Application of finite element methods to photonic crystal modelling

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 & Technology, 149, (5), pp. 293-296. (doi:10.1049/ip-smt:20020642).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1049/ip-smt:20020642
ISSNs: 1350-2344 (print)
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
ePrint ID: 22113
Date :
Date Event
September 2002Published
Date Deposited: 22 Mar 2006
Last Modified: 16 Apr 2017 22:52
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