Orbital Angular Momentum Distribution Research Articles

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets.

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Orbital angular momentum small-x evolution: exact results in the large-Nc limit

We construct an exact solution to the revised small-x orbital angular momentum (OAM) evolution equations derived in [1], based on an earlier work [2]. These equations are derived in the double logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant and x the Bjorken x variable) and the large-Nc limit, with Nc the number of quark colors. From our solution, we extract the small-x, large-Nc expressions of the quark and gluon OAM distributions. Additionally, we determine the large-Nc small-x asymptotics of the OAM distributions to beLq+q¯xQ2∼LGxQ2∼ΔΣxQ2∼ΔGxQ2∼1xαh,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{q+\\overline{q}}\\left(x,{Q}^2\\right)\\sim {L}_G\\left(x,{Q}^2\\right)\\sim \\Delta \\Sigma \\left(x,{Q}^2\\right)\\sim \\Delta G\\left(x,{Q}^2\\right)\\sim {\\left(\\frac{1}{x}\\right)}^{\\alpha_h}, $$\\end{document}with the intercept αh the same as obtained in the small-x helicity evolution [3], which can be approximated as αh ≈ 3.66074αsNc2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 3.66074\\sqrt{\\frac{\\alpha_s{N}_c}{2\\pi }} $$\\end{document}. This result is in complete agreement with [4]. Additionally, we calculate the ratio of the quark and gluon OAM distributions to the flavor-singlet quark and gluon helicity parton distribution functions respectively in the small-x region.

Spectral analysis of intricate orbital angular momentum modes in multiplexing communication using a residual neural network

Vortex beams carrying orbital angular momentum (OAM) modes offer a compelling avenue for increasing optical communication capacity. Despite significant efforts in OAM mode (de)multiplexing, challenges persist in signal demodulation and noise monitoring of multiplexed channels. This challenge largely stems from the absence of efficient feature extraction methods capable of analyzing the OAM spectrum, which delineates mode components and intensity weights. Herein, we introduce a novel strategy for OAM mode spectrum analysis using a residual neural network incorporating interference techniques. By introducing interference between target vortex beams and a spherical wave, resulting in the mapping of OAM distributions onto the stripe features observed in the interferogram. To effectively extract spectrum details from these interferograms, we construct a residual neural network exhibiting high feature processing capabilities, which enables precise analysis of intricate OAM mode spectrum. We demonstrate the effectiveness of this OAM spectrum analysis by obtaining the intensity weights for 15 superimposed modes ranging from −10 to +10, achieving a mean-square-error of 2.3 × 10−4. To validate its practicality, we showcase an 80-channel three-dimensional multiplexing communication system including five OAM modes, two polarizations, and eight wavelengths. The 4 Tbit/s quadrature-phase-shift-keying signals are successfully demodulated with a bit-error rate below 3.34 × 10−6. Additionally, the measured optical signal-to-noise ratio reaches 11.5 dB, indicating the potential applications of this OAM spectrum analysis strategy in signal demodulation and noise monitoring.

Orbital angular momentum at small x revisited

We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant). We solve these evolution equations numerically and extract the leading large-Nc, small-x asymptotics of the quark and gluon OAM distributions, which we determine to beLq+q¯xQ2~LGxQ2~∆ΣxQ2~∆GxQ2~123.66αsNc2π,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{q+\\overline{q}}\\left(x,{Q}^2\\right)\\sim {L}_G\\left(x,{Q}^2\\right)\\sim \\Delta \\Sigma \\left(x,{Q}^2\\right)\\sim \\Delta G\\left(x,{Q}^2\\right)\\sim {\\left(\\frac{1}{2}\\right)}^{3.66\\sqrt{\\frac{\\alpha_s{N}_c}{2\\uppi}}}, $$\\end{document}in agreement with [2] within the precision of our numerical evaluation. (Here Nc is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

Deep-learning assisted fast orbital angular momentum complex spectrum analysis.

Analyzing the orbital angular momentum (OAM) distribution of a vortex beam is critical for OAM-based applications. Here, we propose a deep residual network (DRN) to model the relationship between characteristics of the multiplexed OAM beam and their complex spectrum. The favorable experimental results show that our proposal can obtain both the intensity and phase terms of multiplexed OAM beams, dubbed complex spectrum, with a wide range of OAM modes, varying in intensity, phase ratio, and mode intervals at high accuracy and real-time speed. Specifically, the root mean square error (RMSE) of intensity and phase spectrum is evaluated as 0.002 and 0.016, respectively, with a response time of only 0.020 s. To the best of our knowledge, this work opens a new sight for fast OAM complex spectrum analysis and paves the way for numerous advanced domains that need real-time OAM complex spectrum diagnostic like ultrahigh-dimensional OAM tailoring.

