Out-of-plane band structure of a two-dimensional dispersive photonic crystal

We calculated the out-of-plane band structure of a two-dimensional dispersive photonic crystal (PC). To achieve this goal, the plane wave expansion method was implemented in conjunction with a numerical algorithm, the dispersive photonic crystal iterative method. The PC is an array of circular cross-sectional dispersive MgO Lorentz single-pole rods in a square lattice. The frequency bands are calculated starting at Γ as a function of the oblique component of the wave vector. For the lowest frequencies, it was found that the modes bend drastically to the horizon as the dielectric constant ϵ(ω) is increased to a very positive value. For frequencies above the longitudinal optical phonon circular frequency, where ϵ(ω) has very low positive values, the expected degeneration occurs in the transparency window, and a line of modes behaves close to the line of light.