Fig. 1. (a) Diagram of the experimental device. (b) The relationship between the VMs and the angle of Pol1. (θ₁) and the angle of HWP (θ₂). TEM₀₀, fundamental mode; Pol, polarizer; VWP, vortex waveplate; BS, non-polarizing beam splitter; HWP, half-wave plate; CCD, charge-coupled device.

Fig. 2. Overall flowchart of the DL-SPGD algorithm. A: 1-channel multi-view input; B: N-channel input. Conv.: Convolution layer, Pool.: Pooling layer, Separable Conv.: depthwise separable convolution layer.

Fig. 3. (a) Validation loss for first- and second-order VMs. (b) Their average errors of modal weights and relative phases. (c) The averaged correlations of the SPGD and the DL- SPGD algorithms for first-order VMs over 200 testing samples. (d) Given and predicted weights and relative phases for first-order VMs.

Fig. 4. (a) Measured (Mea.) and reconstructed (Rec.) intensity patterns of a VM by the DL-SPGD algorithm. The measured and predicted modal coefficients in (b) the VM, (c) the CP-OAM, and (d) the LP-OAM mode bases.

Fig. 5. Predicted (red dots and blue triangles) and measured (blue and red lines) modal weights. (a) Mixed TM₀₁ and TE₀₁ modes, (b) mixed HE₂₁^even and HE₂₁^odd modes. Hybrid four VMs when (c) θ₁ = 0 and (d) θ₁ = π/4. (e1), (f1) The output and polarized patterns of the VMs. Interference patterns when the polarized angles are set at (e2), (f2) 0° and (e3), (f3) 90°. (Mes., measured modal coefficients; Pre., predicted modal coefficients.

Fig. 6. Experimental (Exp.) and reconstructed (Rec.) intensity patterns of (a1) first-order and (b1) second-order VMs converted from fiber MSCs. Their predicted modal weights and phases of (a2), (b2) VM modes, (a3), (b3) CP-OAM base, and (a4), (b4) LP-OAM base.