Analysis of two-dimensional electromagnetic crystals consisting of multilayered periodic arrays of circular cylinders

This paper describes a method of efficient and accurate analysis of the problems of scattering and guiding of wave by two-dimensional electromagnetic crystals consisting of multilayered periodic arrays of circular cylinders, making use of the Lattice Sum, the T-matrix, the generalized reflection matrix, and the scattering matrix. According to this method, various characteristics of two-dimensional electromagnetic crystals can be calculated by a simple matrix algorithm. The method can handle cases in which several cylinders of different sizes and materials are contained within the unit cell of the array. Although the periodic spacing of the cylinders in the array must be fixed for all array layers, the size and material of the cylinders in the array and the distance between the array layers can be chosen freely.