Revised homogenization for two-component metamaterial with non-magnetic metallic cylindrical inclusions

Electromagnetic response of the 2-D metamaterial as the regular lattice of infinitely long circular non-magnetic metallic inclusions periodically embedded in a host dielectric material was carried out in the frequency range up to THz frequencies. It has been shown that such a metamaterial behaves like an ultra-low index homogenous material in some frequency range containing the frequencies at which the electric and magnetic resonances are excited. The resonances give rise to the electric and magnetic dipole moments. Averaging of these dipole moments over the volumes of unit cell of the metamaterial enables to derive the expressions of complex effective relative permittivity and permeability of the metamaterial. In some partial cases, the derived expressions are rather very close to microwave approximations of the effective parameters obtained earlier by other authors for the frequencies up to GHz frequencies. Numerical validation of the derived effective parameters is also preformed by making the full-wave simulation using a finite-difference time-domain software.