Approaches to the Homogenization of Periodical Metamaterials

Various metamaterials, very actively studied in recent years, usually consist of metal inclusions of complex shapes periodically arranged in space. If the period of the lattice and the dimensions of the inclusions are small compared with the wavelength, the material is usually considered as an effectively homogeneous medium characterized by effective material parameters (permittivity and permeability). The shape and dimensions of inclusions define the electromagnetic response, which may be rather exotic (negative material parameters, for example) and resonant response. Modelling of typical metamaterial samples with effective material parameters is a non-trivial task, where one has to face several complications as compared with the "usual" materials. These complications as well as various possible approaches to effective medium modelling will be discussed in this review presentation