Equivalent realizations of reciprocal metasurfaces: Role of tangential and normal polarization

We discuss possible topologies of physically different metasurfaces with equivalent macroscopic electromagnetic responses. We specifically demonstrate that the presence of normal components (with respect to the metasurface plane) of the polarization currents does not add any functionality in engineering the reflection and transmission characteristics which cannot occur in metasurfaces maintaining only tangential currents. Therefore, if a certain property is achievable using general volumetric inclusions, polarizable along all three directions, the same response can be achieved using some equivalent perfectly planar elements, polarizable only in the metasurface plane. Our results clarify what physical properties are necessary for realizing desired metasurface responses and promote flat microwave and optical designs, providing possibilities for dramatic complexity reduction of metasurfaces for rather general field transformations, including asymmetric reflection and transmission.