Array Of Vortices Research Articles

Generation of Optical Vortex Array by the Quasi-Talbot Effect With All-Dielectric Metasurface

In this letter, we numerically and experimentally demonstrate the highly efficient generation of optical vortex arrays based on the quasi-Talbot effect with a reflective all-dielectric metasurface, which is composed of six identical orbital angular momentum lenses. Six separated and focused optical vortices at the focal plane can be high efficiently generated, and form a vortex array at the defocusing plane through the quasi-Talbot effect. The proposed metasurface is made from a commercial silicon on insulator wafer with a high integrated level, which enables the integration of our approach in on-chip platforms for optical lithography and manipulation applications.

Experimental and numerical study on the heat transfer and flow characteristics of micro-gap chip with longitudinal vortex generator array

The longitudinal vortex generators (LVGs) are introduced in the 3D stacked chip micro gaps to enhance heat transfer. Experimental and numerical tests on the performance of 3D stacked chip with and without LVGs in the gap are conducted, and the flow and heat transfer performance at various mass flow rate and heating power as well as LVG spacing is investigated. The experimental and numerical results indicate that the LVGs array can effectively improve the cooling performance of the chip with micro gap. Under the experimental condition of q = 41 W/cm2 and Qv = 112 ml/min, the LVGs array can reduce the wall temperature by 14.49 °C compared with smooth channel. Reducing the spacing of the longitudinal vortex array can improve the cooling performance of the micro gap chip since the interaction between the vortexes generated by the LVGs in the pair is enhanced, which also causes the increase of pressure drop. The comprehensive heat transfer performance comparison considering the pump work consumption indicates that the LVGs enhanced chip is more applicable at higher heating power, and chips with smaller spacing are more applicable for conditions with lower flow rate of cooling water.

Orbital Angular Momentum Encoded Beam Tracking and Wavefront Sensing

The working principle of conventional Shack-Hartmann-type wavefront sensors is based on a wavefront division by two-dimensional microlens arrays and a Poynting vector mapping by comparing the focal displacements to reference measurements. At complex phase distortions or steep phase gradients, however, wavefront reconstruction can suffer from ambiguities by crossing or overlapping neighboring sub-beams, or even by a complete loss of beam trajectories. Moreover, the recognition of sub-beams can additionally be affected by parasitic reflections at optical surfaces, or scattering in a medium. A possible solution of the problem is to work with arrays of well distinguishable sub-beams. Recently, high-resolution pixelated liquid crystal spatial light modulators became available which enable to flexibly generate spatially structured light and thus to realize advanced wavefront sensors with individually encoded beams. In our experimental study we investigated the specific advantages of orbital angular momentum beams for a robust beam tracking and wavefront reconstruction. As a key point for a wavefront reconstruction from vortex arrays, the reliable detection of spiral-like image features is addressed and related strategies are proposed.

Optical vortex convolution generator and quasi-Talbot effect.

In this Letter, a simple optical vortex convolution generator is proposed where a microlens array (MLA) is utilized as an optical convolution device, and a focusing lens (FL) is employed to obtain the far field, which can convert a single optical vortex into a vortex array. Further, the optical field distribution on the focal plane of the FL is theoretically analyzed and experimentally verified using three MLAs of different sizes. Moreover, in the experiments, behind the FL, the self-imaging Talbot effect of the vortex array is also observed. Meanwhile, the generation of the high-order vortex array is also investigated. This method, with a simple structure and high optical power efficiency, can generate high spatial frequency vortex arrays using devices with low spatial frequency and has excellent application prospects in the field of optical tweezers, optical communication, optical processing, etc.

Generation of perfect vectorial vortex beams by employing coherent beam combining.

Based on coherent beam combining, we propose a method for generating the perfect vectorial vortex beams (VVBs) with a specially designed radial phase-locked Gaussian laser array, which is composed of two discrete vortex arrays with right-handed (RH) and left-handed (LH) circularly polarized states and in turn adjacent to each other. The simulation results demonstrate that the VVBs with correct polarization order and topological Pancharatnam charge are successfully generated. The diameter and thickness of generated VVBs independent of the polarization orders and topological Pancharatnam charges further prove that the generated VVBs are perfect. Propagating in free space, the generated perfect VVBs can be stable for a certain distance, even with half-integer orbital angular momentum. In addition, constant phases φ0 between the RH and LH circularly polarized laser arrays has no effect on polarization order and topological Pancharatnam charge but makes polarization orientation to rotate φ0/2. Moreover, perfect VVBs with elliptically polarized states can be flexibly generated only by adjusting the intensity ratio between the RH and LH circularly polarized laser array, and such perfect VVBs are also stable on beam propagation. The proposed method could provide a valuable guidance for high power perfect VVBs in future applications.

When optical vortex array meets cycloid.

Optical vortex arrays (OVAs) have drawn widespread attention owing to their multiple optical vortices and higher dimensions. However, existing OVAs have not yet been utilized to exploit the synergy effect as an entire system, particularly for manipulating multiple particles. Thus, the functionality of OVA should be explored to respond to application requirements. Hence, this study proposes a functional OVA, called cycloid OVA (COVA), based on a combination of cycloid and phase-shift techniques. By modifying the cycloid equation, multiple structural parameters are designed to modulate the structure of the COVAs. Subsequently, versatile and functional COVAs are experimentally generated and modulated. In particular, COVA executes local dynamic modulation, whereas the entire structure remains unchanged. Further, the optical gears are first designed using two COVAs, which exhibit potential for transferring multiple particles. Essentially, OVA is endowed the characteristics and capacity of the cycloid when they meet. This work provides an alternative scheme to generate OVAs, which will open up advanced applications for the complex manipulation, arrangement and transfer of multiple particles.

