Microscopic calculations of dielectric properties for hyperbolic metamaterials

We theoretically study macroscopic dielectric properties of hyperbolic metamaterials proceeding from microscopic description. The theory constructed gives the answer to the question “what properties should microscopic elements have in order to macroscopic system consisting of these elements would be a hyperbolic metamaterial.” Generalized Clausius–Mossotti relation as well as existing conditions for such metamaterials is obtained with help of the local field theory. The perpendicular and parallel components of the dielectric permittivity are found as functions of microscopic parameters of a single particle and a dielectric matrix.