A unified analysis framework for tensor metasurfaces

Tensor impedance metasurfaces have attracted much attention recently due to their ability to flexibly manipulate both propagating and surface waves. So far, the analysis of tensor impedance has not been fully supported by commercial electromagnetic simulation software. Also, the representation of formulas of penetrable tensor impedance for both propagating and surface waves is limited in the literature. Hence, a unified analysis framework is proposed for this purpose. It allows the calculation of wave reflection and transmission with arbitrary incident angles, or inversely, the calculation of surface impedance tensors given the desired wave propagation properties. It also allows surface eigenmode analysis, where surface modes with novel isofrequency contours are found for penetrable tensor impedance surfaces. The relationship between penetrable and impenetrable metasurfaces is derived so that the resultant formulas are applicable in both scenarios. A finite difference method code is implemented to validate the derived formulas. The proposed unified formulas are of closed form, hence offering very fast operation for research and design of tensor impedance metasurfaces.