Influence of High-Order Twisting Phases on Polarization States and Optical Angular Momentum of a Vector Light Field

This study investigates the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The twisted vector optical field (TVOF) is experimentally generated based on the orthogonal polarization bases with high-order twisting phases. The initial SoP of a TVOF modulated by the high-order twisting phase possesses various symmetric distributions. The propagation properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in a non-isotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. The optical energy flow distribution of a high-order TVOF provides a more profound understanding of the propagation dynamics of high-order TVOF. These results provide a new approach for optical field manipulation in a high-order TVOF.

Modulating and identifying an arbitrary curvilinear phased optical vortex array of high-order orbital angular momentum

Vortex beams can be used in optical communication, imaging, and processing applications. In this study, we generate a phased optical vortex array with high-order orbital angular momentum (OAM) based on a phased Gaussian optical array and high-order phase multiplication. We then analyze the OAM mode distribution using the OAM spectrum expansion, and the number of high-order phase singularities in the array verified in interference experiments. Our results substantiate the feasibility of generating a high-order optical vortex array using this method. At the same time, because the phase Gaussian optics array that forms the phased optical vortex array is discrete and separable, we can use the phase Gaussian optics array with different phase differences to generate the phased optical vortex array with different phase gradients. The shape of the generated optical vortex array can be arranged along any curve. The phase singularity and OAM distributions at high orders are also detailedly analyzed. The ability to control the high-order OAM and phase structure has possible applications in particle manipulation and free-space optical communication.

Analyzing Vortex Light Beam Scattering Characteristics from a Random Rough Surface

The propagation and scattering of vortex light beams in complex media have significant implications in the fields of laser imaging, optical manipulation, and communication. This paper investigates the scattering characteristics of vortex light beams from a random rough surface. Firstly, a two-dimensional Gaussian rough surface is generated using the Monte Carlo method combined with the linear filtering method. Subsequently, the vortex beams are decomposed into the superposition of infinite plane waves, and the scattering of each plane wave from the rough surface is calculated using the Kirchhoff Approximation method. Numerical results of the angle distribution and spatial distribution of OAM scattering Laser Radar Cross Section (LRCS) are presented, varying with different surface roughness parameters for a rough aluminum surface and the beam’s parameters. The results demonstrate that the scattering of vortex beams is influenced by the beam’s parameters, such as Orbital Angular Momentum (OAM) mode number and elevation angle, which may bring new insights into vortex wave-matter interactions and their applications in high resolution imaging.

Controllable Helico-Conical Beam Generated with the Bored Phase

A controllable helico-conical beam is proposed in this paper. The intensity patterns and the local spatial frequency of the controllable helico-conical beams in the focal region are analyzed in detail. The results show that the length of the helico-conical beams can be customized by the variable parameter k, and the angular dimension of the bored spiral trajectory is dependent on the proportion k/l. Moreover, the focal-field energy flow density and orbital angular momentum distributions of the controllable helico-conical beams are also analyzed. The proposed helico-conical beams with controllable lengths can be potentially applied in the field of optical guiding.

Abrupt autofocusing performance of a circular Airyprime beam with vortex pairs

Abrupt autofocusing performance of a circular Airyprime beam (CAPB) with vortex pairs propagating in free space is investigated. Here the vortex pairs are off-axis by default. The influences of topological charges and spatial location of vortex pairs on abrupt autofocusing behaviour of a CAPB with vortex pairs are evaluated by numerical simulations. A intensity contrast, which is the ratio of peak intensity on a certain observation plane to that on initial plane, is used to describe the abrupt autofocusing ability. The focus length of a CAPB with vortex pairs only depends on topological charges and is independent of spatial location of vortex pairs. When the topological charges increase, the abrupt autofocusing ability is enhanced, which is accompanied by the slight extension of the focal length. The spatial location of vortex pairs includes azimuth and radial locations. The effect of the azimuth location of vortex pairs on the abrupt autofocusing behaviour is so slight that it can be neglected. If the radial location of vortex pairs decreases, the abrupt autofocusing ability is improved. Abrupt autofocusing performance of a CAPB with vortex pairs is also compared with that of a CAPB with an optical vortex. Due to large dark-hollow intensity distribution and carrier of much orbital angular momentum, a CAPB with vortex pairs has advantages over a CAPB with an off-axis optical vortex in optical capture and other applications.

