Decoupling metasurface parameters for independent Stokes polarization control via generalized lattice

The ability to achieve comprehensive control over all Stokes parameters, including both the state of polarization (SoP) and the degree of polarization (DoP), is fundamental to advancements in quantum optics, imaging, and optical communications. While metasurfaces have demonstrated remarkable capabilities in polarization manipulation, existing designs typically rely on locally periodic unit cells and deterministic phase profiles, limiting their flexibility in controlling both SoP and DoP simultaneously. Here, we introduce the generalized lattice approach for metasurface design, which enables the decoupling of structural parameters from the full-Stokes polarization response. Our approach introduces a spatially global but structurally disordered arrangement, constructed on a generalized lattice framework. This framework enables the flexible placement of an arbitrary number and type of meta-atoms within a generalized lattice, where the relative quantity ratios among different meta-atoms serve as a new design degree of freedom. This decoupling enables the azimuthal and elevation angles of the SoP on the Poincaré sphere to be governed by the in-plane rotation and size of individual meta-atoms, while the DoP is controlled independently via the quantity ratio. This establishes a direct and analytically tractable mapping between metasurface geometry and polarization space, offering new physical insights into metasurface-based polarization control. A computationally efficient algorithm optimizes the metasurface arrangement, achieving a polarization similarity (evaluated by Stokes Euclidean Distance) of 0.93 in theory and 0.90 in experiment. Our findings demonstrate that the generalized lattice approach provides an effective and versatile route to full-Stokes polarization control with greater flexibility than conventional metasurface designs.