is hence independent of the confinement of the modes. The approach is based on Dirichlet-to-Neumann (DtN) transparent boundary conditions that yield a nonlinear eigenvalue problem. For the solution of this nonlinear eigenvalue problem we present a direct technique using Chebyshev interpolation that requires a band gap calculation of the PhC in advance. For this band gap calculation –- we introduce as a very efficient tool –- a Taylor expansion of the PhC band structure. We show that our algorithm –- like the supercell method –- converges exponentially, however, its computational costs –- in comparison to the supercell method –- only increase moderately since the size of the matrix to be inverted remains constant.
Author: | Klindworth Dirk, Kersten Schmidt |
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URN: | urn:nbn:de:0296-matheon-12525 |
Referee: | Frank Schmidt |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2013/10/30 |
Release Date: | 2013/10/30 |
Institute: | Technische Universität Berlin |
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: | 1038 |