Hyperbolic Medium of Finite-Length Wires

An artificial medium in the form of a cubic uniaxial photonic crystal (PC) with periodically arranged conducting wire cylinders in a dielectric matrix and oriented along the PC axis is considered. Permittivity ε ˜ of the matrix is assumed to be constant, while the permittivity of the cylinders is described by the Drude–Lorentz model. The homogenization of such a medium, the methods of its description, the role of dissipation and spatial dispersion (SD), as well as the possibility of obtaining a hyperbolic dispersion relation are considered. The ambiguity of the PC description with the help of effective material parameters and the introduction of such parameters are demonstrated, as well as the effect of dissipation and SD on the hyperbolicity property under investigation.