Bloch wave analysis of vertical-cavity resonances in photonic crystal films

Summary form only given. We present some results of rigorous calculations for a photonic crystal film positioned between two semi-infinite regions of uniform refractive index, where the photonic crystal film itself is a triangular lattice of cylindrical holes etched into a medium having a higher refractive index than the semi-infinite regions. We start by considering a photonic crystal film of infinite thickness. Let the z axis be perpendicular to the surface of the film, and let the ´in-plane´ coordinates (parallel to the surface of the film) be (x,y).