Fig. 1. Photonic skyrmionium formed in the presence of spin–orbit coupling of light. (a) Schematic of Bloch-type skyrmionium (top panel) formed due to the interplay between electric (red sphere) and magnetic (blue sphere) Hertz potentials in free space. The electric field profiles induced by each Hertz potential are depicted nearby. (b), (c) The radial variations of longitudinal (red solid lines) and azimuthal (blue solid lines) components of (b) SAM density and (c) Poynting vector for single polarized Hertz potentials. (d) The radial variations of Sz (red solid line) and Sφ (blue solid line) for a hybrid OV with η=0.5i, with local spin orientation forming a Bloch-type skyrmionium. The topological charge of the vortex is set to l=1, and the in-plane wave vector kr is set to 0.7k in panels (b)–(d), where k represents the wave vector in the medium. The black dashed lines in panels (b)–(d) delineate the zero points of the azimuthal components for both the SAM density and the Poynting vector.

Fig. 2. Hierarchical structure of skyrmion and meron lattices. (a) The amplitude of the Hertz potential in an OV lattice of hexagonal symmetry with a lattice constant 2λr (λr is the in-plane wavelength). Each lattice point is fed with hybrid polarized OV described by a superposition of electric and magnetic Hertz potentials (red and blue hemispheres). (b) The out-of-plane SAM distribution Sz in the hexagonal OV lattice. The frequency domain spectrum of Sz is shown in the inset, demonstrating three sets of wave vectors. (c) Optical spin orientation distribution within the red dashed square in panel (b), which can be decomposed into three sublattices in panel (d) based on different wave vectors. Within each sublattice, local spin orientations transition progressively from the central “up” state to the edge “down” state, manifesting Bloch-type photonic skyrmion lattices. The scale bar in panels (a) and (b) is 2λr. (e) The amplitude of the Hertz potential for the hybrid polarized OV lattice of square symmetry with a lattice constant λr, with the out-of-plane SAM distribution Sz shown in panel (f), where two sets of wave vectors are observed in the frequency domain spectrum of Sz in the inset of panel (f). (g) Optical spin orientation within the red dashed square in panel (f), which can be decomposed into two Bloch-type photonic meron sublattices in panel (h). Within each sublattice, local spin orientations transition from a central “up” or “down” state toward the edge where spin vectors lie in the transverse plane. The scale bar in panels (e) and (f) is λr. The topological charge is set as l=1 for each OV lattice point in panels (a) and (e). The arrows in panels (c), (d) and (g), (h) indicate the direction of a unit spin vector.

Fig. 3. Experimental demonstration of spin skyrmionium in free space. (a) Schematic diagram of the experiment. A hybrid polarized vortex beam with restricted NA is tightly focused on a metal–dielectric waveguide. A dielectric nanosphere is employed as a probe to characterize the spin texture formed at the center area of the focused field. Red ellipses represent the polarization state of incident light. (b)–(d) Measured (b) x, (c) y, and (d) z components of SAM distributions, with local spin orientation depicted in panel (e), where the arrows indicate the orientation of the normalized spin vectors. The scale bars in panels (b)–(d) are 0.5μm.

Fig. 4. Experimental demonstration of skyrmion and meron lattices in a focused circularly polarized beam. (a), (b) Measured (a) Sx and (b) Sy components of SAM distributions with the field of fourfold symmetry. (c) The co-frequency domain spectrum of Sx and Sy, demonstrating two sets of wave vectors. (d) Local spin orientation of the sublattice extracted by the inner wave vector in panel (c). (e), (f) Measured Sx and Sy components of SAM distributions with the field of sixfold symmetry, with the co-frequency domain spectrum of Sx and Sy depicted in panel (g). Three sets of wave vectors can be obtained, with the local spin orientation of the inner sublattice in panel (h). The scale bar in panels (a) and (b) and (e) and (f) is 0.5μm. In panels (d) and (h), the arrows indicate the orientation of the normalized spin vectors, with the color representing the value in the z direction.

Fig. 5. Topologic diagram of photonic spin skyrmions. (a), (b) The polarization ellipse (red arrows) and SAM (blue arrows) in (a) propagating and (b) evanescent waves in the presence of spin–orbit coupling, where the spin vectors rotate along azimuthal and radial directions, respectively. (c) Topologic diagram of individual photonic spin skyrmions, with the topology determined by both the polarization (η) and wave vector (kr/k) of optical vortices.