Intense vortical-field generation using coherent superposition of multiple vortex beams

Coherent beam combining technology applied to multiple vortex beams is a promising method to generate high-power vortex beams. We utilize the coherent combination of multiple Laguerre-Gaussian beams at the waist plane and propose theoretically a practical generation system for a high-power beam carrying orbital angular momentum by considering oblique incidence. The results demonstrate that the orbital angular momentum distribution of the combined field is similar to that of a single Laguerre-Gaussian beam within the Rayleigh length. Moreover, the combined field has relativistic intensity local spots that exhibit stable spatial propagation. The proposed system may potentially be applied to intense vortical fields, large scale nuclear fusion device, such as suppressing stimulated Raman scattering and filamentation when a laser beam propagates in plasma.

Spin-orbital coupling in strong interaction and global spin polarization

In non-central relativistic heavy ion collisions, the colliding nuclear system possesses a huge global orbital angular momentum in the direction opposite to the normal of the reaction plane. Due to the spin-orbit coupling in strong interaction, such a huge orbital angular momentum leads to a global spin polarization of the quark matter system produced in the collision process. The global polarization effect in high energy heavy ion collisions was first predicted theoretically and confirmed by STAR experiments at the Relativistic Heavy Ion Collider in Brookhaven National Laboratory. The discovery has attracted much attention to the study of spin effects in heavy ion collision and leads to a new direction in high energy heavy ion physics—Spin Physics in Heavy Ion Collisions. In this paper, we briefly review the original ideas, the calculation methods, the main results and recent theoretical developments in last years. First, we present a short discussion of the spin-orbit coupling which is an intrinsic property for a relativistic fermionic quantum system. Then we review how the global orbital angular momentum can be generated in non-central heavy ion collisions and how the global orbital angular momentum can be transferred to the local orbital angular momentum distribution in two limit model---Landan fireball model and Bjorken scaling model. After that, we review how we can describe the scattering process with initial local orbital angular momentum in the formalism of scattering cross section in impact parameter space and how we calculate the polarization of the quarks and antiquarks in quark gluon plasma produced in non-central heavy ion collisions after single or multiple scattering. We also give a brief review on how the global polarization can be predicted from the formalism of relativistic hydrodynamics with the generalized Cooper-Frye formula with spin. Finally, we discuss how the quark's polarization can be transferred to the final hadron's polarization. We focus on the hyperon's polarization and vector meson's spin alignment produced in heavy-ion collisions.

Interaction of spin-orbit angular momentum in the tight focusing of structured light

As an intrinsic property of light, angular momentum has always been an important research object of light field. In the past few years, the interactions between spin angular momentum and orbital angular momentum in tightly focused structured light have attracted much attention. Different from the independent conservation in the paraxial condition, the polarization-dependent spin angular momentum and the phase-dependent orbital angular momentum are coupled under tight focusing condition based on different physical mechanisms. The research on spin-orbit interaction will be helpful to deeply understand the nature of photon as well as extend the applications of light. Here, different forms of spin-orbit interaction during the tight focusing of structured light have been briefly introduced and classified. Besides, the existing problems and development prospects in the research about spin-orbit interaction of light are discussed, including the quantitative detection of the local distribution of optical spin and orbital angular momentum in experiments and the further applications of spin-orbit interaction.

Generation and verification of optical vortices with controlled phase based on coherent beam combining

Optical vortices (OVs) with controllable orbital angular momentum (OAM) distributions have potential applications in optical communication and optical manipulation. However, the source of optical vortices with segmented phase gradients generated by existing methods can be used only at a short distance because of their low power. In this study, based on coherent combining technology, we proposed a method to generate a controlled-phase optical vortex (COV). Compared with traditional OVs, the magnitude and direction of the local OAM of the COV are controllable. The transmission characteristics of the COV in free space were numerically examined using a split-step Fourier transform algorithm. We theoretically and experimentally proved the feasibility of the coherent combining technology to generate an COV and proved that it has the properties of non-diffraction and self-healing.

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence.

