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Inspired by neural network algorithms in deep learning, diffractive optical networks have arisen as new platforms for manipulating light-matter interactions. Seemly inherited from the deep learning black box nature, clear physical meanings have never been given for these complex diffractive networks at the layer level, even though the systems are visible in physical space. Using exemplified mode conversion systems, this work showed how various physical transformation rules within diffractive networks can be unveiled with properly defined input/output relations. Surprising physical transformation division phenomenon and an optical analogy of gradient-vanishing-effect have been observed and discussed for high-dimensional mode sorting tasks. The use of physical transparency for the effective design of parameter-varying networks is also demonstrated. These physically transparent optical networks resolve the contradiction between rigorous physical theorem and operationally vague network structure, and pave the way for transparentizing other physical neural networks.

Quasicrystals,characterized by long-range order without translational symmetry,have catalyzed transformative advances in various fields,including optics in terms of field quasicrystals.Here,we present the first demonstration of photonic quasicrystals formed by spin angular momentum, unveiling novel spin-orbit coupling effects absent in traditional field quasicrystals.A de Bruijn tiling like theoretical framework was built elucidating the formation mechanism of spin quasicrystals for diverse symmetries.Moreover,the configurations of these spin textures can be manipulated through the adjustments of the wavefronts,among which phason-like discontinuous dynamics is observed and quantitatively measured. Unlike optical quasicrystals shaped by electromagnetic fields,these spin-governed quasicrystals exhibit quasi-periodic properties of kinematic parameters,extending their potential applications to other physical systems. These findings hold promise for novel advancements in optical trapping,quasicrystal fabrication,and optical encryption systems.

Electromagnetic waves characterized by intensity, phase, and polarization degrees of freedom are widely applied in data storage, encryption, and communications. However, these properties can be substantially affected by phase disorders and disturbances, whereas high-dimensional degrees of freedom including momentum and angular momentum of electromagnetic waves can offer new insights into their features and phenomena, for example topological characteristics and structures that are robust to these disturbances. Here, we discover and demonstrate theoretically and experimentally spin-momentum locking and topological defects in unpolarized light. The coherent spin is locked to the kinetic momentum except for a small coupling spin term, due to the simultaneous presence of transverse magnetic and electric components in unpolarized light. To cancel the coupling term, we employ a metal film acting as a polarizer to form some skyrmion-like spin textures at the metal/air interface. Using an in-house scanning optical microscopic system to image the out-of-plane spin density of the focused unpolarized vortex light, we obtained experimental results that coincide well with our theoretical predictions. The theory and technique promote the applications of topological defects in optical data storage, encryption, and decryption, and communications., Comment: 9 pages, 3 figures, 47 references

The two-dimensional (2D) bulk photovoltaic effect (BPVE) is a cornerstone for future highly efficient 2D solar cells and optoelectronics. The ferromagnetic semiconductor 2H-FeCl2 is shown to realize a new type of BPVE in which spatial inversion (P), time reversal (T), and space-time reversal (PT) symmetries are broken (PT-broken). Using density functional theory and perturbation theory, we show that 2H-FeCl2 exhibits giant photocurrents, photo-spin-currents, and photo-orbital-currents under illumination by linearly polarized light. The injection-like and shift-like photocurrents coexist and propagate in different directions. The material also demonstrates substantial photoconductance, photo-spin-conductance, and photo-orbital-conductance, with magnitudes up to 4650 (nm{\cdot}{\mu}A/V2), 4620 (nm{\cdot}{\mu}A/V2 {\hbar}/2e), and 6450 (nm{\cdot}{\mu}A/V2 {\hbar}/e), respectively. Furthermore, the injection-currents, shift-spin-currents, and shift-orbital-currents can be readily switched via rotating the magnetizations of 2H-FeCl2. These results demonstrate the superior performance and intriguing control of a new type of BPVE in 2H-FeCl2., Comment: 12 pages, 5 figures. Accepted by Frontiers of Physics

