Photonic band gap in thin wire metamaterials

We investigate the band structure of a class of photonic crystals made from only thin wires. Using a different method, we demonstrate that a complete photonic band gap is possible for such materials. Band gap materials normally consist of space filling dielectric or metal, whereas thin wires occupy a very small fraction of the volume. We show that this is related to the large increase in scattering at the Brillouin zone boundary. The method we developed brings together the calculation techniques in three different fields. The first is the calculation of scattering from periodic, tilted antennas, which we improve upon. The second is the standard technique for frequency selective surface design. The third is obtained directly from low energy electron diffraction theory. Good agreements with experiments for left handed materials, negative materials, and frequency selective surfaces are demonstrated.