Fig. 1. Experiment setup used to generate composite Bessel-like VOFs and manipulate propagation and evolution of the embedded PSs. P, polarizer; SLM, spatial light modulator; BS, beam splitter; L1–L3, lenses; A-QWP, assembled quarter-wave plate; G, Ronchi grating.

Fig. 2. Numerical and experimental demonstrations of the manipulated propagation trajectories of PSs in form of braiding. (a) Simulated side-view propagation of the composite Bessel-like beam and (b) transverse beam patterns at three different positions. (c) The spiral propagation trajectories of the C-points (i.e., C-lines, depicted by continuous lines) are accompanied by a top-view image at the bottom, and the polarization distribution in the Fourier plane is indicated as an inset to suggest the initial field with lemon–star topological configuration, where the red and blue colors denote RH and LH polarization states. (d) and (e) Measured transverse beam patterns and Stokes phases ϕ12 at different positions, where the white and black circles represent the Stokes vortices, corresponding to positive and negative C-points marked by dots on the C-lines in (c), respectively.

Fig. 3. Customization of the hexapetalous PSs topological configuration. (a) Simulated side-view propagation of the composite Bessel-like beam and (b) transverse beam patterns at three different positions. (c) Dislocated trefoil propagation trajectories of the C-points and their top-view images, together with an inset depicting the polarization distribution in the Fourier plane, where the red and blue colors denote RH and LH polarization states. (d) and (e) Measured transverse beam patterns and Stokes phases ϕ12 at different positions, where the Stokes vortices are marked by white and black circles, corresponding to positive and negative C-points marked by dots on the C-lines in (c), respectively.

Fig. 4. Numerical and experimental demonstrations of the manipulated evolution of PSs in 3D space. (a) Simulated side-view propagation of the composite Bessel-like beam and (b) transverse beam patterns at three different positions. (c) The evolution trajectories (continuous lines) are accompanied by three slices of Stokes phase and polarization distributions at the same three positions as those in (b), where the red and blue colors describe RH and LH polarization states, white and black dots denote positive and negative C-points, and gray dots represent the annihilation points of the C-points, respectively. (d) and (e) Measured transverse beam patterns and Stokes phases at different positions, where the white and black circles denote the Stokes vortices corresponding to the positive and negative C-points marked by dots on the lines in (c), and the dotted circles denote the annihilation points.

Fig. 5. Piecewise design of the z-axis evolution of PS topological morphology. (a) Simulated side-view propagation of the composite Bessel-like beam and (b) transverse beam patterns at three typical positions. (c) Evolution trajectories (continuous lines) with three slices of Stokes phase and polarization distributions at six characteristic positions, where the red and blue colors describe RH and LH polarization states, white and black dots denote positive and negative C-points, green and yellow dots denote positive and negative V-points, and gray dots represent the annihilation points of PSs, respectively. (d) and (e) Measured transverse beam patterns and Stokes phases at different positions. In (e), the white, black, green, and yellow circles represent the Stokes vortices corresponding to the positive C-points, negative C-points, positive V-point, and negative V-point, respectively, while the dotted circles denote the annihilation points.