Efficient Analysis of Radiation from a Dipole Source in Woodpile EBG Structures

An efficient and rigorous approach to analyze the radiation from an electric dipole placed in 3-D woodpile electromagnetic bandgap material (EBG) structures consisting of layered periodic arrays of circular cylinders is presented. The response in the spectral domain of the woodpile EBGs excited by a dipole source is calculated using one-dimensional lattice sums, the 3-D transition matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The closed-form expression of the radiated field is rigorously obtained by a finite integral of the spectral response. Comparisons with the far fields calculated using reciprocity both with the present approach and with a fully independent commercial EM software package are presented showing excellent agreement with the proposed method and demonstrating the high computational efficiency of the semianalytical formalism.