Optical spin-orbit coupling is ubiquitous in nanoscale light-matter interactions. An in-depth study of these phenomena not only contributes to the discovery of new optical phenomena but also provides many opportunities for developing new technologies for light manipulation. In recent years, planar photonic devices such as geometric phase metasurfaces have shown many attractive applications, including multi-wavelength spin-dependent wavefront steering, spin-polarized photon generation, and spin-polarized thermal light emission. Most of these functions are achieved based on particularly designed nanostructures with certain types of spatial symmetry breaking, which aims to manipulate light in a subwavelength resolution and spin bases. In comparison, the interactions between light and disordered micro- and nanostructures also begin to catch our attention. However, the inherent randomness of disordered structures has made the research on spin-orbit coupling effects quite challenging, as stochastic processes must be considered in a statistic manner. Particularly, the emerging photonic spin Hall effect in random systems has not yet been fully understood. For instance, even though random geometric phase fluctuations and random vortices can both induce a photonic spin Hall effect, they have distinct physics origins. Thus, the underlined physics of the photonic spin split effects from different disordered geometric phases remains to be explored. This paper introduces the basic concept of the spin of light and spin-orbit coupling phenomena in different micro- and nano-optical systems and then focuses on analyzing the spin split effects of two-dimensional random systems, including anisotropic disorder, magneto-optical fluctuations, vortices, and random dipole radiation. Meanwhile, we attempt to utilize the photonic spin Hall effect in disordered systems as a potential means to precisely detect and manipulate two-dimensional magnetic and thermodynamic systems for the sensing and control of phase transition phenomena.

A typical result of optical spin-orbit coupling is the photonic spin Hall effect (PSHE), which describes the spatial split between light that carries opposite spins. For example, PSHE occurs when a polarized Gaussian beam is reflected or refracted at the air-dielectric material interface [Fig. 2(b)]. It also emerges when the propagation direction of a polarized paraxial light is slowly changing in free space, where the light polarization will rotate accordingly. In 2009, Bliokh et al. coupled a paraxial beam into a cylindrical glass and realized a spiral trajectory of light through continuous total internal reflections on the inner surface of the cylindrical glass. The separation of spin-up and spin-down components of light is gradually amplified by accumulating geometric phases during this progress, and a PSHE was finally observed. In 2015, it was also demonstrated that the spin-momentum locking in the evanescent wave exhibits an inherent quantum spin Hall effect of light, which is a unidirectional spin transfer phenomenon of light along the interface surface. Around 2001, Hasman's group developed a set of planar geometric phase optical elements by spatially-varying subwavelength grating structures called Pancharatnam-Berry phase optical element [Fig. 2(d)], which is the earliest version of the geometric phase metasurfaces. Currently, geometric phase metasurfaces have been widely applied to construct versatile planar photonic devices for spin-based light manipulation and detection. Nonparaxial beams sometimes can behave counterintuitively. For instance, it has long been thought that linearly polarized dipole radiation does not carry angular momentum. However, recent theories and experiments have shown that the near-field of linear polarized dipole radiation can have a spin texture [Fig. 2(j)], and this nearfield spin information can be observed through waveguide coupling or scattering processes of isotropic nanoparticles. The interaction between light and disordered structures can produce novel phenomena and unpredictable results. For instance, disorders can be engineered to eliminate laser speckles for better wavefront shaping. In 2021, it has also been shown that, through the design of disordered noise, the information capacity limit of traditional metasurfaces can be broken, and wavefront control with more polarization degrees of freedom can be obtained. In 2017, Maguid et al. reported on photonic spin-symmetry breaking and unexpected spin-optical transport phenomena arising from subwavelength-scale disordered geometric phase structures. Weak disorder induces a photonic spin Hall effect, which is observed via quantum weak measurements, whereas strong disorder leads to random spin-split modes in momentum space, which is called a random optical Rashba effect. As the geometric phase of the metasurface to the spin of light has the same mechanism as the Berry phase, a similar spin Hall effect can be produced in principle. In 2019, Wang et al. observed photonic topological defects of bound vortex pairs and unbound vortices generated from a two-dimensional array of nanoantennas, which is achieved by randomly inserting local deformations in the metasurfaces. The spin Hall effect of light is established based on discrete topological structures, or subwavelength vortex and antivortex pairs. Light does not carry an electric charge and therefore does not directly interact with the magnetic field, but a magnetized medium does affect the light propagation path. In 2020, Wang et al. studied a stochastic photonic spin Hall effect arising from space-variant Berry-Zak phases, which are generated by disordered magneto-optical effects. This spin shift is observed from a spatially bounded lattice of ferromagnetic meta-atoms displaying nanoscale disorders. A random variation of the radii of the meta-atoms induces the nanoscale fluctuation. This spin separation of light is in analogy to a Stern-Gerlach experiment, and photons of opposite spin are deflected into opposite directions as they interact with a magnetic material with random spatial gradients. The luminescence of quantum dots, 2D semiconductor materials, perovskite particles, and some atoms or molecules can be considered as dipole radiation randomly generated in time and space. Efficient polarization and phase control of this kind of radiation requires novel metasurfaces that have strong mode coupling between nanostructures. To achieve efficient control of randomly radiated dipoles [Fig. 11(d)], Rong et al. designed a geometric phase defective photonic crystal. The insertion of geometric phase structures into a photonic crystal that has a bandgap realizes many local defect modes. These defect modes not only achieve localized light emission but also select radiation polarization. Via tight-binding coupling between nanoantennas, the light emitted by each dipole can propagate to neighboring nanostructures to obtain a geometric phase accumulation that radiates into space with a predesigned spin-dependent momentum [Fig. 11(c)]. This configuration realizes efficiency polarization and momentum control of the light from random emitters.

As we have witnessed over the past two decades, optical spin-orbit coupling is ubiquitous in many optical systems. An in-depth understanding of these phenomena not only contributes to basic physics understanding but also brings forth a diversity of applications. Nowadays, the development of nano-photonics enters a stage where higher information dimensionality, higher spatial-time resolution, and many other extreme conditions are required. One promising direction is utilizing high-quality factor metasurfaces that can manipulate the polarization and wavefront of light beyond lasers, such as thermal light and quantum emitters. The other direction is to combine spin-optics and nano-magnetism. In particular, magnetic phenomena, such as those in magnetic metasurfaces or artificial spin ice, can be potentially detected by PSHE and quantum weak measurement. Finally, an optical means is provided to detect and manipulate the magnetic ordering and phase transition in correlated physical systems.