Homogenization of Metamaterials by Dual Interpolation of Fields: a Rigorous Treatment of Resonances and Nonlocality

Abstract

The paper extends and enhances in several ways the recently proposed homogenization theory of metamaterials [J. Opt. Soc. Am. B 28, 577 (2011)]. The theory is based on a direct analysis of fields in the lattice cells rather than on an indirect retrieval of material parameters from transmission / reflection data. The theory is minimalistic, with only two fundamental premises at its core: (i) the coarse-grained fields satisfy Maxwell's equations and boundary conditions exactly; and (ii) the material tensor is a linear relationship between the pairs of coarse-grained fields. There are no heuristic assumptions and no artificial averaging rules. Nontrivial magnetic behavior, if present, is a logical consequence of the theory. The method yields not only all 36 standard material parameters, but also additional ones quantifying spatial dispersion rigorously. The approximations involved are clearly identified. A tutorial example and an application to a resonant structure with high-permittivity inclusions are given.