Transmittance and Bragg reflectivity of two-dimensional photonic lattices

Abstract

A general method based on the plane-wave expansion for calculating the transmittance and the Bragg reflectivity of two-dimensional photonic lattices is presented. According to this method, the transmission and the Bragg reflection spectra of a triangular and a square lattice of circular rods were numerically calculated for two independent polarizations. In addition to the opaque frequency ranges accompanied by the photonic band gaps, the existence of an uncoupled mode which cannot be excited by an external plane wave, a large amount of energy transfer to the Bragg waves, and pronounced interference structures were found. These three properties are not accounted for by the band calculation and the theoretical investigation which fully allows for the boundary condition at the surface of a specimen is necessary for proper understanding of experimental observations.