Electromagnetic scattering from a PBG material excited by an electric linesource

A general procedure is presented to determine the fields scattered by a per iodic structure due to a complex excitation in terms of the structure's pla ne-wave response. Specifically, the scattered held from an electric line so urce over a semiinfinite metallo-dielectric photonic bandgap (PBG) material is described. An effective description for the artificial crystal's plane- wave response is used, consisting of angularly parameterized response funct ions, A methodology for analyzing the electromagnetic response of such a ma terial to a nonplane-wave excitation is provided, whereby a general complex excitation is spectrally decomposed into an integral over a continuous spe ctrum of homogeneous and inhomogeneous plane waves. An analytic solution fo r the scattering of each plane wave by the PEG material halfspace is then u tilized. The complete scattered field is given in a closed integral form, w hich is computed both numerically and in the asymptotic limit. The effect o f the PEG crystal half-space on the scattered field due to an electric line source is presented for frequencies that correspond, for a normally incide nt plane wave, to a transmission bandgap, a transmission band edge, and an antireflecting plateau, The focusing effects and electric- and magnetic-wal l behavior of the PEG crystal are demonstrated. The presented approach prom otes both the physical understanding of PEG material systems and the effici ency of the numerically modeling of these systems at frequencies beyond the quasi-static limit of the traditional effective medium theories.