This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell–Descartes laws. Our main finding is that the generalized laws of refraction and reflection as previously stated have to be modified in order to describe the propagation of light through metasurfaces made of diffractive elements. We provide the appropriate laws that take a different form depending on the properties of the metasurface. Our models apply to both periodic and nonperiodic metasurfaces. We show that the generalized law of refraction strictly exists only for linear-phase profiles and sawtooth-wave phase profiles under constraints that we specify. It can be approximately defined for nonlinear phase profiles.

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广义折射定律的概念：现象学模型

本文研究了由衍射元素构成的超颖表面的折射和反射的一般规律。它引入了一种现象学模型，该模型再现了专用于广义斯涅尔-笛卡尔定律的实验的所有特征。我们的主要发现是，如前所述，一般的折射和反射定律必须加以修改，以描述光通过由衍射元件制成的超颖表面的传播。我们提供了适当的定律，这些定律根据超颖表面的属性采用不同的形式。我们的模型适用于周期性和非周期性的超表面。我们表明，在我们指定的约束条件下，广义折射定律仅对线性相位剖面和锯齿波相位剖面严格存在。