Fig. 1. Vector vortex beams generation with vortex retarders (VR)^[5]. (a) Setup; (b) Vector vortex beams of different orders

Fig. 2. Machining results on glass with tightly focused vortex beams. (a) Annular rings ablated by linearly polarized beams^[16]; Polarization-sensitive structures produced on fused silica galss with (b) mixed and (c) radially- or azimuthally-polarized beams^[17]

Fig. 3. LIPSS imprinted on Silicon wafer with different vector vortex beams of various polarization state^[21]. (a) Radial; (b) Azimuthal; (c) Spiral; (d) Linear. Insets (b1) and (b2) show the zoom-in LSFLs in the peripheral regions and the grooves in the internal region marked in (b)

Fig. 4. Twisted nanoneedles on (a) Tantalum sheet^[34] and (b) nanocones on Silicon surface^[35]

Fig. 5. Machining results with ultrafast Bessel beams. (a) Nanochannels in glass^[38]; (b) Waveguiding tubes fabricated by Bessel vortex beams^[42] ；(c) Vector Bessel vortex beams；^[43] (d) Nanorods by vector Bessel vortex beams^[44]

Fig. 6. (a) Schematics of 3D structurally polarized Bessel beams generation and twisted nanograting inscribing; (b) The SEM of inscribed microstructures^[48]

Fig. 7. Twisted magnetization structures induced by vector Gaussian vortex beams ^[55]. (a) Schematic of magnetization generation at subdiffraction-limited scale; (b) Simulation of the light-induced twisted 3D magnetizations

Fig. 8. Caustics of Bessel vortex beams in different theories. (a) Any hyperboloid formed by the rays emitting from a circle in the initial plane; (b) Ideal nondiffracting tubular caustics as deduced in Berry’s work^[60] (red dashed line); (c) Expanding tubular caustics (blue lines) in reference [61]

Fig. 9. Globally analytical caustics of axially symmetric vortex beams^[63]. (a) Vortex beams; (b) Bessel vortex beams; (c) Vortex beams generated from parabolic vortex toroidal lens

Fig. 10. Comparison of different light fields with and without vortices ^[63]. (a) and (b) Bessel-like beams; (c) Abruptly autofocusing vortex beams. Column 1 and 2 represent, respectively, the intensity profiles along propagation in simulations and in the experiments; Column 3 illustrates the differences between the global caustics of the abruptly autofocusing vortex beams with and without the OAM

Fig. 11. Vortex beams designed by solving the inverse problem^[63]. (a) Quartic; (b) Logarithmic; (c) Parabolic; (d) Exponential tubular profiles

Fig. 12. Polymer microtubes fabricated with different vortex beam-based schemes. (a) Uniform tube size enabled by scanning the focused vortex beams^[67]; (b) Controllable tube profiles by dynamic hologram-assisted axial scan of the focused vortex beams^[69]; (c) Cylindrical micro-tubes fabricated by Bessel vortex beams^[70]; (d) Bowl-shaped microstructures fabricated by abruptly autofocusing vortex beams with tailored parabolic caustics highlighted by the yellow rays^[71]

Fig. 13. Schematics of the setup to generate arbitrary vector beams with a single liquid crystal spatial light modulator^[72]

Fig. 14. (a) Patterns fabricated on LiNbO₃ with vector beam arrays ^[75]; (b) Dynamically trajectory assisted fabrications of periodic nested microstructures; (c) Polygonal and spiral fan-leaf-like structures ^[76]; (d) Chinese character “Nan” and irregular quadrilateral grid structures ^[77]

Fig. 15. Multi-scaled micro/nano-structures fabricated on SiC surface with specially designed vector beams^[78]. (a) Radial-hybrid vector beams; (b) Spiral-hybrid vector beams