Vectorial Diffractive Neural Metasurfaces for Multiplexed Synthesis of Optical Skyrmions

The synthesis of complex vectorial light fields with nontrivial topological polarization textures requires the coordinated control of spatial amplitude, phase, and polarization. A central challenge is to realize such multidimensional control in a compact physical architecture while retaining multiplexing capability. Here, we propose a vectorial diffractive neural network (VDNN) based on three cascaded metasurfaces for compact passive synthesis of topological vector light fields. By jointly encoding phase and polarization responses across the cascaded layers, the VDNN enables spatially multiplexed generation of multiple skyrmionic and bimeronic states. In a representative design, we demonstrate up to 16 topological textures with numerically evaluated average skyrmion numbers of $\left|s\right|>0.86$ , and an average orbital angular momentum (OAM) mode purity exceeding $90\%$ . Full-wave simulations and tolerance analysis further show that this functionality can be preserved under realistic meta-atom responses and inter-layer perturbations. This work provides an inverse-design approach for compact and multiplexed synthesis of complex topological vector light fields for potential applications in free-space optical communications, particle manipulation, and polarization imaging.