Radiation from a line source in a 3D wire media photonic crystal

The calculation of the radiation pattern of an antenna that is near or inside a periodic structure is a rather involved task. In fact, we must take into account the interaction of the antenna with a very large number of discontinuities in the medium (which may be air or dielectric implants, perfect electric conductor (PEC) inclusions, etc). A brute force numerical analysis is impracticable in most cases. We assume in our analysis that the photonic crystal is infinite. The radiation pattern of a short dipole embedded in an infinite 3-dimensional crystal is calculated. We compute the radiation pattern of an infinite electric line of current embedded in a 3-dimensional wire media crystal. This crystal is made of long thin PEC wires, which are distributed periodically in air. We note that although the source is inherently two-dimensional, the studied problem is not (because the crystal is not invariant in the direction of the line current).