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We investigate the effects of the sign of the Rashba spin–orbit coupling (RSOC) on electron transmission through a single-channel nanowire (NW) in the quantum coherent regime. We show that, while for a finite length NW with homogeneous RSOC contacted to two electrodes the sign of its RSOC does not affect electron transport, the situation can be quite different in the presence of an inhomogeneous RSOC and a magnetic field applied along the NW axis. By analyzing transport across an interface between two regions of different RSOC we find that, if the two regions have equal RSOC signs, the transmission within the magnetic gap energy range is almost perfect, regardless of the ratio of the spin–orbit energies to the Zeeman energy. In contrast, when the two regions have opposite RSOC signs and are Rashba-dominated, the transmission gets suppressed. Furthermore, we discuss the implementation on a realistic NW setup where two RSOC regions are realized with suitably coupled gates separated by a finite distance. We find that the low-temperature NW conductance exhibits a crossover from a short distance behavior that strongly depends on the relative RSOC sign of the two regions to a large distance oscillatory behavior that is independent of such relative sign. We are thus able to identify the conditions where the NW conductance mainly depends on the sign of the RSOC and the ones where only the RSOC magnitude matters.

This article reviews recent progress leading to the generation of optical vortex beams. After introducing the basics of optical vortex beams and their promising applications, we summarized different approaches for optical vortex generation by discrete components and laser cavities. We place particular emphasis on the recent development of vortex generation by the planar phase plates, which are able to engineer a spiral phasefront via dynamic or geometric phase in nanoscale, and highlight the independent operation of these two different phases which leads to a multifunctional optical vortex beam generation and independent spin-orbit interaction. We also introduced the recent progress on vortex lasing, including vortex beam generation from the output of bulk lasers by modification of conventional laser cavities with phase elements and from integrated on-chip microlasers. Similar approaches are also applied to generate fractional vortex beams carrying fractional topological charge. The advanced technology and approaches on design and nanofabrications enable multiple vortex beams generation from a single device via multiplexing, multicasting, and vortex array, open up opportunities for applications on data processing, information encoding/decoding, communication and parallel data processing, and micromanipulations.

Magnetic textures, such as skyrmions and domain walls, engender rich transport phenomena, including anomalous Hall effect and nonlinear response. In this work, we discuss an anomalous Hall effect proportional to the net magnetic monopole charge and dependent on the skyrmion helicity that occurs by a skew scattering in a noncentrosymmetric two-dimensional magnet. This mechanism, which arises from the spin–orbit interaction (SOI), gives rise to a finite anomalous Hall effect in a ferromagnetic domain wall whose spins rotate in the xy plane despite no out-of-plane magnetic moment. We show that the presence and absence of the monopole contribution is related to crystal symmetry, which gives a guideline for finding candidate materials beyond the Rashba model. The results demonstrate the rich features arising from the interplay of SOI and magnetic textures, and their potential for detecting various magnetic textures in micrometer devices.

Temporal metamaterials, based on time-varying constitutive properties, offer new exciting possibilities for advanced field manipulations. In this study, we explore the capabilities of anisotropic temporal slabs, which rely on abrupt changes in time from isotropic to anisotropic response (and vice versa). Our findings show that these platforms can effectively manipulate the wave-spin dimension, allowing for a range of intriguing spin-controlled photonic operations. We demonstrate these capabilities through examples of spin-dependent analog computing and spin–orbit interaction effects for vortex generation. These results provide new insights into the field of temporal metamaterials, and suggest potential applications in communications, optical processing and quantum technologies.

A theoretical study is presented of the effect of an in-plane magnetic exchange field on the band structure of centrosymmetric films of noble metals and topological insulators. Based on an ab initio relativistic k ⋅ p theory, a minimal effective model is developed that describes two coupled copies of a Rashba or Dirac electronic system residing at the opposite surfaces of the film. The coupling leads to a structural gap at Γ ¯ and causes an exotic redistribution of the spin density in the film when the exchange field is introduced. We apply the model to a nineteen-layer Au(111) film and to a five-quintuple-layer Sb 2 Te 3 film. We demonstrate that at each film surface the exchange field induces spectrum distortions similar to those known for Rashba or Dirac surface states with an important difference due to the coupling: at some energies, one branch of the state loses its counterpart with the oppositely directed group velocity. This suggests that a large-angle electron scattering between the film surfaces through the interior of the film is dominant or even the only possible for such energies. The spin-density redistribution accompanying the loss of the counterpart favors this scattering channel.

