Waveguide-Floquet Mapping Using Surface Susceptibilities for Passive and Active Metasurface Unit-Cell Characterization

A simple waveguide-Floquet mapping is proposed and theoretically investigated that links the scattering response of a sub-wavelength metasurface unit cell under an infinite periodic array configuration and when measured inside a shielded rectangular waveguide environment. This mapping is based on extracting the effective surface susceptibilities as the fundamental constitutive parameters of the cells, via the generalized sheet transition conditions (GSTCs) of the unit cell using the waveguide measurements, and then reconstructing the unit-cell response at an arbitrary incidence angles. Using two examples of a transmissive Huygens’ metasurface and a purely reflective metasurface, the proposed waveguide-Floquet mapping is numerically confirmed to determine the complete angular scattering of the unit cells. The proposed waveguide-Floquet mapping thus represents a simple technique to experimentally determine the angular scattering characteristics of the unit cell using a low-cost effective waveguide measurements.