Array Of Vortices Research Articles

Zigzag instability of columnar Taylor–Green vortices in a strongly stratified fluid

We investigate the dynamics of a columnar Taylor–Green vortex array under strong stratification, focusing on Froude numbers $0.125\leq Fr \leq 1.0$ , with the aim of identifying and understanding the primary instabilities that lead to the vortices’ breakdown. Linear stability analysis reveals that the fastest-growing vertical wavenumber scales with $Fr^{-1}$ , while the dimensionless growth rate remains approximately constant. The most unstable eigenmode, identified as the mixed hyperbolic mode by Hattori et al. (J. Fluid Mech., vol. 909, 2021, A4), bears significant similarities to the zigzag instability, first discovered by Billant & Chomaz (J. Fluid Mech., vol. 418, 2000, pp. 167–188). Direct numerical simulations further confirm that the zigzag instability is crucial in amplifying initial random perturbations to finite amplitude, with the flow structure and modal growth rate consistent with the linear stability analysis. In particular, the characteristic vertical length scale of turbulence matches that of the fastest-growing linear mode. These findings underscore the broader relevance of the zigzag instability mechanism beyond its initial discovery in vortex pairs, demonstrating its role in facilitating direct energy transfer from vertically uniform vortical motions to a characteristic vertical length scale proportional to $Fr$ in strongly stratified flows.

Asymmetric vertical transport in weakly forced shallow flows

In this paper, we report on an investigation of the vertical transport of tracer particles released within a shallow, continuously-forced flow by means of numerical simulations. The investigation is motivated by the shallow flows encountered in many environmental situations and inspired by the laboratory experiments conducted in electromagnetically forced shallow fluid layers. The flow is confined to a thin fluid layer by stress-free top and no-slip bottom walls. The dynamics and the transport properties of the shallow flow are investigated under various flow conditions characterized by a Reynolds number related to the forcing, ReF, and the aspect ratio of vertical and horizontal length scales δ. The forcing generates an array of vortices that becomes unsteady when ReFδ2≳10. These vortices are accompanied by upwellings in their cores which are surrounded by narrower, stronger downwellings. Hence, upwellings occur where the horizontal flow is vorticity-dominated, while downwellings where it is strain-dominated. The magnitude of the asymmetry in strength and size of the vertical flows and their correlation with horizontal structures depends on the flow conditions and significantly influences the vertical spreading of particles within the fluid volume. Under conditions leading to a large asymmetry, particles within updrafts are transported slowly upwards, while particles within downdrafts rapidly move downwards. In addition, particles are trapped for longer within the updrafts than downdrafts because of their correlation with vorticity-dominated regions. However, when the flow becomes fully three-dimensional and highly unsteady for large ReFδ2 values, this transport asymmetry subsides because the updrafts and downdrafts exhibit similar strength and size in such flow conditions. Consequently, similar amounts of particles are transported upwards and downwards at similar rates.

Generation of vectorial vortex beams by a coherently combined laser array

With the superpositions of spin and orbital angular momentum, vectorial vortex beams (VVBs) have attracted great attention in recent years. Many approaches have been developed to generate such beams, but high-power output is not supported. Here, we report the coherent beam combining (CBC) for generating VVBs that are compatible with high-power fiber amplifiers. The laser array is composed of two discrete vortex arrays with left-handed and right-handed circular polarization states. The phase and polarization of each beamlet are manipulated simultaneously. Experimentally, the phase noise in the amplifiers is compensated by the all-fiber internal phase control feedback structure. Quarter-wave plates are employed as polarization state converters. When the system is in the closed loop, a distinct and stable VVB can be obtained in the far-field. This work could provide a significant reference for the future implementation of high-power structured beams.

Suppression of the superfluid Kelvin-Helmholtz instability due to massive vortex cores, friction and confinement

We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform.

Ballistic to diffusive transition for swimmers in a periodic vortex array.

We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of sectionin phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of sectionsurrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.

Antiferromagnetic Ising model in a triangular vortex lattice of quantum fluids of light.

