Fig. 1. Schematic illustration of HyOPS with l=3 and m=1. Only the main polarization distribution is marked.

Fig. 2. Schematic of experimental arrangement for generating arbitrary vector vortex beams on the HyOPS.

Fig. 3. Generated states on equator of HyOPS under φ0=0. First, second, third, and fourth rows correspond to output fields with δ(V)=2θ, δ(V)=2θ+π, δ(V)=3θ, and δ(V)=4θ, respectively. First column shows the corresponding CGH loaded onto the LC-SLM. The next four columns show the intensity distributions observed by the CCD without or with a polarizer at different orientations.

Fig. 4. Measurement results of normalized Stokes parameters S0,S1,S2, and S3. The first and second rows are theoretical and experimental results when we set φ0=π/8. The third and fourth rows are the theoretical and experimental results when we set φ0=π/4.

Fig. 5. Schematic of the interference scheme for clarifying the phase distribution of the generated HyOPS states.

Fig. 6. Numerically simulated and experimentally observed interference patterns. First, second rows correspond to the generated HyOPS states with δ(V)=2θ and δ(V)=4θ, respectively. First, second, third columns show the corresponding CGH loaded onto the LC-SLM with the numerically simulated interference pattern and the experimentally observed interference pattern.