Metasurface diffraction orders analysis

We analyze the transmission response of a periodic metasurface, synthesized to refract a wave from a specified incidence angle into a specified transmission angle, as the angle of incidence is swept over the whole visible region. We compare this metasurface, that is characterized by a continuous susceptibility function, with a binary diffraction grating having the same period, that is characterized by a binary susceptibility and is hence much simpler. We find a striking correspondence between the two structures: the metasurface produces diffraction orders for incidence angles different from the specified one and these orders are a subset of the grating orders whose elements depend on specific rules that are established in the paper. These rules allow one to instantaneously predict the global behavior of the metasurface, that would otherwise require extremely lengthy numerical analysis.