Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals

We analytically calculate the spectra of plasma waves and electromagnetic waves (EMW’s) in metallic photonic crystals consisting of parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high-frequency regime $\omega \tau \gg 1,$ where τ is the relaxation time. The proposed analytical theory is based upon small parameters $f\ll 1,$ where f is the volume fraction of the metal, and $\mathrm{kR}\ll 1,$ where k is the wave vector and R is the radius of the cylinder. It is shown that there are five different branches of the EMW that cover all frequency ranges under consideration except one very small omnidirectional gap in the vicinity of the frequency of the surface plasmon. However, at some directions of propagation and polarizations the gap may be much larger. The reflection and refraction of the EMW are also considered. A general theory of refraction is proposed which is complicated by the spatial dispersion of the dielectric constant, and one particular geometry of an incident EMW is considered.