Finite element modelling of photonic crystals

Hiett, B.P., Generowicz, J.M., Cox, S.J., Molinari, M., Beckett, D., Parker, G.J. and Thomas, K.S. (2001) Finite element modelling of photonic crystals. In, PREP 2001: Third conference on postgraduate research in electronics, photonics, communications and software : 9-11 April 2001,University of Keele, UK. Engineering and Physical Sciences Research Council, pp. 87-88.

Abstract

This paper presents an efficient finite element method (FEM) for computing spectra of photonic band gap materials. Such computations have traditionally been approached using plane wave expansion techniques. These have the disadvantages of being expensive in terms of computation and memory. By contrast, the FEM is considerably more efficient due mainly to the fact that the eigensystem matrices are very sparse. Furthermore, FEM operates on a real space representation of the discontinuous dielectric constants. An implementation of the method is described and it is used to compute the band structure for a variety of photonic crystal (PC) geometries. We compare our results with those obtained from other sources, including plane wave expansion techniques, finite difference (FD) methods and experimental data. The performance of the algorithm is also analysed in terms of memory and computational cost.

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