Electromagnetic characterization of planar and bulk metamaterials: A theoretical study

Using an example of a bilayer of plasmonic nanospheres, we generalize a method of electromagnetic characterization of metasurfaces (metafilms) recently suggested in the literature. We theoretically demonstrate that the results of this characterization method are suitable to predict scattering parameters of bilayer metasurfaces. Further, we develop an original electrodynamic approach which allows one to extract the effective material parameters of bulk lattices from reflection and transmission coefficients of a single generic metasurface. The results of this retrieval are compared with the results of an alternative method based on the quasistatic homogenization model. The difference between these results is discussed from the point of view of the electromagnetic interaction of scatterers forming the lattice.