Measuring Topological Charges of Optical Vortices with Multi-Singularity Using a Cylindrical Lens

We present a simple method to measure the topological charges of optical vortices with multiple singularities. Using a cylindrical lens, a vortex beam can decay into a light field distribution with multiple separated dark holes, whose number just equals the topological charge of the input beam. This conclusion is then verified via experiments and numerical simulations of the propagation of vortex beams with multiple singulaxities. This method is also reliable to measure the topological charges of broadband vortex beams with different distributions of singularities, which does not resort to multiple beam interferometrie experiments.

Large-scale particle trapping by acoustic vortices with a continuously variable topological charge

Strengthened directivity with higher-order side lobes can be generated by the transducer with a larger radius at a higher frequency. The multi-annular pressure distributions are displayed in the cross-section of the acoustic vortices(AVs)which are formed by side lobes. In the near field, particles can be trapped in the valley region between the two annuli of the pressure peak, and cannot be moved to the vortex center. In this paper, a trapping method based on a sector transducer array is proposed, which is characterized by the continuously variable topological charge(CVTC). This acoustic field can not only enlarge the range of particle trapping but also improve the aggregation degree of the trapped particles. In the experiments, polyethylene particles with a diameter of 0.2 mm are trapped into the multi-annular valleys by the AV with a fixed topological charge. Nevertheless, by applying the CVTC, particles outside the radius of the AV can cross the pressure peak successfully and move to the vortex center. Theoretical studies are also verified by the experimental particles trapping using the AV with the continuous variation of three topological charges, and suggest the potential application of large-scale particle trapping in biomedical engineering.

High-harmonic-generation-inspired preparation of optical vortex arrays with arbitrary-order topological charges

In the process of high-harmonic generation with a Laguerre-Gaussian （LG） mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.

Spin-orbit-locked hyperbolic polariton vortices carrying reconfigurable topological charges

The topological features of optical vortices have been opening opportunities for free-space and on-chip photonic technologies,e.g.,for multiplexed optical communications and robust information transport.In a parallel but disjoint effort,polar anisotropic van der Waals nanomaterials supporting hyperbolic phonon polaritons(HP2s)have been leveraged to drastically boost light-matter interactions.So far HP2 studies have been mainly focusing on the control of their amplitude and scale features.Here we report the generation and observation of mid-infrared hyperbolic polariton vortices(HP2Vs)associated with reconfigurable topological charges.Spiral-shaped gold disks coated with a flake of hexagonal boron nitride are exploited to tailor spin-orbit interactions and realise deeply subwavelength HP2Vs.The complex interplay between excitation spin,spiral geometry and HP2 dispersion enables robust reconfigurability of the associated topological charges.Our results reveal unique opportunities to extend the application of HP2s into topological photonics,quantum information processing by integrating these phenomena with single-photon emitters,robust on-chip optical applications,sensing and nanoparticle manipulation.

Model-based adaptive locomotion and clustering control of microparticles through ultrasonic topological charge modulation

We present a novel motion control technique for microrobot clusters to exploit the characteristics of the ultrasonic field.The method comprises two steps,i.e.,introducing an ultrasonic actuation(UA)linear model for three-dimensional(3D)locomotion and controlling the topological charge(TC)in the ultrasonic vortex for microrobot clustering.Here,the TC is a controllable parameter for the expansion and contraction of the pressure null space inside the vortex.We present a TC control method to cluster sporadically distributed microrobots in a specific workspace.To validate the concept,a UA system composed of 30 ultrasonic transducers with 1 MHz frequency is fabricated,and the characteristics of the generated acoustic pressure field are analyzed through simulations.Subsequently,the performances of the adaptive controller for precise 3D locomotion and the TC control method for clustering are evaluated.Finally,the UA technology,which performs both clustering and locomotion in a complex manner,is validated with a gelatin phantom in an in-vitro environment.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci,which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates(ERZPs) and the advantage of spiral zone plates(SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates(ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate;therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices,ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Spatial quantum coherent modulation with perfect hybrid vector vortex beam based on atomic medium

The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we investigate the spatial quantum coherent modulation effect with PHVVB based on the atomic medium,and we observe the absorption characteristic of the PHVVB with different TCs under variant magnetic fields.We find that the transmission spectrum linewidth of PHVVB can be effectively maintained regardless of the TC.Still,the width of transmission peaks increases slightly as the beam size expands in hot atomic vapor.This distinctive quantum coherence phenomenon,demonstrated by the interaction of an atomic medium with a hybrid vector-structured beam,might be anticipated to open up new opportunities for quantum coherence modulation and accurate magnetic field measurement.

