Spin/momentum properties of the paraxial optical beams

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 reference

Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum

In magnetic materials, skyrmions are nanoscale regions where the orientation of electron spin changes in a vortex-type manner1-4. Electromagnetic waves carry both spin and orbital angular momenta5,6. Here we show that spin-orbit coupling7-12 in a focused vector beam results in skyrmion-like structure of local photonic spin. While diffraction limits the spatial size of intensity variations, the direction of the electromagnetic field, which defines the polarization and local photonic spin state, is not subject to this limitation. We demonstrate that the local spin direction in the skyrmion-like 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 local spin state of the field, not its intensity, can be applied to achieve deep-subwavelength optical patterns

Transverse spin dynamics in structured electromagnetic guided waves

Spin-momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin-momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.</p

The hidden spin-momentum locking and topological defects in unpolarized light fields

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 reference

Evolution of Microstructural Characteristics of Carbonated Cement Pastes Subjected to High Temperatures Evaluated by MIP and SEM

The microstructural evolutions of both uncarbonated and carbonated cement pastes subjected to various high temperatures (30 degrees C, 200 degrees C, 400 degrees C, 500 degrees C, 600 degrees C, 720 degrees C, and 950 degrees C) are presented in this study by the means of mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM). It was found that the thermal stabilities of uncarbonated cement pastes were significantly changed from 400 to 500 degrees C due to the decomposition of portlandite at this temperature range. More large pores and microcracks were generated from 600 to 720 degrees C, with the depolymerization of C-S-H. After carbonation, the microstructures of carbonated cement pastes remained unchanged below 500 degrees C and started to degrade at 600 degrees C, due to the decompositions of calcium carbonates and calcium modified silica gel. At 950 degrees C, both uncarbonated and carbonated cement pastes showed a loosely honeycombed microstructure, composed mainly of beta-C2S and lime. It can be concluded that carbonation improves the high-temperature resistance of cement pastes up to 500 degrees C, but this advantage is lost at temperatures over 600 degrees C

General Automatic Solution Generation of Social Problems

Given the escalating intricacy and multifaceted nature of contemporary social systems, manually generating solutions to address pertinent social issues has become a formidable task. In response to this challenge, the rapid development of artificial intelligence has spurred the exploration of computational methodologies aimed at automatically generating solutions. However, current methods for auto-generation of solutions mainly concentrate on local social regulations that pertain to specific scenarios. Here, we report an automatic social operating system (ASOS) designed for general social solution generation, which is built upon agent-based models, enabling both global and local analyses and regulations of social problems across spatial and temporal dimensions. ASOS adopts a hypergraph with extensible social semantics for a comprehensive and structured representation of social dynamics. It also incorporates a generalized protocol for standardized hypergraph operations and a symbolic hybrid framework that delivers interpretable solutions, yielding a balance between regulatory efficacy and function viability. To demonstrate the effectiveness of ASOS, we apply it to the domain of averting extreme events within international oil futures markets. By generating a new trading role supplemented by new mechanisms, ASOS can adeptly discern precarious market conditions and make front-running interventions for non-profit purposes. This study demonstrates that ASOS provides an efficient and systematic approach for generating solutions for enhancing our society

Mode-matching metasurfaces: coherent reconstruction and multiplexing of surface waves

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 documen