Fig. 1. Vector projection mapping of the skyrmion^[35]. (a) Mapping relationship between the three-dimensional skyrmion vector sphere and the two-dimensional plane skyrmion vector; (b) distribution of transverse vector components of skyrmions with different m and γ values

Fig. 2. Three-dimensional vector structure distribution (top) and transverse component distribution (bottom) of fundamental type skyrmions, Néel-type skyrmions (left), Bloch-type skyrmions (middle), and anti-skyrmions with N=-1 (right)^[35,44]

Fig. 3. Skyrmions with various helicities and vorticities^[42]. (a) Anti-skyrmion with a vorticity m=-1; (b) skyrmion with an intermediate helicity γ=π/4 between Bloch and Néel type skyrmions; (c) higher-order skyrmion with vortex degree m=2 and skyrmion number N=2; (d) biskyrmion; (e) higher-order biskyrmion with skyrmion number N=2; (f) skyrmionium with skyrmion number N=0; (g)(h) ferrimagnetic and synthetic antiferromagnetic skyrmions; (i)(j) skyrmion "tube"; a pair of Bloch and anti-Bloch points constituting the building block of (k) a three-dimensional crystal (hedgehog lattice) and (l) the hopfion with three-dimensional toroidal topological structure

Fig. 4. Generating and manipulating electromagnetic field vector optical skyrmions using surface plasmon wave interference. (a) Generating Néel-type electric field vector optical skyrmion distribution using surface plasmon wave interference (color gradient represents the magnitude of its longitudinal component), with arrows indicating the unit vector direction of local electric field^[23]; (b) dynamic measurement of electric field vector optical skyrmions using time-resolved vector microscopy^[27]; (c) changing position and shape of skyrmions by adjusting the phase relationship of six excitation beams^[60]; (d) generating magnetized vector optical skyrmions with topological stability characteristics using artificially localized surface plasmons^[34]

Fig. 5. Generating and manipulating electromagnetic field vector optical skyrmions in free space. (a) Generating electromagnetic field vector optical skyrmions using ultrashape pulses with complex topological structures^[31]; (b) generating electromagnetic field vector optical skyrmions using vector holographic control^[65]; (c) generating electromagnetic field vector optical skyrmions in the focal space by using two pairs of counter-propagating cylindrical vector incident beams under the 4π focusing condition^[66]

Fig. 6. Spin vector optical skyrmions and merons in evanescent fields. (a) Generating Néel-type spin vector optical skyrmions on the surface of a metal film using vortex light with total angular momentum quantum number A=1^[24]; (b) generating Bloch-type spin vector optical skyrmions on a metal surface using tightly focused circularly polarized vortex light and achieving unrestricted spatial displacement of skyrmions^[69]; (c) realizing optical merons with a quadrilateral symmetric structure by combining energy stability conditions^[29]

Fig. 7. Constructing skyrmions with skyrmion number 1 based on rational mapping^[41]

Fig. 8. Skyrmionium with longitudinal vector angles kπ corresponding to the Néel-type skyrmion (left), including skyrmionium with 3π radial twist (middle) and 5π radial twist (right)^[35]

Fig. 9. Methods for generation and manipulation of Stokes vector optical skyrmions. (a) Generating Stokes vector optical skyrmions using the anisotropy of liquid crystals^[28]; (b) generating Stokes vector optical skyrmions with adjustable skyrmion number using ring microcavities^[70]; (c) interconversion between Néel-type and Bloch-type Stokes vector optical skyrmions using polarization conversion devices^[71]

Fig. 10. Generation and polarization distribution of optical hopfion^[32]. (a) Optical hopfions are generated by focusing a paraxial beam with a Stokes vector skyrmion structure; (b) each “strand” of the hopfion corresponds to a specific polarization elliptical trajectory, forming a hopfion vector beam

Fig. 11. Realizing equiphase line scalar hopfion using spatiotemporal beam shaping techniques^[74]

Fig. 12. Other optical vector skyrmions. (a) Generating Poynting vector optical skyrmions using two pairs of counter-propagating cylindrical vector vortex beams^[75]; (b) pseudospin vector optical skyrmions in nonlinear photonic crystals^[36]

Fig. 13. Applying spin vector optical skyrmions to displacement measurement^[25]. (a) Generating a spin vector optical skyrmion pair, with opposite topological charges, by overlaying counter-propagating optical vortices on a metal film; (b) sensing the motion of polystyrene nanoparticles between the skyrmion pair using a rotating linear polarization system

Fig. 14. High-security information encryption based on optical topological quasiparticles^[100]