Abstract: The photonic band structure of 2D photonic crystals consisting of cylindrical dielectric rods on a square and on a triangular lattice is computed by a method which is commonly used in studying low-energy electron diffraction in conventional crystals. The matrices involved in the present method are substantially smaller than those required for the plane-wave method. Unlike the multiple-scattering method, a root searching procedure is not needed. In addition, with this method, the attenuation lengths for frequencies within the forbidden bands are computed automatically with the band structure calculation. Reflection and transmission characteristics of crystals of finite thicknesses are also computed. !17
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