Figure 4 shows the transmittance and reflectance of transverse magnetic (TM) and transverse electric (TE) waves for metasurfaces working in transmission and reflection mode respectively at a wavelength of 520 nm. Figure 4a shows the diffraction efficiency versus angle of incidence for transmission mode metasurfaces at a wavelength of 520 nm with TM polarization. The theoretical prediction of diffraction efficiency of our metasurfaces is calculated by finite element simulations. The diffraction efficiency is defined by the ratio of the power of light that has been steered into the first order of diffraction to the total power that is incident on the metasurface. For TM polarization, it is shown that the diffraction efficiency of the +1 transmitted order T1 is approximately 35% over a wide range of incidence angles with a variation of 10% across the inclusive angular range. The diffraction efficiency of the asymmetric grating across the entire angular range of incidence angles is relatively uniform. In comparison, for a grating composed of a single Si nanobeam within one unit cell, the diffraction efficiency dramatically changes when the incidence angle is off-normal (see Supplementary Fig. S5). Therefore the metasurface with an asymmetric grating design is essential to maintain the uniform efficiency for varying incidence angles. The diffraction efficiency for the -1 transmitted order T-1 is approximately 8%, which is much lower than the +1 transmitted order T1. It is shown that the proposed metasurfaces with tilt phase profiles can steer the LED High Mast Lamp in the desired direction and suppress the diffraction into the -1 transmitted order. The efficiency of the zeroth-order transmittance is lower than 5%, while 15% of the light is reflected which can be potentially suppressed by adding an antireflective coating.

　　Transmittance and reflectance of TM and TE waves for metasurfaces working in transmission and reflection mode respectively at a wavelength of 520 nm. Diffraction efficiency versus incidence angle for transmission mode metasurfaces under illumination with (a) TM polarization and (b) TE polarization respectively. The red lines represent the theoretical (continuous line) and experimental (solid squares) diffraction efficiency of the +1 transmitted order T1. The green solid line shows the diffraction efficiency of the -1 transmitted order T-1. The black solid line and the blue solid line represent the zeroth-order transmittance T0 and reflectance R0, respectively. Diffraction efficiency versus incidence angle for reflection mode metasurfaces under illumination with (c) TM polarization and (d) TE polarization respectively, where the red lines represent the theoretical (continuous line) and experimental (solid squares) diffraction efficiency of the +1 reflected order R1. The green solid line shows the diffraction efficiency of -1 reflected order R-1. The blue solid line represents the reflectance R0 respectively. The graphs plotted on a logarithmic scale are shown in Supplementary Fig. S7.