First-Principle Homogenization Theory for Periodic Metamaterials

We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form expressions for the effective constitutive parameters, pointing out the relevance of inherent spatial dispersion effects, present even in the long-wavelength limit. Our results clarify the limitations of quasi-static homogenization models, restore the physical meaning of homogenized metamaterial parameters and outline the reasons behind magnetoelectric coupling effects that may arise also in the case of center-symmetric inclusions.