Can Isotropic Negative Permittivity ε and Permeability μ Metamaterials Exist?

Abstract

An attempt is made to answer the question posed in the title. Periodic metamaterials, namely, cubic photonic crystals with dielectric inclusions (including those with metallic properties), methods for introducing material equations (homogenization), and the possibility of describing metamaterials by scalar permeability and permittivity (or two scalar parameters) including negative values of their real parts, are considered. For photonic crystals, the Landau conclusion about the absence of high-frequency (optical) magnetic properties is confirmed. In particular, negative values of magnetic permeability or any of its components are impossible. Configurations of metamaterials with almost isotropic properties are presented without regard for spatial dispersion.