Scattering-method calculation of propagation modes in two-dimensional photonic crystals of finite thickness

We present a scattering-method calculation of electromagnetic wave propagat ion modes inside dielectric waveguides of finite thickness. The algorithm i s based on an expansion into propagation eigenmodes within the layer with a ppropriate wave matching at the boundaries. It is applicable to waveguide s tructures made of layers of dielectric material where the structure of each layer is periodic in two dimensions but is translationally invariant in th e third dimension. The method is useful for extracting such information as the effect of the finite thickness on the band structure, the influence of cladding layers and the substrate on dispersion, and the escape rates of ra diative modes. As a demonstration, we present the dispersion relations for an Al0.1Ga0.9As photonic-crystal core layer with a triangular lattice of cy lindrical perforations, either placed on top of a uniform alpha -Al2O3 subs trate or suspended freely in the air. (C) 2001 Optical Society of America.