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The paper extends and enhances in several ways the recently proposedhomogenization theory of metamaterials [J. Opt. Soc. Am. B 28, 577 (2011)]. Thetheory is based on a direct analysis of fields in the lattice cells rather thanon an indirect retrieval of material parameters from transmission / reflectiondata. The theory is minimalistic, with only two fundamental premises at itscore: (i) the coarse-grained fields satisfy Maxwell's equations and boundaryconditions exactly; and (ii) the material tensor is a linear relationshipbetween the pairs of coarse-grained fields. There are no heuristic assumptionsand no artificial averaging rules. Nontrivial magnetic behavior, if present, isa logical consequence of the theory. The method yields not only all 36 standardmaterial parameters, but also additional ones quantifying spatial dispersionrigorously. The approximations involved are clearly identified. A tutorialexample and an application to a resonant structure with high-permittivityinclusions are given.

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