Local bianisotropic effective parameters formulas for reciprocal metamaterials

Summary form only given. The emphasis placed on the novel properties and application potential of metamaterials in recent years has increased research interest in understanding the interaction between these composite structures and electromagnetic radiation. Such an interaction can be conveniently characterized using homogenization methods, which describe metamaterials as bulk homogeneous materials with certain effective parameters. In contrast to natural materials, the size of the lattice constant in these composite structures is typically only moderately smaller than the wavelength and consequently the derivation of the homogenized description must duly take into account spatial dispersion effects. A comprehensive description of both spatial and frequency dispersion phenomena is provided by a recently introduced homogenization approach for nonmagnetic periodic metamaterial (M. G. Silveirinha, Phys. Rev. B, 75, 115104, 2007). The method is based on the Floquet representation of the field and introduces a single generalized permittivity tensor that takes into account all the polarization effects, (artificial magnetism, bianisotropy, and higher-order spatial dispersion effects). Whenever possible, it is more convenient to adopt a local homogenization scheme of material and describe the weak spatial dispersion effects in terms of local parameters. A procedure to extract the local bianisotropic effective parameters from the nonlocal permittivity has been proposed by exploiting the Taylor series expansion of the generalized tensor (M. G. Silveirinha, Non homogenization theory of structured materials, Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009)). However, inherent difficulties in calculating the local permeability through this procedure come up. A Taylor expansion of the polarization and magnetization currents has also been used to define effective constitutive parameters that have local properties in the long-wavelength limit (A. Alù, Phys. Rev. B, 84, 075153/1-18, 2011) but it relies upon the assumption of slow variation of the induced microscopic polarization and magnetization vectors within a unit cell. The objective of this work is to develop a straightforward retrieval procedure to extract the local effective bianisotropic parameters of reciprocal metamaterials from the nonlocal spatially dispersive generalized dielectric function, incorporating all the polarization effects. Closed-form expressions for the local nondispersive permittivity, permeability and magnetoelectric coupling parameters are provided.