Metasurfaces with anisotropic electric and magnetic conductivities: Parameter retrieval for arbitrary incidence and polarization

Metasurfaces come in a great variety of unit cell geometries and material composition. A common approach for describing them relies on retrieving effective surface parameters (e.g., electric and magnetic conductivities) from plane-wave scattering data. Conventional retrieval methods are often limited to isotropic unit cells, a uniform host material, or lead to increased complexity by requiring reflection and transmission coefficients from both sides of the metasurface. Here, we derive analytical expressions for the equivalent surface conductivities of an electrically and magnetically polarizable anisotropic metasurface under oblique plane-wave incidence with arbitrary polarization. The proposed formulation does not require bidirectional scattering information, thus simplifying the process especially in experimental studies. The method is validated through representative electric and magnetic meta-atoms at THz and microwave frequencies, respectively. Their ability for polarization conversion is demonstrated and discussed, relying on the physical insight provided by the retrieved anisotropic conductivities. In addition, we present the inverse expressions for calculating the reflection and transmission coefficients from known surface conductivity tensors, which can prove useful for metasurface synthesis and radiation problems.