Spin angular momentum, an elementary dynamical property of classical electromagnetic fields, plays an important role in spin-orbit and light-matter interactions, especially in near-field optics. The research on optical spins has led to the discovery of phenomena such as optical spin-momentum locking and photonic topological quasiparticles, as well as applications in high-precision detection and nanometrology. Here, we investigate spin-momentum relations in paraxial optical systems and show that the optical spin angular momentum contains transverse and longitudinal spin components simultaneously. The transverse spin originates from inhomogeneities of field and governed by the vorticity of the kinetic momentum density, whereas the longitudinal spin parallel to the local canonical momentum is proportional to the polarization ellipticity of light. Moreover, the skyrmionlike spin textures arise from the optical transverse spin can be observed in paraxial beams, and their topologies are maintained free from the influence of the Gouy phase during propagation. Interestingly, the optical singularities, including both phase and polarization singularities, can also affect the spin-momentum properties significantly. Our findings describe the intrinsic spin-momentum properties in paraxial optical systems and apply in the analysis of the properties of spin-momentum in optical focusing, imaging, and scattering systems., Comment: 20 pages; 6 figures, 151 references

Skyrmions are topologically stable quasiparticles that have been predicted and demonstrated in quantum fields, solid-state physics, and magnetic materials, but only recently observed in electromagnetic fields, triggering fast expanding research across different spectral ranges and applications. Here we review the recent advances in optical skyrmions within a unified framework. Starting from fundamental theories, including classification of skyrmionic states, we describe generation and topological control of different kinds of optical skyrmions in structured and time-dependent optical fields. We further highlight generalized classes of optical topological quasiparticles beyond skyrmions and outline the emerging applications, future trends, and open challenges. A complex vectorial field structure of optical quasiparticles with versatile topological characteristics emerges as an important feature in modern spin-optics, imaging and metrology, optical forces, structured light and topological and quantum technologies.

Spin-momentum locking is an intrinsic property of surface electromagnetic fields and its study has led to the discovery of photonic spin lattices and diverse applications. Previously, dispersion was ignored in the spin-momentum locking, giving rise to abnormal phenomena contradictory to the physical realities. Here, we formulate four dispersive spin-momentum equations for surface waves, revealing universally that the transverse spin vector is locked with the momentum. The locking property obeys the right-hand rule in the dielectric but the left-hand rule in the dispersive metal/magnetic materials. In addition to the dispersion, the structural features can affect the spin-momentum locking significantly. Remarkably, an extraordinary longitudinal spin originating from the coupling polarization ellipticity is uncovered even for the purely polarized state. We further demonstrate the spin-momentum locking properties with diverse photonic topological lattices by engineering the rotating symmetry. The findings open up opportunities for designing robust nanodevices with practical importance in chiral quantum optics., Comment: 6 pages, 4 figures in main text 36 pages, 15 figures and 81 equations in supplemental materials

Electromagnetic spins, including longitudinal and transverse ones, have been playing important roles in light-matter interactions. Here, we formulate a unified equation to uncover the physical origins and topological properties of longitudinal and transverse spins in a generic electromagnetic field. The equation reveals universally that the transverse spin is locked with the kinetic momentum and originated from the transverse inhomogeneities of field, whereas the helix-dependent longitudinal spin orients parallel to the local wavevector. Remarkably, a hidden extraordinary helix-dependent transverse spin possessing helix-dependent spin-momentum locking is discovered and the number of locking states consistent with the nontrivial topological spin Chern number. Furthermore, this spin which determines the inverted helical components is related to the Berry curvature closely. The findings, which are demonstrated experimentally by measuring the three-dimensional spin components in the focusing configuration, will deepen the understanding the underlying physics of spins and open an avenue for chiral quantum optical applications., Comment: 15 pages, 3 figures, 2 table, 7 equations, 56 references in main text; 39 pages, 16 figures, 100 equations, 16 references in supplemental materials

Chiral spin textures are researched widely in condensed matter systems and show potential for spintronics and storage applications. Along with extensive condensed-matter studies of chiral spin textures, photonic counterparts of these textures have been observed in various optical systems with broken inversion symmetry. Unfortunately, the resemblances are only phenomenological. This work proposes a theoretical framework based on the variational theorem to show that the formation of photonic chiral spin textures in an optical interface is derived from the system's symmetry and relativity. Analysis of the optical system's rotational symmetry indicates that conservation of the total angular momentum is preserved from the local variations of spin vectors. Specifically, although the integral spin momentum does not carry net energy, the local spin momentum distribution, which determines the local subluminal energy transport and minimization variation of the square of total angular momentum, results in the chiral twisting of the spin vectors. The findings here deepen the understanding of the symmetries, conservative laws and energy transportation in optical system, construct the comparability in the formation mechanisms and geometries of photonic and condensed-matter chiral spin textures, and suggest applications to optical manipulation and chiral photonics., Comment: 20 pages, 4 figures

