Fig. 1. Conceptual illustration of a multifunctional metasurface.

The proposed single-layer multifunctional metasurface can achieve arbitrary and independent amplitude and phase control for a pair of orthogonal polarization states. Upon transmission, the handedness of each output polarization (|λ₁⁻〉, |λ₂⁻〉) is flipped, with respect to the incident polarization (|λ₁⁺〉, |λ₂⁺〉). The output wavefront can possess any combination of arbitrary complex-amplitude distributions of $E_1{e}^{i{\phi }_1}$ and $E_2{e}^{i{\phi }_2}$. The phase and amplitude profiles (φ₁, φ₂, E₁, and E₂, respectively) for the two orthogonal polarization states are independent of each other