Fig. 1. Three fundamental representations of SoPs

Fig. 2. New types of Poincaré sphere for topological charge equal to 1^［40-42］

Fig. 3. Several schematic diagrams of optical setup for highly efficient generation of VOFs based on the split-screen method^{［35，61，62］}

Fig. 4. Two compact and efficient Generators of VOFs for specific purposes^［64-65］

Fig. 5. Schematic of principle of generating VOFs by utilizing metasurface^［66］

Fig. 6. Generation of PPBs based on metasurface^［67］

Fig. 7. A modulated case of completely shaping 2D VOFs ^［34］

Fig. 8. Schematic representation of a 3D vectorial optical field with a z-dependent degree of entanglement^［85］

Fig. 9. Polarization modulations on axis by controlling the axial phase distributions of zero-order Bessel beams^［98］

Fig. 10. Comparison between the simulation and the experimentally obtained data for the case of the zero-order Bessel beams

Fig. 11. Generation of 3D vectorial zero-order Bessel beams by reshaping the axial intensity distributions of quasi-Bessel beams^［99］

Fig. 12. Generation of Bessel beams with different types of path and intensity distribution along the z direction^［100］

Fig. 13. Two kinds of full Poincaré beams and C point and L line in these fields^［110］

Fig. 14. Generation of the BPB synthesized from the combination of the LCP Bessel beam with m₁=0 and the RCP Bessel beam with m₂=1^［101］

Fig. 15. Experimental results showing independent SoPs’ manipulation on multi-planes^［114］

Fig. 16. The experimental generation of three-dimensional vectorial multifocal arrays created by pseudo-period encoding^［115］

Fig. 17. Simulation of generating four typical 3D curves based on the scalar beam-shaping technique^［118］

Fig. 18. An experimentally generated 3D VOF consisting of a 2D ring curve and a 3D Achimedean curve with continuously varying locally linear SoPs^［37］

Fig. 19. Experimentally generated vectorial focusing curves with continuously varying hybrid SoPs^［121］

Fig. 20. Simulation and experimental results of the 3D CPVB consisting of double tilt-ring-shaped trajectories in the focal space^［122］

Fig. 21. Experimental results of two generated 3D TCVBs^［123］

Fig. 22. Generation of curvilinear arranged optical vortex arrays^［128］

Fig. 23. Simulations of generating curvilinear V-type polarization singularity arrays along square and quatrefoil trajectories^［129］

Fig. 24. Schematic illustrations of arbitrary 3D linear SoPs interacting with randomly aligned gold nanorods^［139］

Fig. 25. An optical trapping with tractor beams^{［140，141］}

Fig. 26. Optical tweezer experiments based on vectorial vortex beams under tight focusing^［27］

Fig. 27. A Möbius strip and polarization topology Möbius-strip structures caused by polarization singularities with different singularity under tight focusing^［145］

Fig. 28. Topological traits of optical polarization knots characterized by their torus structures^［108］