Finite element computation of grating scattering matrices and application to photonic crystal band calculations

Authors:
Kokou Dossou;Michael A. Byrne;Lindsay C. Botten
Affiliations:
Centre for Ultrahigh-Bandwidth, Devices for Optical Systems and Department of Mathematical Sciences, University of Technology, Sydney, Australia;Centre for Ultrahigh-Bandwidth, Devices for Optical Systems and Department of Mathematical Sciences, University of Technology, Sydney, Australia;Centre for Ultrahigh-Bandwidth, Devices for Optical Systems and Department of Mathematical Sciences, University of Technology, Sydney, Australia
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

We consider the calculation of the band structure and Bloch mode basis of two-dimensional photonic crystals, modelled as stacks of one-dimensional diffraction gratings. The scattering properties of each grating are calculated using an efficient finite element method (FEM) and allow the complete mode structure to be derived from a transfer matrix method. A range of numerical examples showing the accuracy, flexibility and utility of the method is presented.