Terahertz quasi-perfect vortex beam with integer-order and fractional-order generated by spiral spherical harmonic axicon

We propose a new method to generate terahertz perfect vortex beam with integer-order and fractional-order. A new optical diffractive element composed of the phase combination of a spherical harmonic axicon and a spiral phase plate is designed and called spiral spherical harmonic axicon. A terahertz Gaussian beam passes through the spiral spherical harmonic axicon to generate a terahertz vortex beam. When only the topological charge number carried by spiral spherical harmonic axicon increases, the ring radius of terahertz vortex beam increases slightly, so the beam is shaped into a terahertz quasi-perfect vortex beam. Importantly, the terahertz quasi-perfect vortex beam can carry not only integer-order topological charge number but also fractional-order topological charge number. This is the first time that vortex beam and quasi-perfect vortex beam with fractional-order have been successfully realized in terahertz domain and experiment.

Robust measurement of orbital angular momentum of a partially coherent vortex beam under amplitude and phase perturbations

The ability to overcome the negative effects,induced by obstacles and turbulent atmosphere,is a core challenge of long-distance information transmission,and it is of great significance in free-space optical communication.The spatial-coherence structure,that characterizes partially coherent fields,provides a new degree of freedom for carrying information.However,due to the influence of the complex transmission environment,the spatial-coherence structure is severely damaged during the propagation path,which undoubtedly limits its ability to transmit information.Here,we realize the robust far-field orbital angular momentum(OAM)transmission and detection by modulating the spatial-coherence structure of a partially coherent vortex beam with the help of the cross-phase.The cross-phase enables the OAM information,quantified by the topological charge,hidden in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions and turbulence within the communication link.This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross-phase.We demonstrate experimentally that the topological charge information can be recognized well by measuring the spatial-coherence structure in the far field,exhibiting a set of distinct and separated dark rings even under amplitude and phase perturbations.Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

The global monopole spacetime and its topological charge

We show that the global monopole spacetime is one of the exact solutions of the Einstein equations by treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case of spacetime with global monopole charge.

Settled fast measurement of topological charge by direct extraction of plane wave from vortex beam

A method of measuring the vortex beam topological charge(TC)is proposed based on a device that can directly extract the plane wave form from the vortex beam in which the different propagation angles of the plane waves are uniquely related to the different TCs.Then the TC can be obtained by simply comparing the energy values perceived by two fixed sensors in the detection location with the help of twin omnidirectional energy absorbers(OEAs).Because the settled detection relies only on the simple quantitative value at two fixed positions,neither pattern recognition nor field analysis procedure is applied,thus allowing faster measurement.Some features of the methodology are investigated,and the numerical simulations verify the feasibility and robustness of the system.

Competition of Quantum Anomalous Hall States and Charge Density Wave in a Correlated Topological Model

We investigate the topological phase transition driven by non-local electronic correlations in a realistic quantum anomalous Hall model consisting of d_(xy)–d_(x^(2)-y^(2)) orbitals. Three topologically distinct phases defined in the noninteracting limit evolve to different charge density wave phases under correlations. Two conspicuous conclusions were obtained: The topological phase transition does not involve gap-closing and the dynamical fluctuations significantly suppress the charge order favored by the next nearest neighbor interaction. Our study sheds light on the stability of topological phase under electronic correlations, and we demonstrate a positive role played by dynamical fluctuations that is distinct to all previous studies on correlated topological states.

Evolution of polarization singularities accompanied by avoided crossing in plasmonic system

The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied.The lateral inversion symmetry of the system,which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously,yields abundant polarization states.A complete evolution process with geometry for the polarization states is traced.In the evolution,circularly polarized points(C points)can stem from 3 different processes.In addition to the previously reported processes occurring in an isolated band,a new type of C point appearing in two bands simultaneously due to the avoided band crossing,is observed.Unlike the dielectric system with a similar structure which only supports at-Γbound states in the continuum(BICs),accidental BICs off theΓpoint are realized in this plasmonic system.This work provides a new scheme of polarization manipulation for the plasmonic systems.

