Fig. 1: Design principle of vectorial Fourier metasurface for arbitrary far-field light distribution of intensity and polarization.

a Top view of one pixel of the metasurface. Arbitrary polarization requires superposition of two orthogonal polarizations (chosen here as RCP and LCP) with controllable relative amplitudes and phases. To do so, each CP state is produced by two lines of the same handiness with different SOA of \(\triangle {\delta }_{\pm }\) to control the relative amplitude and \({\delta }_{\pm }\) to control the relative phase. b Perspective view of the metasurface and far-field light distribution. The LP input light can be decomposed into two CP beams, which are deflected to the same angle of \({\theta }_{\mathrm{t}}\). The holographic phase information is encoded in the LCP and RCP independently, so that arbitrary polarization is realized by the superposition of the two CP beams. c Schematic of the intensity and polarization decoupling using vectorial Fourier metasurface. The orientation angle and ellipticity of the polarization exhibiting a “Blade” and a “Rocket” images are encoded in a uniformly distributed intensity profile.