Surface Susceptibility Bianisotropic Matrix Model for Periodic Metasurfaces of Uniaxially Mono-Anisotropic Scatterers Under Oblique TE-Wave Incidence

A bianisotropic matrix technique is presented for the development of a homogenized surface susceptibility model of metasurfaces with arbitrary uniaxially mono-anisotropic scatterers, illuminated by obliquely incident TE waves. Based on the sole assumption that the scatterers can be described by point-dipoles, the proposed formulation establishes a simple relation between the homogenized metasurface susceptibility matrix and the scatterer polarizability matrix. For this purpose, the exact interaction coefficients, associating the metasurface local field vectors with the dipole moment vectors, are extracted in terms of rapidly convergent series. The resulting analytical expressions for the interaction coefficients are applicable to both near- and far-field problems. Moreover, the derived formula for the surface susceptibility matrix reveals the existence of off-diagonal terms, corresponding to a magnetoelectric coupling effect at the lattice level. The accuracy of the method is verified via comparisons with full-wave-simulation results for several metasurfaces of planar resonators and magnetodielectric spheres. It is observed that the efficiency of the model is contingent upon the electrical size of the scatterers rather than the lattice periodicity, since the former determines the validity of the point-dipole approximation, which is the only assumption throughout the analysis.