Vortices are topologically distinctive objects appearing as phase twists in coherent fields of optical beams and Bose-Einstein condensates. Structured networks and artificial lattices of coupled vortices could offer a powerful platform to study and simulate interaction mechanisms between constituents of condensed matter systems, such as antiferromagnetic interactions, by replacement of spin angular momentum with orbital angular momentum. Here, we realize such a platform using a macroscopic quantum fluid of light based on exciton-polariton condensates. We imprint all-optical hexagonal lattice that results into a triangular vortex lattice, with each cell having a vortex of charge l = ±1. We reveal that pairs of coupled condensates spontaneously arrange their orbital angular momentum antiparallel, implying a form of artificial orbital "antiferromagnetism." We discover that correlation exists between the emergent vortex patterns in triangular condensate lattices and the low-energy solutions of the corresponding antiferromagnetic Ising system. Our study offers a path toward spontaneously ordered vortex arrays with nearly arbitrary configurations and controlled couplings.

Production of high-purity non-diffracting optical vortex arrays with high topological charge

In this paper, we have realized the high purity non-diffracting optical vortex arrays with a high topological charge using quasi-symmetrical plane waves for the first time. The triangular vortex arrays with l = ±2 can be generated by six quasi-symmetrical plane waves, and the square vortex arrays with l = ±3 can be generated by eight quasi-symmetrical plane waves. The adjacent vortex units have opposite topological charges. We have also obtained the relations between the periods of the field formed by the six/eight quasi-symmetrical plane waves and the periods of the field formed by the three/four symmetrical plane waves. The simulation and experimental results demonstrate the feasibility of this method.

Pattern formation in odd viscoelastic fluids

Nonreciprocal interactions fueled by local energy consumption can be found in biological and synthetic active matter at scales where viscoelastic forces are important. Such systems can be described by “odd” viscoelasticity, which assumes fewer material symmetries than traditional theories. Here we study odd viscoelasticity analytically and using lattice Boltzmann simulations. We identify a pattern-forming instability which produces an oscillating array of fluid vortices, and we elucidate which features govern the growth rate, wavelength, and saturation of the vortices. Our observation of pattern formation through odd mechanical response can inform models of biological patterning and guide engineering of odd dynamics in soft active matter systems. Published by the American Physical Society 2024

Characterizing the propagation evolution of optical vortex lattices in astigmatic transformations of frequency-doubled laser modes

We develop a wave representation to characterize the propagation evolution of vortex lattice beams, which are produced through a frequency-doubling process of various high-order laser modes, followed by mode conversion. Their phase fields and phase gradients are further analyzed to verify the topological charge for each isolated vortex, as well as the symmetry and net charges of the vortex lattices. In the experiment, we demonstrate the generation of frequency-doubled high-order modes by utilizing an off-center pumped solid-state laser combined with intracavity second-harmonic generation. Subsequently, we employ an astigmatic mode converter to transform the generated frequency-doubled laser modes, obtaining vortex arrays. The strong agreement between theoretical analysis and experimental data not only validates the derived formula but also confirms the creation and characteristics of the vortex lattice beams.

Uniform intensity chiral optical field by multifocal synthesis.

Chiral optical beams that carry orbital angular momentum (OAM) have a broad range of applications such as optical tweezers, chiral microstructure fabrication, and optical communications. However, some chiral optical beams have inhomogeneous intensity distribution that limits the application in these fields. In this Letter, two different types of chiral optical fields with uniform intensity and arbitrary length were proposed based on the amplitude encoding method and multifocal synthesis. The intensity distribution of the chiral optical fields is determined by the distance between the focal points that can greatly extend the modulation length of the chiral optical field. Moreover, since each focal point contains modulable amplitude and phase, an arbitrary interception of the optical field can be realized by selectively retaining a part of the focal points. By partitioning the chiral optical field and assigning different topological charges, the OAM space-division multiplexing and independent tunability of the topological charges can be realized. In addition, the composite multi-petal vortex array formed by combining two different chiral optical fields can greatly enhance the information capacity of the optical communications and may have potential applications in fields such as particle manipulation.

