Fig. 1. Shifting the (a) incident position onto the P-B phase metasurface carrying the original phases is equivalent to (b) centrally incident on the P-B phase metasurface carrying the original phase and gradient phase.

Fig. 2. (I) Illustration of the twisting phase adding together with the gradient phase. (a)–(c) Two-dimensional slow-axis orientation patterns of the twisting phase, gradient phase, and combination phase. (d)–(i) Phases introduced to the LCP and RCP light. (II) Illustration of the lens phase adding together with the gradient phase. (j)–(l) Two-dimensional slow-axis orientation patterns of the lens phase, gradient phase, and combination phase. (m)–(r) Phases introduced to the LCP and RCP light.

Fig. 3. (a) Illustration of the Gaussian beam illuminating the dielectric P-B phase metasurface. (b) Captured picture of the fabricated metasurface. (c) Polariscopic analysis carried out by optical polarization imaging. (d)–(f) Measured SDS intensity (normalized) images of Gaussian beams at different wavelengths (633, 532, and 475 nm).

Fig. 4. (a) Measured Stokes parameters S3 of the linearly polarized Gaussian beams at the incident position shifts of ±0.9,±1.2, and ±1.5  mm. (b) and (c) Intensity curves corresponding to the white dashed lines across the intensity images at the incident position shifts of ±0.60,±0.75,±0.90,±1.05,±1.20, and ±1.35  mm.

Fig. 5. Measured intervals between LCP and RCP components with different incident position shifts at the transmission distance of 500 mm. Cal., calculated; Exp., experimental.

Fig. 6. Measured ellipticities versus the incident polarization (a function of β). (a)–(f) Optical intensity (normalized) profiles correspond to situations of β=45°,75°,85°,95°,105°, and 135° at the wavelength of 633 nm. Cal., calculated; Exp., experimental.

Fig. 7. (a) Schematic diagram of the experimental setups of arbitrarily singular beams detection based on the geometric P-B phase metasurface. P, polarizer; QWP, quarter-wave plate; MS, metasurface; FL, Fourier lens; CCD, charge-coupled device. (b) Measured S3 parameters of the output beams with different transmission distances (z=100, 200, 300, 400, and 500 mm).

Fig. 8. (a) and (b) Experimental results of the VBs (the topological charges are 1 and 2) diffracting through the metasurface. (c) and (d) Experimental results of the CVBs (the polarization orders are −1 and 2) diffracting through the metasurface. (e) and (f) Experimental results of the CVVBs [the topological charges and polarization orders are (1, 2) and (2, −1)] diffracting through the metasurface. The gray lines represent the theoretical polarization profiles.