Unified approach for retrieval of effective parameters of metamaterials

We propose the method of effective parameters retrieval based on the Bloch mode analysis of periodic metamaterials. We perform the surface and volume averaging of the electromagnetic field of the dominating (fundamental) Bloch mode to determine the Bloch and wave impedances, respectively. We show that our method is able to retrieve both material and wave EPs for a wide range of materials, which can be lossy or lossless, dispersive, possess negative permittivity, permeability and refractive index values. It is simple and unambiguous, free of the "branch" problem, which is an issue for the reflection/transmission based method and has no limitations on a metamaterial slab thickness. The method does not require averaging different fields' components at various surfaces or contours. The retrieval of both wave and material EPs is performed within a single computational cycle, after exporting fields on the unit cells facets or in its volumes directly from Maxwell's equations solver.