Analytical and experimental characterization of metasurfaces with normal polarizability

To date, research on metasurfaces has predominantly focused on those with polarizabilities that are tangent to the metasurface. Only a few theoretical works have characterized metasurfaces with normal polarizabilities. Here, we provide full analytical, numerical, and experimental characterizations of a metasurface that can be described with polarizabilities in all three spatial directions. First, a set of equations is derived that allows a surface distribution of scatterers to be replaced by a sheet boundary condition. It is shown that the extraction of unknown polarizabilities in the normal direction necessarily requires scattering parameters obtained from oblique incidence. Closed-form expressions that relate scattering parameters to surface susceptibilities in all three spatial directions are given. It is shown that the reflection and transmission properties of the metasurface can be predicted, for an arbitrary angle of incidence, from the sheet parameters. In addition, we report the experimental characterization of a metasurface with polarizabilities in the normal direction. The free-space measurements were performed on a recently proposed DB metasurface at 10 GHz. Experiments confirmed that the sheet parameters do not change with angle of incidence. Consequently, it was possible to extract surface susceptibilities in the normal direction from measured transmission parameters alone.