Generation of elliptical airy vortex beams based on all-dielectric metasurface

Elliptical airy vortex beams(EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m| + 1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.

Study of the topological quantities of lattice QCD using a modified DCGAN frame

A modified deep convolutional generative adversarial network(M-DCGAN)frame is proposed to study the N-dimensional(ND)topological quantities in lattice QCD based on Monte Carlo(MC)simulations.We construct a new scaling structure including fully connected layers to support the generation of high-quality high-dimensional images for the M-DCGAN.Our results suggest that the M-DCGAN scheme of machine learning will help to more efficiently calculate the 1D distribution of topological charge and the 4D topological charge density compared with MC simulation alone.

Average Capacity of OAM-Multiplexed FSO System with Vortex Beam Propagating Through Non-Kolmogorov Turbulence

The propagation of vortex beam in atmospheric turbulence is of significant importance in theoretical study and practical applications. Based on extended Huygens-Fresnel integral and the Rytov approximation, the average capacity of orbital angular momentum(OAM)-multiplexed Laguerre-Gaussian(LG) beam propagating through non-Kolmogorov turbulence is presented, and the analytical expression of spiral spectrum of LG beam has been deduced. The average capacity of FSO system is numerically calculated and the influence of exponent parameter, transmission height, structure constant, wavelength, outer scale and inner scale on average capacity are also analyzed in detail. Outcomes show that smaller structure constant, outer scale, higher transmission height and larger wavelength, inner scale are conducive to improve average capacity in different extent. Results acquires in this paper have potential application value in optical communication within non-Kolmogorov turbulence.

Composite optical vortices in noncollinear Laguerre–Gaussian beams and their propagation in free space

Taking two Laguerre-Gaussian beams with topological charge 1 = ±1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre-Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ξ, or off-axis distance ratio μ. The net topological charge lnet is not always equal to the sum lsum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.

Measuring orbital angular momentum of acoustic vortices based on Fraunhofer's diffraction

Acoustic vortex (AV) beam is triggering the significant research interest in information and communication sciences due to its infinite and mutual orthogonal orbital angular momentums (OAMs). Therefore, measuring the topological charges of an AV beams become a task with great significance. In this work, we present a Fraunhofer diffraction (FD) pattern of an AV beam that can be used to quantitatively detect the OAMs of AV beams. We both theoretically and numerically investigate the FD patterns of AV beams passing through a multipoint interferometer (MPI). It is demonstrated that the topological charges of the AV beams can be determined from the interference intensity patterns. The proposed method may pave the way to the practical applications of AV beams.

Multiple off-axis acoustic vortices generated by dual coaxial vortex beams

As a kind of special acoustic field, the helical wavefront of an acoustic vortex（AV） beam is demonstrated to have a pressure zero with phase singularity at the center in the transverse plane. The orbital angular momentum of AVs can be applied to the field of particle manipulation, which attracts more and more attention in acoustic researches. In this paper,by using the simplified circular array of point sources, dual coaxial AV beams are excited by the even-and odd-numbered sources with the topological charges of l_E and l_O based on the phase-coded approach, and the composite acoustic field with an on-axis center-AV and multiple off-axis sub-AVs can be generated by the superimposition of the AV beams for｜l_E｜ ≠ ｜l_O｜. The generation of edge phase dislocation is theoretically derived and numerically analyzed for l_E=-l_O. The numbers and the topological charges as well as the locations of the center-AV and sub-AVs are demonstrated, which are proved to be determined by the topological charges of the coaxial AV beams. The proposed approach breaks through the limit of only one on-axis AV with a single topological charge along the beam axis, and also provides the feasibility of off-axis particle trapping with multiple AVs in object manipulation.

Coherent Vortices Properties of Partially Coherent Elegant Laguerre-Gaussian Beams in the Free Space

The analytical expression of the cross-spectral density of partially coherent elegant Laguerre-Gaussian beams propagating in free space has been derived. The coherence vortex properties of such beams have been investigated. The effect of the beam parameters, including the topological charge, radial mode index and coherence length on the coherent vortex, is analyzed. The results show that the higher order (lth) of coherent vortices split to lth first order of coherent vortex. New coherent vortices of opposite sign appear, and then pairs of coherent vortices form. The propagation distance and coherence length affect the generation of coherent vortices, while the radial mode index doesn’t affect the coherent vortices. These results might be helpful for potential application of such beams in optical communication.