Electromagnetic modelling of propagation in photonic crystal lattices

Abstract

We outline a theory for electromagnetic scattering by cylinder gratings in conical incidence, based on a multipole method. The theory, and its numerical implementation; can be applied to photonic crystaLs consisting of stacks of one-dimensional gratings. One such configuration is the woodpile structure, consisting of layers of crossed rods with a stacking sequence, which repeats itself every four layers. We show how to use the plane wave scattering matrices of the layers in combination with Bloch's theorem to determine the band structure of the photonic crystal from the solution of an eigenvalue problem. We deduce the spectral properties of the woodpile layering, and show transmission spectra and band diagrams for woodpile photonic crystals.