Fig. 1. (a) Basic Poincaré sphere. Selected points a1–a6 on the surface include polarization states from linear polarization to elliptical polarization. (b) First-order HOPS. Selected points b1–b6 represent six CVBs on the surface. 2υ is polar angle, and 2γ is equator angle of arbitrary state vectors directing to points on the surfaces. Points a1–a6 map b1–b6 one by one, which is just realized by the proposed device.

Fig. 2. (a) Fabrication of polarization-selective cylindrical lens. (b) PGPS, which contains two symmetric polarization-selective cylindrical lenses and operates on LCP only. (c) Gouy phases accumulated by PGPS for modes with different indices m=0 to 5; the special points involved in the device are marked with red angles.

Fig. 3. Schematic of the experimental setup for generating arbitrary CVBs.

Fig. 4. Stokes parameters of CVBs. The left column displays the tailoring polarization vectors of CVBs, followed by columns of Stokes parameters S0 to S3. Subpictures in the lower-left corner are theoretical values. CVBs are sampled from the first-order HOPS, where (π/2,0), (π/2,π), (π/2,π/2), (π/4,π/4), and (π/4,3π/4) represent their positions on the spherical surface.

Fig. 5. Petal-like profiles collected by CCD when launching high-order LG modes. The first row is set for p=0, ℓ=1,2,3, 4, and the second row is for p=1, ℓ=1,2,3, 4, respectively. The third row exhibits results for ℓ=10, p=2,3, 5 and an ultrahigh order ℓ=50, p=1.