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A theory of the homogenization of a certain class of metamaterials is stated. These metamaterials are volume lattices of electric and magnetic dipoles that are resonant with frequencies that are considerably lower than that of the first Bragg resonance of the lattice. It was shown that, for plates of a metamaterial, which are described by bulk material parameters, transition layers play an important role, and the known Drude notion of transition layers is significantly revised. The paper also discusses a more widespread method of determining the material parameters of metamaterials based on the extraction of the refractive index and the characteristic impedance from the scattering matrix of the plate of the metamaterial. The physical meaning of the material parameters obtained in this way is clarified, and the concept of Bloch lattices related to it is discussed. It is shown that the bulk material parameters and the parameters of transition layers can also be extracted from components of the scattering matrix of plates.
Constantin Simovski (Sun,) studied this question.