Dielectric Slab Photonic Crystals Containing Metallic Components for E Polarization Mode

Abstract

By using plane wave expansion method, we calculated the photonic band structure of metal cylinders in a
dielectric medium. The photonic crystal is an identical, symmetrical structure with an infinite array of metallic
rods. Arrangement of the metallic rods used is square lattice. The dielectric function of the metal from which the
cylinders are formed has a simple, free electron form  where ?p is the plasma frequency of the
conducting electron. We manage to show the band structure of the square lattice. We found the relation between
the band gap size and the filling fraction for some widely used material. For an example, FR-4, silicon, resin,
teflon etc. The relation between the band gap size and the dielectric constant of the medium was studied.