Fig. 1. Photonic spin and its presentation. (a) Poincaré sphere, left-handed and right-handed circular polarization are located at the south and north poles of the Poincaré sphere, respectively; (b) electric field of the circularly polarized light rotates around the wave vector k; (c)(d) difference of spin between free-space propagated light and evanescent waves (light possesses longitudinal spin in free-space propagation, while it exhibits transverse spin in evanescent waves)^[13]

Fig. 2. Ubiquitous spin-orbit coupling phenomena in micro- and nano-optics. (a) Separation of left-handed and right-handed circularly polarized light is induced by continuous total internal reflections of light on the inner surface of a cylindrical glass^[4]; (b) when a polarized Gauss beam illuminates a homogeneous air-dielectric interface, the reflected or refracted light exhibits a PSHE^[24]; (c) spin momentum locking of evanescent waves exhibits an intrinsic quantum spin hall effect of light^[16]; (d) spin distribution of light in the waveguide^［15］; (e) PSHE is realized by spatial-varying sub-wavelength grating structures^［41］; (f) spin locking at the energy-momentum bandstructure valley from a photonic crystal slab in a honeycomb configuration^[46-47]; (g) strong spin orbit coupling implementation of topological vortices around BIC^[52]; (h) boundary of two different photonic topological insulator performs light quantum transmission with unidirectional spin^[54]; (i) a vortex is generated when a circularly polarized plane wave illuminates a sub-wavelength spherical nanoparticle^[58]; (j) near field of linear polarized dipole possesses spin angular momentum^[60]; (k) radiation of a circularly polarized dipole induces wavelength scale centroid deviation in the far field^[56]

Fig. 3. Spin split effects and inversion symmetry breaking

Fig. 4. Applications of spin photonics. (a) Full stokes parameter measurement of chiral molecules is realized by a multifunctional geometry phase metasurface^[70]; (b) spatial differentiation of spin-separated light in an isotropic optical plan interface^[73]; (c) multispectral chiral imaging by metalens^[66]; (d) macroscopic spin optical force of light on the geometry phase structure^[75]; (e) multi-wavelength visible holograms is realized by dielectric metasurface^[68]; (f) quantum entangled photon pairs generated by metamaterials^[77]; (g) second harmonic wave carrying a series of different orbiital angular momentum is generated by the fundamental spin polarized light^[79]

Fig. 5. PSHE from order or disordered geometric phases. (a) PSHE induced by a conventional blazed grating geometric phase distribution; (b) PSHE induced by a disordered geometric phase metasurfce

Fig. 6. Spin splitting patterns in momentum space^[86]. (a) Scanning electron microscopic images of metasurfaces with different disorder parameter (ε) values (0, 0.5, 0.85, 0.95, and 1, from left to right); (b) different geometric phase pick-ups represented on the Poincaré sphere; (c) spatial phase distributions of the disordered geometric phase for different ε values; (d) measured momentum space intensity distributions of light from disordered geometric phases

Fig. 7. Time-reversal symmetry of spin split effects in random geometric phase structures

Fig. 8. Topological Hall effect of electron

Fig. 9. Photonic topological spin Hall effect and vortex pairs^[94]. (a) Schematic of topological defects and effective magnetic field; (b) schematic of vortex pairs in the near field; (c) PSHE generated by multiple geometry phase vortex pairs obeys the principle of vectoral superposition

Fig. 10. Kerr rotation, geometric phase and PSHE from a disordered ferromagnetic metasurface^[98]. (a) Calculated Kerr rotation θK and reflection as a function of the radius R of circular nickel nanoantennas in a periodic lattice; (b) calculated resonant phases φ0x and geometric phases φgx of an example 1D disordered metasurface with a radius distribution R(x) for the meta-atoms; (c) magnetization-induced geometric phase interpreted on the Poincaré spheres using two meta-atoms with radii R1 and R2 (left and right panels show the cases before and after the metasurface is magnetized, respectively)

Fig. 11. Manipulate the spin of quantum dots emission by a geometric phase photonic crystal^[61]. (a) Schematic of the Berry-phase defective photonic crystal incorporated with quantum dots; (b) measured spin-split modes in momentum space [dotted red (σ+) and blue (σ-) curves denote calculations based on the spin-orbit momentum-matching condition]; (c) dipole radiation can be coupled with adjacent nano antennas to obtain geometric phase accumulation in geometric phase photonic crystals; (d) dipole radiation is difficult to reach adjacent nano antennas to obtain geometric phase in geometric phase metasurfaces