Symmetry governs many electronic and photonic phenomena in optics and condensed matter physics. Skyrmions and merons are prominent topological structures in magnetic materials, with the topological features determined by the interplay between anisotropy of a material and its magnetization. Here we theoretically show and experimentally demonstrate that the symmetry of the electromagnetic field determines the spin topological properties of the guided modes via spin-orbit coupling and may only result in either hexagonal spin-skyrmion or square spin-meron lattices. We also show that in the absence of spin-orbit coupling these spin topologies are degenerated in dynamic field-skyrmions, unifying description of electromagnetic field topologies. The results provide new understanding of electromagnetic field topology and its transformations as well as new opportunities for applications in quantum optics, spin-optics and topological photonics.

Magnetic skyrmions are topological quasiparticles in magnetic field. Until recently, as one of their photonic counterparts, N\'eel-type photonic skyrmion is discovered in surface plasmon polaritons. The deep-subwavelength features of the photonic skyrmions suggest their potentials in quantum technologies and data storage. So far, the Bloch-type photonic skyrmion has yet to be demonstrated in this brand new research field. Here, by exploiting the quantum spin Hall effect of a plasmonic optical vortex in multilayered structure, we predict the existence of photonic twisted-N\'eel- and Bloch-type skyrmions in chiral materials. Their chirality-dependent features can be considered as additional degrees-of-freedom for future chiral sensing, information processing and storage technologies. In particular, our findings enlarge the family of photonic skyrmions and reveal a remarkable resemblance of the feature of chiral materials in two seemingly distant fields: photonic skyrmions and magnetic skyrmions., Comment: 6 pages, 5 figures

Optical spin angular momenta in a confined electromagnetic field exhibit remarkable difference with their free space counterparts, in particular, the optical transverse spin that is locked with the energy propagating direction lays the foundation for many intriguing physical effects such as unidirectional transportation, quantum spin Hall effect, photonic Skyrmion, etc. In order to investigate the underlying physics behind the spin-orbit interactions as well as to develop the optical spin-based applications, it is crucial to uncover the spin texture in a confined field, yet it faces challenge due to their chiral and near-field vectorial features. Here, we propose a scanning imaging technique which can map the near-field distributions of the optical spin angular momenta with an achiral dielectric nanosphere. The spin angular momentum component normal to the interface can be uncovered experimentally by employing the proposed scanning imaging technique and the three-dimensional spin vector can be reconstructed theoretically with the experimental results. The experiment is demonstrated on the example of surface plasmon polaritons excited by various vector vortex beams under a tight-focusing configuration, where the spin-orbit interaction emerges clearly. The proposed method, which can be utilized to reconstruct the photonic Skyrmion and other photonic topological structures, is straightforward and of high precision, and hence it is expected to be valuable for the study of near-field spin optics and topological photonics.

Quantum spin-Hall effect, a manifestation of topological properties that govern the behavior of surface states, was studied intensively in condensed matter physics resulting in the discovery of topological insulators. The quantum spin-Hall effect of light was introduced for surface plane-waves which intrinsically carry transverse optical spin, leading to many intriguing phenomena and applications in unidirectional waveguiding, metrology and quantum technologies. In addition to spin, optical waves can exhibit complex topological properties of vectorial electromagnetic fields, associated with orbital angular momentum or nonuniform intensity variations. Here, by considering both spin and angular momentum, we demonstrate a generalized spin-momentum relationship that governs vectorial properties of guided electromagnetic waves, extending optical quantum spin-Hall effect to a two-dimensional vector field of structured guided wave. The effect results in the appearance of the out-of-plane transverse optical spins, which vary progressively from the 'up' state to the 'down' state around the energy flow, and their variation is uniquely locked to the energy propagation direction. The related spin-momentum locking in a chiral spin swirl is demonstrated with four kinds of surface structured waves and proven both theoretically and experimentally. The results provide understanding of the spin dynamics in electromagnetic guided waves and show great importance in spin optics, topological photonics and optical spin-based devices and techniques., Comment: 30 pages; 13 figures; 44 equations; 1 table; 41 references for main text and 45 references for Supplementary Materials

