Analysis of Metasurfaces at Oblique Incidence

The theory of analytical modeling of periodic metasurfaces for normal incidence is extended to the general oblique case. The metasurface is considered as a periodic planar array with electrically small dipolar scatterers. The induced polarization currents are calculated by combining the information obtained from the response of individual scatterer to the incident wave and the interaction of scatterers with each other. All required interaction coefficients for the most general analysis of metasurfaces are analytically derived. The expressions in terms of the polarization currents are presented for the reflected/transmitted fields from metasurfaces at oblique illumination. Although theoretically known that adding normal polarization currents to the tangential ones will not provide extra degrees of freedom in the manipulation of the reflection and transmission properties of metasurfaces, in most practical applications, it is required to consider both tangential as well as normal polarization currents. Thus, the effect of oblique illumination in the modification of normal and tangential polarization currents is clarified. Our theory is used to analyze two canonical examples of bianisotropic metasurfaces composed of chiral and omega inclusions. The results of this paper provide an effective tool to push the analysis as well as the synthesis of metasurfaces one step forward.