Photonic band structures of two-dimensional systems containing metallic components.

Abstract

By use of the plane-wave method, we calculate the photonic band structure for electromagnetic waves of E and H polarization propagating in a system consisting of an infinite array of identical, infinitely long, parallel, metal cylinders of circular cross section, embedded in vacuum, whose intersection with a perpendicular plane forms a simple square or triangular lattice. The dielectric function of the metal from which the cylinders are formed has the simple, free-electron form \ensuremath{\epsilon}(\ensuremath{\omega})=1-(${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}^{2}$/${\mathrm{\ensuremath{\omega}}}^{2}$), where ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ is the plasma frequency of the conduction electrons. For electromagnetic waves of both polarizations, the problem of obtaining the photonic band structure is reduced to the solution of a standard eigenvalue problem despite the frequency dependence of the dielectric constant of the two-dimensional, periodic system. For electromagnetic waves of E polarization the photonic band structure at low filling fractions of the metallic cylinders is a slightly perturbed version of the dispersion curves of electromagnetic waves in vacuum, except for the appearance of a band gap below the lowest frequency band, whose width increases with increasing filling fraction. A band gap between the first and second bands is present in the photonic band structure of the square lattice, but no band gap is found in the band structure of the triangular lattice. In the case of electromagnetic waves of H polarization the photonic band structure at low filling fractions of the metallic cylinders is also, for the most part, a slightly perturbed version of the dispersion curves of electromagnetic waves in vacuum, but possesses additional, nearly dispersionless, bands in the frequency range \ensuremath{\omega}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$. A possible origin of these flat bands is described.