Fig. 1. Schematic and working mechanism of VSB sorting enabled by spin-multiplexed diffractive metasurfaces. (a) The VSBs exhibit polarization DoFs and spatial DoFs with LG beams, HG beams, and BG beams (including arbitrary superpositions of them). The red line denotes the LCP component, while the blue line signifies the RCP component. (b) Schematic diagram of VSBs sorting based on spin-multiplexed diffractive metasurfaces. The input is a VSB composed of an LG beam, the hidden layer is composed of multilayer spin-multiplexed metasurfaces acting as neurons, and the output is a focused Gaussian bright spot in the planar detection area. (c) The architecture of the DNN. Phase and intensity information of the incident light is processed through several hidden layers and then optimized by an error backpropagation algorithm.

Fig. 2. Structure design of a spin-multiplexed metasurface. (a) Left, schematic of a metasurface composed of ${\mathrm{TiO}}_2$ nanopillars. Right, perspective view and top view of the unit cell placed on a quartz substrate. The incident wavelength is 532 nm, the nanopillar period is $U=400\mathrm{nm}$, and the height is $H=600\mathrm{nm}$. (b) and (c) Phase shifts and transmission under $x$-polarized light and $y$-polarized light, respectively. (d) Phase delay and PCE of the selected 16 nanopillars. (e) Design method for generating arbitrary spin-multiplexed metasurfaces. Given two arbitrary phase maps (${\phi }_{\mathrm{RCP}}$, ${\phi }_{\mathrm{LCP}}$), the propagation phase (${\phi }_x$, ${\phi }_y$) and the geometric phase $\theta$ of the metasurface pixels are calculated to design the in-plane sizes and rotation angles.

Fig. 3. Training of diffractive metasurface for pattern detection. (a) Flowcharts of vector diffraction calculation simulation. (b) Identifying the crosstalk of mode numbers as a function of different numbers of hidden layers. (c) Scalar diffraction calculation results for incident mode identification. (d) Energy distribution matrix results of 36 modes (see the text for details on the modes).

Fig. 4. Characterization of spin-multiplexed diffractive metasurfaces for identifying high-order VSBs. (a) Poincaré sphere representation of HOVVBs. (b) Intensity patterns of three typical VSBs. The red line denotes the LCP component, the blue line signifies the RCP component, and the yellow line represents the linearly polarized (LP) component. (c)–(e) The polarization distributions and intensity patterns of the input light fields, and the intensities of $E_x$ and $E_y$ components. (f)–(h) Measured intensity distribution of the output plane. (i)–(k) The normalized energy ratio of 72 output channels.

Fig. 5. Characterization of spin-multiplexed diffractive metasurfaces for identifying arbitrary VSBs. (a)–(c) The polarization distributions and intensity profiles of the input light fields, and the intensity results of the $E_x$ and $E_y$ components. (d)–(f) Measured intensity distribution of the output plane. (g)–(i) The normalized energy ratio of 72 output channels.