In magnetic materials, skyrmions are nanoscale regions where the orientation of electron spin changes in a vortex-type manner. Here we show that spin-orbit coupling in a focused vector beam results in a skyrmion-like photonic spin distribution of the excited waveguided fields. While diffraction limits the spatial size of intensity distributions, the direction of the field, defining photonic spin, is not subject to this limitation. We demonstrate that the skyrmion spin structure varies on the deep-subwavelength scales down to 1/60 of light wavelength, which corresponds to about 10 nanometre lengthscale. The application of photonic skyrmions may range from high-resolution imaging and precision metrology to quantum technologies and data storage where the spin structure of the field, not its intensity, can be applied to achieve deep-subwavelength optical patterns.

In this letter, we demonstrate a novel diffraction-free Bloch surface wave (DF-BSW) sustained on all-dielectric multilayers that does not diffract after being passed through three obstacles or across a single mode fiber. It can propagate in a straight line for distances longer than 110 {\mu}m at a wavelength of 633 nm and could be applied as an in-plane optical virtual probe, both in air and in an aqueous environment. The ability to be used in water, its long diffraction-free distance, and its tolerance to multiple obstacles make this DF-BSW ideal for certain applications in areas such as the biological sciences, where many measurements are made on glass surfaces or for which an aqueous environment is required, and for high-speed interconnections between chips, where low loss is necessary. Specifically, the DF-BSW on the dielectric multilayer can be used to develop novel flow cytometry that is based on the surface wave, but not the free space beam, to detect the surface-bound targets.

On-chip twisted light emitters are essential components for orbital angular momentum (OAM) communication devices, which could address the growing demand for high-capacity communication systems by providing an additional degree of freedom for wavelength/frequency division multiplexing (WDM/FDM). Although whispering gallery mode enabled OAM emitters have been shown to possess some advantages, such as being compact and phase accurate, their inherent narrow bandwidth prevents them from being compatible with WDM/FDM techniques. Here, we demonstrate an ultra-broadband multiplexed OAM emitter that utilizes a novel joint path-resonance phase control concept. The emitter has a micron sized radius and nanometer sized features. Coaxial OAM beams are emitted across the entire telecommunication band from 1450 to 1650 nm. We applied the emitter for OAM communication with a data rate of 1.2 Tbit/s assisted by 30-channel optical frequency combs (OFC). The emitter provides a new solution to further increase of the capacity in the OFC communication scenario.

The ability to tailor a coherent surface plasmon polariton (SPP) field is an important step towards a number of new opportunities for a broad range of nanophotonic applications such as sensing [1,2], nano-circuitry [3,4], optical data storage [5,6], super-resolution imaging [7,8], plasmonic tweezers [9,10] and in-plane communications [11]. Scanning a converging SPP spot or designing SPP profiles using an ensemble of spots have both been demonstrated previously [12-14]. SPPs, however, are normally excited by intense, coherent light sources-lasers. Hence, interference between adjacent spots is inevitable and will affect the overall SPP field distributions. Here we report a reconfigurable and wavelength-independent platform for generating a tailored 2D SPP field distribution by considering the coherent field as a whole rather than individual spots. The new perspective also enables us to reveal the inherent constraints implied in a 2D coherent field distribution. Our generic design methodology works not only for SPP waves but also for other two-dimensional wave systems like surface acoustic waves [15].

Metasurfaces are promising two-dimensional metamaterials that are engineered to provide unique properties or functionalities absent in naturally occurring homogeneous surfaces. Here, we report a type of metasurface for tailored reconstruction of surface plasmon waves from light. The design is generic in a way that one can selectively generate different surface plasmon waves through simple variation of the wavelength or the polarization state of incident light. The ultra-thin metasurface demonstrated in this paper provides a versatile interface between the conventional free-space optics and a two-dimensional platform such as surface plasmonics., Comment: 7 figures, supplementary information at the end of the document