Minimalist single-atom geometric metasurface for far-field amplitude and polarization manipulation

Metasurfaces offer a compact platform for subwavelength control of multidimensional optical fields, making them promising for high-fidelity vectorial light-field reconstruction. Existing approaches typically address this requirement by introducing additional degrees of freedom, either through nanostructures of varying dimensions or through supercell-based multiplexing. However, using nanostructures with different dimensions can increase fabrication complexity, while supercell-based implementations may introduce unwanted diffraction orders. Here, we present a single-atom geometric metasurface for independent far-field control of amplitude and polarization. The modulation is realized with a modified Gerchberg-Saxton algorithm that optimizes amplitude and polarization using a phase-only hologram. By exploiting the centrosymmetric geometric phase response, the left- and right-handed circularly polarized components are independently encoded and coherently superposed in a selected region, enabling vectorial light fields with arbitrary intensity and polarization distributions. This compact strategy provides a general route toward polarization-encoded encryption, structured light beam generation, and optical data storage.