Dynamic manipulation of high-order Poincaré sphere polarization states via a transmissive space-time-coding metasurface

The state of polarization (SOP) on high-order Poincaré spheres (HOPSs), characterized by their distinctive phase profiles and polarization distributions, plays a crucial role in both classical and quantum optical applications. However, most existing metasurface-based implementations face inherent limitations: passive designs are restricted to represent a few predefined HOPS SOPs, while programmable versions typically constrain to 1-bit or 2-bit phase control resolution. In this paper, dynamic generation of HOPS beams with arbitrary SOP based on a transmissive space-time-coding metasurface is demonstrated. By combining 1-bit phase discretizations via PIN diodes with a time-coding strategy, the metasurface enables quasi-continuous complex-amplitude modulation for harmonic waves in both x - and y -polarizations. Based on near-field diffraction theory, arbitrary SOPs on any HOPS m , n can be precisely generated using a linearly polarized basis, which is independently controlled by FPGA reconfiguration. We experimentally demonstrate that polarization holography on HOPS 0,0 achieves high polarization purity >91.28 % , and vector vortex beams on HOPS 1,3 and HOPS −1,3 exhibit high orbital angular momentum mode purities >91.25 % . This methodology holds great potential for structured wavefront shaping, vortex generation, and high-capacity planar photonics.