The field transmitted into a PBG crystal due to an electric line source

The analytic solution for the field transmitted from an electric line source into a photonic bandgap (PBG) crystal half-space is presented. This solution demonstrates the extension of the effective functional description of PBG crystals of Kyriazidou, Contopanoagos, Merrill and Alexopoulos (see IEEE Trans. Ant. Prop. 1998) to a description of a PBG crystal excited by a non-plane wave source. The integral solution is solved numerically, compared with the exact solution of Wait (1962) for the limiting case of a homogeneous dielectric half-space, and plotted to demonstrate the field penetration into the PBG crystal both within and without its bandgaps.