Closed-form expressions of local effective bianisotropic constitutive parameters for reciprocal metamaterials

A straightforward approach is proposed to retrieve the local effective electromagnetic constitutive parameters of reciprocal bianisotropic metamaterials. The derivation is based on the Floquet representation of the field in periodic arrays and assumes that the metamaterial can be described by a nonlocal spatially dispersive generalized dielectric function incorporating all the polarization effects, including artificial magnetism, bianisotropy, and higher-order spatial dispersion effects. Closed-form expressions that directly relate the local bianisotropic model parameters to the nonlocal generalized effective permittivity are developed. The proposed formulas provide a homogenized description of the metamaterials that takes into account implicit weak spatial dispersion effects in terms of local nondispersive permittivity, permeability and magnetoelectric coupling parameters. Numerical examples are presented to demonstrate the applicability of these formulas for the retrieval of effective parameters of metamaterials with different types of lattices and inclusions.