Application of finite element methods to photonic crystal modelling
Application of finite element methods to photonic crystal modelling
Photonic Crystals (PCs) are materials with a periodically modulated dielectric constant, through which certain frequencies of electromagnetic radiation cannot propagate. The modes admitted by PCs can be investigated effectively using the finite element method with the assistance of the Floquet-Bloch theorem, by considering a unit cell of the material and imposing periodic boundary conditions. Along with the Dirichlet and metric matrices, a third type of elemental matrix emerges. The types of results that are of interest to photonic crystal manufacturers are introduced and presented; in this context, the benefits of using the subspace iteration method to solve the eigensystems are discussed. The performance of the algorithm is investigated with respect to mesh granularity and interpolation order.
crystals finite element analysis interpolation iterative methods matrix algebra optical materials permittivity photonic band gap Dirichlet matrices Floquet-Bloch theorem algorithm performance eigensystems electromagnetic radiation frequencies elemental matrix finite element method finite element methods interpolation order mesh granularity metric matrices periodic boundary conditions periodically modulated dielectric constant photonic band gap materials photonic crystal modelling subspace iteration method
293-296
Hiett, B.P.
244a4b4e-ac70-4a3c-a8ef-3474f5ef9f8c
Generowicz, J.M.
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Cox, S.J.
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Molinari, M.
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Beckett, D.H.
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Thomas, K.S.
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September 2002
Hiett, B.P.
244a4b4e-ac70-4a3c-a8ef-3474f5ef9f8c
Generowicz, J.M.
ecb61cdf-854c-4928-b71f-8e7708bf267b
Cox, S.J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
Molinari, M.
47944a31-9242-4dcf-a527-40309e104fbf
Beckett, D.H.
71fdbee9-30b4-4a11-accd-fee7b28f7257
Thomas, K.S.
b107015f-c7d9-42cc-b87b-207c49e5369a
Hiett, B.P., Generowicz, J.M., Cox, S.J., Molinari, M., Beckett, D.H. and Thomas, K.S.
(2002)
Application of finite element methods to photonic crystal modelling.
IEE Proceedings - Science, Measurement and Technology, 149 (5), .
(doi:10.1049/ip-smt:20020642).
Abstract
Photonic Crystals (PCs) are materials with a periodically modulated dielectric constant, through which certain frequencies of electromagnetic radiation cannot propagate. The modes admitted by PCs can be investigated effectively using the finite element method with the assistance of the Floquet-Bloch theorem, by considering a unit cell of the material and imposing periodic boundary conditions. Along with the Dirichlet and metric matrices, a third type of elemental matrix emerges. The types of results that are of interest to photonic crystal manufacturers are introduced and presented; in this context, the benefits of using the subspace iteration method to solve the eigensystems are discussed. The performance of the algorithm is investigated with respect to mesh granularity and interpolation order.
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hiett_AppFEMinPCxMod_MST_2002_p293-296.pdf
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Published date: September 2002
Keywords:
crystals finite element analysis interpolation iterative methods matrix algebra optical materials permittivity photonic band gap Dirichlet matrices Floquet-Bloch theorem algorithm performance eigensystems electromagnetic radiation frequencies elemental matrix finite element method finite element methods interpolation order mesh granularity metric matrices periodic boundary conditions periodically modulated dielectric constant photonic band gap materials photonic crystal modelling subspace iteration method
Identifiers
Local EPrints ID: 22113
URI: http://eprints.soton.ac.uk/id/eprint/22113
ISSN: 1350-2344
PURE UUID: 6263411c-d48f-4e45-b4be-adb5e42bf2cc
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Date deposited: 22 Mar 2006
Last modified: 15 Mar 2024 06:35
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Contributors
Author:
B.P. Hiett
Author:
J.M. Generowicz
Author:
M. Molinari
Author:
D.H. Beckett
Author:
K.S. Thomas
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