Image authentication with exclusive-OR operated optical vortices

Optical vortices carrying orbital angular momentum have drawn much attention because they provide high-dimensional encoding. Employing an array of optical vortices, we demonstrate an authentication verification system. For security authentication, an exclusive-OR logic operation has been implemented employing a light beam consisting of an array of vortices. A liquid crystal spatial light modulator has been used to generate orthogonal states of optical vortices. The proposed technique can provide a secure method of authentication with straightforward implementation. We have presented simulation and experimental results to verify the proposed scheme.

Generating Optical Vortex Array Laser Beams of Superimposing Hermite–Gaussian Beams with a Dual–Phase Modulation Digital Laser System

This study presents an efficient and practical intra-cavity approach for selectively generating vortex array laser beams employing a dual-phase modulation digital laser system, which has not yet been completed in single-phase modulation digital laser. The stable optical vortex array laser beams were formed by superimposing cavity Hermite–Gaussian (HG) eigenmodes. In particular, when the selected cavity HG modes shared the same Gouy phase, the resulting optical vortex beam could preserve its light field pattern, thereby maintaining the optical vortex properties in the near and far fields. Numerical results demonstrated that employing dual-phase modulation could establish optimal boundary conditions for the selection of HG modes within the cavity, successfully generating various vortex array laser beams. The experimental validation of the proposed method confirmed the ability to select optical vortex array lasers solely by controlling the loaded phase of the dual-phase modulation digital laser. These results demonstrate the ability of digital lasers to generate and dynamically control optical vortex array lasers.

Archimedes spiral optical vortex array emitter

Optical vortex arrays (OVAs) are important for large-capacity optical communications, optical tweezers, and optical imaging. However, there is an urgent need to generate an optical vortex emitter to construct a specific OVA with a functional structure for the accurate transport of particles. To address this issue, we propose an Archimedes spiral OVA emitter that uses an Archimedes spiral parametric equation and coordinate localization techniques to dynamically regulate the position of each optical vortex. We discuss the phenomena of the location coordinates and Archimedes spiral from unclosed to closed on the OVA emitter. Furthermore, the propose of multiple OVA emitters demonstrates a chiral structure that has the potential for optical material processing. This study lays the foundation for generating OVAs with functional structures, which will facilitate advanced applications in the complex manipulation, separation, and transport of multiple particles.

Enhancing recognition performance of vortex arrays through conditional generative adversarial network-based data augmentation

Enhancing recognition performance of vortex arrays through conditional generative adversarial network-based data augmentation

Engineered 3D Vortex Array with Customized Energy and Topological Charges for Multi‐View Display

AbstractArrays of multiple vortex beams enhance parallel processing capabilities from particle manipulation to information communication. However, the spatial position, topological charge, and energy parameters of the vortex beams within the array have yet to be precisely controlled, posing significant challenges to the realization of multi‐view 3D Orbital Angular Momentum (OAM) display using vortex arrays as information carriers. To address this issue, a method for generating vortex arrays based on a phase‐only hologram, customizing the array by using the energy and OAM spectrum of each vortex beam as the loss function is developed. Experimental results indicate that a 2D array generates 100 vortex beams in the spatial frequency domain, while a 3D array in the Fresnel zone produces 252 vortex beams across 7 planes, each with 36 unprecedentedly controllable energy and topological charge vortex beams. Subsequently, images of 4 views using the 3D vortex arrays and decoded through coordinate transformation to achieve a multi‐view 3D OAM display are encoded. The results demonstrate imaging quality with Mean Peak Signal‐to‐Noise Ratio (MPSNR) of 12.7, 13.0, 13.4, and 12.2 dB in 4 views, respectively, offering promising opportunities for applications in 3D optical manipulation, high‐capacity communication, and 3D OAM holography.