The photonic spin Hall effect (SHE) originates from the interplay between the photon-spin (polarization) and the trajectory (extrinsic orbital angular momentum) of light, i.e. the spin-orbit interaction. Metasurfaces, metamaterials with a reduced dimensionality, exhibit exceptional abilities for controlling the spin-orbit interaction and thereby manipulating the photonic SHE. Spin-redirection phase and Pancharatnam-Berry phase are the manifestations of spin-orbit interaction. The former is related to the evolution of the propagation direction and the latter to the manipulation with polarization state. Two distinct forms of splitting based on these two types of geometric phases can be induced by the photonic SHE in metasurfaces: the spin-dependent splitting in position space and in momentum space. The introduction of Pacharatnam-Berry phases, through space-variant polarization manipulations with metasurfaces, enables new approaches for fabricating the spin-Hall devices. Here, we present a short review of photonic SHE in metasurfaces and outline the opportunities in spin photonics.

The manipulation of nonlinear spin–orbit interaction at the nanoscale is crucial for advancing information processing in integrated nanophotonics. However, the weak spin–orbit interaction (SOI) in conventional waveguide materials significantly limits the efficiency of nonlinear optical processes. In this work, we design a hybrid plasmonic waveguide composed of a gold film and a Y-branch CdSe nanowire, which addresses the aforementioned limitations. The designed hybrid structure enables efficient directional emission of second-harmonic generation (SHG) via control of the polarization of the excitation light. The transversely emitted SHG can be visualized for directly imaging the SOI. Our work not only provides a way to enhances the efficiency of the nonlinear SOI but also a promising platform for further advances in integrated photonics and nonlinear optics.

Asymmetric spin–orbit interaction (ASOI) breaks the limitations in conjugate symmetry of traditional geometric phase metasurfaces, bringing new opportunities for various applications such as spin-decoupled holography, imaging, and complex light field manipulation. Since anisotropy is a requirement for spin–orbit interactions, existing ASOI mainly relies on meta-atom with C1 and C2 symmetries, which usually suffer from an efficiency decrease caused by the propagation phase control through the structural size. Here, we demonstrate for the first time that ASOI can be realized in meta-atoms with rotational symmetry ≥3 by combining the generalized geometric phase with the propagation phase. Utilizing an all-metallic configuration, the average diffraction efficiency of the spin-decoupled beam deflector based on C3 meta-atoms reaches ∼84 % in the wavelength range of 9.3–10.6 μm, which is much higher than that of the commonly used C2 meta-atoms with the same period and height. This is because the anisotropy of the C3 metasurface originates from the lattice coupling effect, which is relatively insensitive to the propagation phase control through the meta-atom size. A spin-decoupled beam deflector and hologram meta-device were experimentally demonstrated and performed well over a broadband wavelength range. This work opens a new route for ASOI, which is significant for realizing high-efficiency and broadband spin-decoupled meta-devices.

Spatial differentiator is the key element for edge detection, which is indispensable in image processing, computer vision involving image recognition, image restoration, image compression, and so on. Spatial differentiators based on metasurfaces are simpler and more compact compared with traditional bulky optical analog differentiators. However, most of them still rely on complex optical systems, leading to the degraded compactness and efficiency of the edge detection systems. To further reduce the complexity of the edge detection system, a monolithic metasurface spatial differentiator is demonstrated based on asymmetric photonic spin-orbit interactions. Edge detection can be accomplished via such a monolithic metasurface using the polarization degree. Experimental results show that the designed monolithic spatial differentiator works in a broadband range. Moreover, 2D edge detection is experimentally demonstrated by the proposed monolithic metasurface. The proposed design can be applied at visible and near-infrared wavelengths by proper dielectric materials and designs. We envision this approach may find potential applications in optical analog computing on compact optical platforms.

Photonic skyrmions have applications in many areas, including the vectorial and chiral optics, optical manipulation, deep-subwavelength imaging and nanometrology. Much effort has been focused on the experimental characterization of photonic skyrmions. Here, we give an insight into the spin and orbital features of photonic skyrmions constructed by the -polarized and -polarized surface waves at an interface with various electric and magnetic properties by analyzing the continuity of chirality, energy flow and momentum densities through the electric and magnetic interface. The continuity of chirality density indicates that the photonic skyrmion has a property of the optical transverse spin. Most importantly, the continuity of energy flow and momentum densities results in four spin–orbit interaction quantities, which indicate the gradient of electric polarizability or permeability governs the spin–orbit interaction of photonic skyrmions and leads to the discontinuity and even the reversal of spin orientation through the optical interface. Our investigations on the spin–orbit properties of photonic skyrmions, which can give rise to the spin-dependent force and topological unidirectional transportation, is thorough and can be extended to other classical wave, such as acoustic and fluid waves. The findings help in understanding the spin–orbit feature of photonic topological texture and in constructing further optical manipulation, sensing, quantum and topological techniques.