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This paper presents investigations on the generalized laws of refraction andreflection for metasurfaces made of diffractive elements. It introduces aphenomenological model that reproduces all the features of the experimentsdedicated to the generalized Snell-Descartes laws. Our main finding is that thegeneralized laws of refrac-tion and reflection as previously stated have to bemodified in order to describe the propagation of light through metasurfacesmade of diffractive elements. We provide the appropriate laws that take adifferent form depending on the properties of the metasurface. Our models applyto both periodic and non-periodic metasurfaces. We show that the generalizedlaw of refraction strictly exists only for linear-phase profiles andsawtooth-wave phase profiles under constraints that we specify. It can beapproximatively defined for non-linear phase profiles. This document includesthe article as the part I and the supporting informations as the part II.

On the concept of a generalized law of refraction: A phenomenological model The Article and the Supporting Informations