Fig. 1: Two degrees of freedom enable independent and complete control of the optical amplitude and phase.

a Schematic of the holographic experiment: circularly polarized light is partially converted by the metasurface to its opposite handedness and is then filtered by an analyzing polarization filter before forming an image on the camera. b Geometrical parameters of the meta-atoms sweep the amplitude (black-white gradient axis) and phase (rainbow axis) of the output signal. c The meta-atoms in b can take incident left circularly polarized light (south pole) to any other point on the Poincaré sphere with near-unity efficiency representing two independent degrees of freedom controlled by the metasurface. d Geometric parameters of a meta-atom. e Full-wave simulations varying W_y and α for H = 800 nm, W_x = 200 nm, P = 650 nm, and λ = 1.55 μm. The colormap depicts the amplitude, A, of converted light by the saturation and the phase, ϕ, by the hue. f “Look-up table” inverting an interpolated version of (e) to specify the values of W_y (saturation) and α (hue) required to achieve a desired A and ϕ