On 2D photonic crystals and the shaping of radiation diagrams

Photonic band-gap materials have been widely used to mold the flow of light. The scaling property of crystals has allowed studying their behaviour at microwaves, where periodic structures have been profitably adopted to shape the radiation pattern of low-directivity antennas. In particular spatial filters can be achieved using two-dimensional periodicity in two different manners: the one relies on the excitation of a proper Bloch wave at the edge of the band-gap, whereas the other exploits the interference between standing waves in a crystal defect. Strengths and weaknesses of the two mechanisms are discussed comparing the radiative and electrical parameters of several optimized geometries. These are made by circular dielectric rods, arranged in either square or triangular lattices, and fed by a current wire radiating a TM-polarized cylindrical wave. The method using the forbidden band is shown to achieve the highest directivities for low profile structures, whereas the other mechanism, besides being more efficient, is more suitable when antennas consist of few cylinders per row. Suggestions for an experimental validation of drawn conclusions are given.