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.

中文翻译：

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通过在接地电介质板上使用局部无源超表面片，实现具有偏振控制的完美非镜面反射

本文研究了通过调制超表面的完美异常反射的条件，该超表面由印刷在接地板上的金属覆层组成。与之前发表的内容不同，该问题通过通过等效可穿透阻抗对金属覆层建模并通过问题的格林函数考虑接地板来严格解决。结果表明，在没有偏振变换的情况下，精确解只存在于逆反射的特殊情况，在这种情况下，它可以同时对两个正交偏振进行，两者之间具有任意相移。另一方面，改变反射波的偏振可以为入射角和反射角的任意组合找到精确解。通过强加以格林函数辐射的感应电流同时产生所需的反射光束并消除接地板的镜面反射，可以找到确切的解决方案。这种方法导致推导出均匀可穿透阻抗曲线的封闭形式表达式，提供完美的反常反射，即确保与不需要的衍射级相关的波的所有系数消失，包括镜面反射波和渐逝波. 这个结果具有很大的实际意义，因为通过金属贴片的简单分布可以很容易地实现导出的可穿透阻抗分布。