Mapping Full-Stokes Parameters to Metasurface Design via Globally Engineered Disorder

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, polarization imaging, and optical communications. While metasurfaces have demonstrated remarkable capabilities in polarization control, existing approaches often struggle to simultaneously manipulate SoP and DoP with high flexibility. Here, we introduce a paradigm shift in metasurface-based polarization engineering by proposing a globally engineered disordered metasurface that enables a one-to-one correspondence between structural parameters and the full-Stokes polarization space. Unlike conventional metasurfaces that rely solely on unit-cell-level deterministic phase profiles, our approach incorporates a statistical design principle, introducing a spatial statistical parameter: the meta-atom quantity ratio. By uniformly distributing two distinct types of meta-atoms with controlled ratios, we effectively decouple the design parameters, enabling independent control over all Stokes parameters. Specifically, the azimuthal and elevation angles of the SoP on the Poincaré sphere are governed by the rotation and size of individual meta-atoms, while the DoP is precisely tuned through global disorder engineering via the quantity ratio of the meta-atoms. This approach establishes a direct mapping between metasurface design and polarization space, revealing new physical insights into disorder-assisted 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 advance the development of metasurfaces that harness disorder as a functional design strategy, enabling enhanced flexibility in full-Stokes polarization engineering.