Photonic crystal devices modelled as grating stacks: matrix generalizations of thin film optics

Abstract

A rigorous semi-analytic approach to the modelling of coupling, guiding and propagation in complex microstructures embedded in twodimensional photonic crystals is presented. The method, which is based on Bloch mode expansions and generalized Fresnel coefficients, is shown to be able to treat photonic crystal devices in ways which are analogous to those used in thin film optics with uniform media. Asymptotic methods are developed and exemplified through the study of a serpentine waveguide, a potential slow wave device.