Fig. 1. Schematic illustration of the HyOPS. (θ,Φ) are the spherical coordinates. The north pole |Nl⟩ and south pole |Sm⟩ represent orthogonal circularly polarized eigenstates with topological charges of l and m, and the points |Hm,l⟩ and |Vm,l⟩ represent the horizontal and vertical polarization bases, respectively. The polarization and intensity distribution of four different points are shown with l=0 and m=2.

Fig. 2. (a) Experimental setup to generate arbitrary vector vortex beams on the HyOPS. A Gaussian beam emerging from the He–Ne laser (632.8 nm, 17 mW, Thorlabs HNL210L-EC) passes through part (I) (GLP1, QWP1, and QP) to produce a vector beam. Then the vector beam is transformed into a vector vortex beam by part (II) (SPP). Part (III) (QWP2 and GLP2) is used to measure the Stokes parameters. GLP, Glan laser polarizer; QWP, quarter-wave plate; QP, q-plate; SPP, spiral phase plate; CCD, charge-coupled device (Coherent LaserCam HR). (b) Schematic illustration of generating a vector vortex beam (right), which can be theoretically decomposed into the vector part (left) and the vortex part (middle).

Fig. 3. (a) and (b) Theoretical and measured optical axis distributions of the q-plate (q=1/2). (c) and (d) Polariscopic images of optical axis distribution of the q-plate under crossed polarizers. Pin and Pout stand for the polarization states of the input and output beams, respectively.

Fig. 4. (a) and (b) 3D schematic view and measured phase retardance value distribution of spiral phase plate (l=1). (c) and (d) Measured interference patterns of the generated vortex beam with a spherical wave and a plane wave.

Fig. 5. Polarization and intensity distribution of the theoretical and experimental results of vector beams. The first row shows the theoretical results of the points (1,0,0), (0,1,0), (−1,0,0) and (0,−1,0) on the HOPS in order from left to right. The second row is the corresponding experimental results. The third row shows the theoretical results of points (0,0,1), (0,0,−1), (0,−22,22), and (22,0,22) on the HOPS. The fourth row is the corresponding experimental results.

Fig. 6. Polarization and intensity distribution of the theoretical and experimental results of vectorial vortex beams. The first row shows the theoretical results of the points (1,0,0), (0,1,0), (−1,0,0), and (0,−1,0) on the HyOPS in order from left to right. The second row is the corresponding experimental results. The third row shows the theoretical results of points (0,0,1), (0,0,−1), (0,−22,22), and (22,0,22) on the HyOPS, The fourth row is the corresponding experimental results.

Fig. 7. Intensity distributions of the radially and azimuthally polarized vortex beam behind the polarization analyzer at different angles (represented by the white arrows).