Perfect non-specular reflection with polarization control by using a locally passive metasurface sheet on a grounded dielectric slab

This paper investigates the conditions for a perfect anomalous reflection through a modulated metasurface consisting of a metallic cladding printed over a grounded slab. Differently to what has been previously published, the problem is rigorously addressed by modeling the metallic cladding through an equivalent penetrable impedance and accounting for the grounded slab through the problem's Green's function. It is shown that without polarization transformation, the exact solution exists only for the special case of retroreflection, and, in that case, it can be done simultaneously for the two orthogonal polarizations, with an arbitrary phase shift among the two. On the other hand, changing the polarization of the reflected wave allows one to find an exact solution for arbitrary combinations of incidence and reflection angles. The exact solution is found by imposing that the induced currents radiating with the Green's function of the background problem simultaneously create the desired reflected beam and cancel the specular reflection from the grounded slab. This approach leads to the derivation of a closed-form expression for the homogenized penetrable impedance profile providing perfect anomalous reflection, i.e., ensuring the vanishing of all the coefficients of the waves associated with unwanted diffraction orders, including the specular reflected wave and the evanescent waves. This result is of great practical interest, since the derived penetrable impedance profile can be readily implemented through a simple distribution of metallic patches. The feasibility of this approach is verified through full wave simulations of both the ideal impedance and the patch-based structure, which confirm the effectiveness of the proposed solution.