Stability of Stuart vortices in rotating stratified fluids

The linear stability of the Stuart vortices, which is a model of arrays of vortices often observed in the atmosphere and the oceans, in rotating stratified fluids is investigated by local and modal stability analysis. As in the case of the two-dimensional (2-D) Taylor–Green vortices, five types of instability appear in general: the pure-hyperbolic instability, the strato-hyperbolic instability, the rotational-hyperbolic instability, the centrifugal instability and the elliptic instability. The condition for each instability and the estimate of the growth rate derived by Hattori & Hirota (J. Fluid Mech., vol. 967, 2023, A32) are shown to also be useful for the Stuart vortices, which supports their applicability to general flows. The properties of each instability depend on stratification and rotation in a way similar to the case of the 2-D Taylor–Green vortices. For the Stuart vortices, however, the centrifugal instability and the elliptic instability become more dominant than the three hyperbolic instabilities in comparison to the 2-D Taylor–Green vortices; this is explained by the larger ratios of the maximum vorticity and the strain rate at the elliptic stagnation points to the strain rate at the hyperbolic stagnation points. Direct correspondence between the modal and local stability results is further established by comparing unstable modes to solutions to the local stability equations; this is useful for identifying the types of modes since the mechanism of instability is readily known in the local stability analysis. This helps us to discover the modes of the ring-type elliptic instability, which have been predicted only theoretically.

Collective control of a vortex array in a ferroelectric ultrathin film

Recently, the observation of ferroelectric vortex arrays has triggered the investigation of topological domain structures and their characteristics. Vortices are typical topological domain structures with chirality in nanoscale ferroelectric materials. The chirality of a single vortex in a nanodot can be easily manipulated, but the collective control of a vortex array is exceptionally difficult and has not yet been realized. This Letter proposes an effective scheme for the collective control of a vortex array and investigates it via phase-field simulations. The results indicate that the collective control of a vortex array with bidirectional switching can be realized by introducing a bending film with periodic large curvatures under alternative electric fields. Furthermore, a general rule for determining the electrically controllable chirality of ferroelectric vortices is proposed. This Letter demonstrates the feasibility of the collective control of vortex arrays and provides insights for developing ferroelectric nanoelectronic devices based on vortex arrays.

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

Robust high-order petal-mode laser with tunable topological charge pumped by an axicon-based annular beam

In this work, we demonstrate a watt-level laser producing high-order, petal-shaped output modes with tunable topological charge, by using an axicon-based divergent annular pump beam. The topological charge of the output beam could be varied in the range of 34–72 by adjusting the position of the Nd:YVO4 crystal relative to the focal plane of the pump beam. The highest order petal-mode beam generated from the system had a topological charge of 72 and a power of 1.3 W. The highest output power up to 2.1 W with a topological charge of 34 was achieved at an absorbed pump power of 5.8 W. The generated output modes were observed to be robust under power scaling and on propagation, with the same spatial profiles being maintained in the near- and far-fields. We anticipate that this system design may find use as a laser source in applications such as 3D optical trapping, fabrication of optical vortex arrays, optical communications, and high-sensitivity spatial measurement.

Experimental study on control of transverse jet mixing by arrayed plasma energy deposition

The efficient and prompt mixing of fuel is crucial in the operation of scramjet engines. This paper presents the findings from wind tunnel experiments that examined the influence of plasma energy deposition on transverse jets at a Mach number of 6.13. The study took into account various inlet flow total pressures and momentum flux ratios between the jet and the main flow. Utilizing a database containing time-resolved intensities from instantaneous schlieren images, we perform turbulence analysis employing various techniques such as the root mean square, fast Fourier transform, proper orthogonal decomposition, and the two-point correlation method. Specifically, we aim to compare and analyze the pulsation characteristics and spatial self-organization of the jet flow field, both with and without energy deposition control. The findings reveal that intermittent “hot bubbles” created by plasma energy deposition interact with the bow shock induced by the jet, resulting in the formation of an array of large-scale vortices. These vortices emerge as the dominant structures within the jet, effectively amplifying its pulsations. At low inlet flow pressures, energy deposition primarily disrupts the jet, causing large-scale vortices to propagate primarily within the jet plume region. However, at high inlet flow pressures, the impact of energy deposition extends to both the jet and the turbulent boundary layer, encompassing their respective disturbance ranges. Increasing the inlet flow pressure constraints the evolution of large-scale vortices, thus limiting the efficacy of energy deposition in governing the mixing process.