Wave propagation phenomena in structured materials and problems of metamaterials homogenization

One of the most convenient ways to describe metamaterials (MM) is to homogenize structured composites and assign them with effective parameters (EPs), provided that they can be introduced. The most common way to determine EPs in literature is to derive them from the refection/transmission spectra at a fixed incident angle (conventionally, under the normal incidence). We propose to introduce EPs by analysing wave propagation in a MM consisting of at least several unit cells (quasi-periodic). We use numerical simulations with a standard full-wave Maxwell solver and Bloch mode post-processing to retrieve EPs. We demonstrate our approach on several characteristic examples and formulate constrains on the MMs homogenization.