Bloch-mode analysis for effective parameters restoration

We utilize the Bloch-mode analysis of periodic composite structures to introduce an approach for retrieving effective parameters of homogenized metamaterials. In the case of single-mode propagation we can restore a complex effective refractive index with a high accuracy. By further employing surface or volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes we are able to determine the Bloch and wave impedances, leading to wave and material effective parameters, respectively.

The approach is demonstrated on several examples. We focus our discussion on the nature of microfields returned by Maxwell's solvers, showing that ignoring of difference between magnetic strength and induction lead to incorrect determination of the Poynting vector.