The Rayleigh Hypothesis for Metasurface Optimization: Anomalous Grazing Refraction by Corrugated Silicon

We study dielectric metasurfaces based on periodically corrugated subwavelength-thin silicon layers and explore their ability to control the light propagation direction. We apply the Rayleigh hypothesis that drastically facilitates the evaluation of diffraction efficiencies and perform multi-parametric numerical optimization of the optical performance. In particular, we obtain the Fourier coefficients of periodic profiles providing anomalous refraction of normally incident light of 500 nm wavelength into grazing directions with efficiency of more than 70 %.