Equivalence of Magnetic Metamaterials and Composites in the View of Effective Medium Theories

The electromagnetic response of metamaterials is governed by the collective behavior of engineered electric and magnetic dipoles. Therefore metamaterials may be replaced by hypothetical composites of spherical particles embedded in a host material. The effective electric permittivity and magnetic permeability of such systems can be computed with high-frequency extension of the Maxwell-Garnett mixing rule. The validity of this assumption is discussed and the features of the model are presented by calculating the effective electromagnetic material parameters of a deep subwavelength spherical composite in three different ways: with the Maxwell-Garnett mixing rule, high-frequency mixing rule and directly extracted from transmission reflection data. Afterwards the developed theory is applied to find the parameters of a composite with similar magnetic response as a metamaterial built of split ring resonators or fishnet structures.