Theory of dielectric photonic crystals sandwiched between parallel metal plates

Photonic crystals based on silicon-air-geometries sandwiched between parallel metal plates are studied theoretically. Compared with in-plane propagation in corresponding infinite-height photonic crystals, modes with one of the two possible polarizations are eliminated for small plate separations. Consequently, 2D photonic crystals that usually do not have a band gap for both polarizations possess a complete band gap in the sandwich geometry. A procedure for obtaining the maximum allowed photonic-crystal height between plates that preserves the in-plane band gap is described. The effect on the band gap of adding an air-gap or a silicon substrate to the photonic crystal structure between plates is also studied. Finally, it is shown that, for terahertz frequencies, a useful distance between metal plates is comparable to the thickness of thin silicon wafers, and that propagation losses are sufficiently small that the structures are of practical interest. We briefly discuss the numerical method that was used for calculating band diagrams and band gaps, which is based on a modification to the plane-wave-expansion method [R. D. Meade et. al., Phys. Rev. B 48, 8434 (1993)] based on an iterative search algorithm exploiting Fast Fourier Transforms for fast calculations.