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

Orbital angular momentum comb generation from azimuthal binary phases

Since Allen et al. demonstrated 30 years ago that beams with helical wavefronts carry orbital angular momentum (OAM), the OAM of beams has attracted extensive attention and stimulated lots of applications in both classical and quantum physics. Akin to an optical frequency comb, a beam can carry multiple various OAM components simultaneously. A series of discrete, equally spaced, and equally weighted OAM modes comprise an OAM comb. Inspired by the spatially extended laser lattice, we demonstrate both theoretically and experimentally an approach to producing OAM combs through azimuthal binary phases. Our study shows that transition points in the azimuth determine the OAM distributions of diffracted beams. Multiple azimuthal transition points lead to a wide OAM spectrum. Moreover, an OAM comb with any mode spacing is achievable through reasonably setting the position and number of azimuthal transition points. The experimental results fit well with theory. This work presents a simple approach that opens new prospects for OAM spectrum manipulation and paves the way for many applications including OAM-based high-security encryption and optical data transmission, and other advanced applications.

Spin Hall effect of fractional order radially polarized beam in its tight focusing

Different from the traditional radially polarized beams, the fractional order radially polarized beam possess the symmetry broken structure of the polarization state distribution. The symmetry broken of the optical beams’ intrinsic structure can lead to the spin–orbit coupling of light. In this paper, we investigate the tight focusing of the fractional order radially polarized beam and show some interesting phenomena induced by the symmetry broken structure of the polarization state distribution. Firstly, the intensity and the spin angular momentum density are split in the focal plane, and the focal field intensity distribution can be controlled (split or focused) by modulating the initial phase of the polarization state. Furthermore, just like the spin angular momentum, the orbital angular momentum density also is split into two opposite parts (positive and negative). Though, the evolutions of the spin and the orbital angular momentum are different: as the change of the initial phase of the polarization state, the spin angular momentum distribution just is rotated slightly, yet the orbital angular momentum distribution is reversed. All these phenomena can be considered as the manifestations of the spin Hall effect of the fractional order radially polarized beam. Our results provide further potential applications of the vector beams in the focal field shaping.

Orbital angular momentum evolution of twisted multi-Gaussian Schell model beams in anisotropic turbulence

Twist phase is an unconventional phase that allows a partially coherent beam to carry orbital angular momentum (OAM). In this work, based on the Mercer’s expansion and the nonnegativity of the cross-spectral density function, we obtain a twistable condition for the multi-Gaussian Schell model (MGSM) correlation structure. The expression of an elliptical twisted multi-Gaussian Schell model (TMGSM) beam through non-Kolmogorov anisotropic atmospheric turbulence is rigorously derived, and its spectral density and OAM variation in anisotropic turbulence are studied in detail. The results show that the spectral density and OAM flux density distributions rotate with increasing transmission distance, and increasing the multi-Gaussian modulus and twist factor can significantly suppress the negative effects of atmospheric turbulence. The difference of turbulence anisotropy, beam modulus, and coherence length can affect the distribution of OAM. Furthermore, the twist phase affects both the OAM distribution and magnitude. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications.

Controllable perfect optical vortex generated by complex amplitude encoding.

We propose a new paradigm for generating the perfect optical vortex (POV) with a controlled structure and orbital angular momentum (OAM) distribution in the focal region of a tightly focused system. The superiority of the proposed technique is demonstrated with an experiment involving the dynamic manipulation of small particles. This technique for creating the POV could open new routes to optical manipulation based on OAM.

Triple-vortex bremsstrahlung

Particles in vortex states have gained arising interests due to the additional degree of freedom—the orbital angular momentum (OAM) inherently existing in the state. With the increasing energy of vortex particles (photons, leptons etc), the research has gradually transitioned from the classical field regime to collisions of vortex particles in the quantum-field regime. The latter provides a new way to study the rich properties of particle physics. Here, we show the characteristics of vortex states in bremsstrahlung by deriving the corresponding scattering probability following the quantum-electrodynamics theory. The theory allows us to obtain the OAM distribution of the outgoing vortex photon and the law of OAM transfer during interaction. It is shown that the generated photon takes most of the initial electron OAM, especially when the latter is more energetic. The opening angle of outgoing particles in vortex bremsstrahlung is also significantly different from plane wave scattering. The effects of polarization and non-zero impact parameter are also discussed. The results illustrate the unique feature of vortex scattering and suggest a feasible way to generate high-energy vortex photons—a novel source in studying nuclear physics.