Energy balances for the collision of gravity currents of equal strengths

Collision of two counterflowing gravity currents of equal densities and heights was investigated by means of three-dimensional high-resolution simulations with the goal of understanding the flow structures and energetics in the collision region in more detail. The lifetime of collision is approximately $3 \tilde {H}/\tilde {u}_f$ , where $\tilde {H}$ is the depth of heavy and ambient fluids, and $\tilde {u}_f$ is the front velocity of the approaching gravity currents, and the lifetime of collision can be divided into three phases. During Phase I, $-0.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 0.5$ , where $\tilde {t}$ is the time, and $\tilde {t}_c$ is the time instance at which the two colliding gravity currents have fully osculated, geometric distortions of the gravity current fronts result in stretching of pre-existing vorticity in the wall-normal direction inside the fronts, and an array of vertical vortices extending throughout the updraught fluid column develop along the interface separating the two colliding gravity currents. The array of vertical vortices is responsible for the mixing between the heavy fluids of the two colliding gravity currents and for the production of turbulent kinetic energy in the collision region. The presence of the top boundary deflects the updraughts into the horizontal direction, and a number of horizontal streamwise vortices are generated close to the top boundary. During Phase II, $0.5 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 1.2$ , the horizontal streamwise vortices close to the top boundary induce turbulent buoyancy flux and break up into smaller structures. While the production of turbulent kinetic energy weakens, the rate of transfer of energy to turbulent flow due to turbulent buoyancy flux reaches its maximum and becomes the primary supply in the turbulent kinetic energy in Phase II. During Phase III, $1.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 2.8$ , the collided fluid slumps away from the collision region, while the production of turbulent kinetic energy, turbulent buoyancy flux and dissipation of energy attenuate. From the point of view of energetics, the production of turbulent kinetic energy and turbulent buoyancy flux transfers energy away from the mean flow to the turbulent flow during the collision. Our study complements previous experimental investigations on the collision of gravity currents in that the flow structures, spatial distribution and temporal evolution of the mean flow and turbulent flow characteristics in the collision region are presented clearly. It is our understanding that such complete information on the energy budgets in the collision region can be difficult to attain in laboratory experiments.

Seagrass deformation affects fluid instability and tracer exchange in canopy flow

Monami is the synchronous waving of a submerged seagrass bed in response to unidirectional fluid flow. Here we develop a multiphase model for the dynamical instabilities and flow-driven collective motions of buoyant, deformable seagrass. We show that the impedance to flow due to the seagrass results in an unstable velocity shear layer at the canopy interface, leading to a periodic array of vortices that propagate downstream. Our simplified model, configured for unidirectional flow in a channel, provides a better understanding of the interaction between these vortices and the seagrass bed. Each passing vortex locally weakens the along-stream velocity at the canopy top, reducing the drag and allowing the deformed grass to straighten up just beneath it. This causes the grass to oscillate periodically even in the absence of water waves. Crucially, the maximal grass deflection is out of phase with the vortices. A phase diagram for the onset of instability shows its dependence on the fluid Reynolds number and an effective buoyancy parameter. Less buoyant grass is more easily deformed by the flow and forms a weaker shear layer, with smaller vortices and less material exchange across the canopy top. While higher Reynolds number leads to stronger vortices and larger waving amplitudes of the seagrass, waving amplitude is maximized at intermediate grass buoyancy. All together, our theory and computations develop an updated schematic of the instability mechanism consistent with experimental observations.

Efficient Energy Conversion through Vortex Arrays in the Turbulent Magnetosheath

Turbulence is often enhanced when transmitted through a collisionless plasma shock. We investigate how the enhanced turbulent energy in the Earth's magnetosheath effectively dissipates via vortex arrays. This research topic is of great importance as it relates to particle energization at astrophysical shocks across the universe. Wave modes and intermittent coherent structures are the key candidate mechanisms for energy conversion in turbulent plasmas. Here, by comparing in-situ measurements in the Earth's magnetosheath with a theoretical model, we find the existence of vortex arrays at the transition between the downstream regions of the Earth's bow shock. Vortex arrays consist of quasi-orthogonal kinetic waves and exhibit both high volumetric filling factors and strong local energy conversion, thereby showing a greater dissipative energization than traditional waves and coherent structures. Therefore, we propose that vortex arrays are a promising mechanism for efficient energy conversion in the sheath regions downstream of astrophysical shocks.

Interplay of Kelvin-Helmholtz and superradiant instabilities of an array of quantized vortices in a two-dimensional Bose-Einstein condensate

We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose–Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin–Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system’s boundary is found to dominate.

Diverse behaviors in non-uniform chiral and non-chiral swarmalators

We study the emergent behaviors of a population of swarming coupled oscillators, dubbed swarmalators. Previous work considered the simplest, idealized case: identical swarmalators with global coupling. Here we expand this work by adding more realistic features: local coupling, non-identical natural frequencies, and chirality. This more realistic model generates a variety of new behaviors including lattices of vortices, beating clusters, and interacting phase waves. Similar behaviors are found across natural and artificial micro-scale collective systems, including social slime mold, spermatozoa vortex arrays, and Quincke rollers. Our results indicate a wide range of future use cases, both to aid characterization and understanding of natural swarms, and to design complex interactions in collective systems from soft and active matter to micro-robotics.

Broadband 2D n × n Vortex Arrays Generated from an Efficient Petal‐Like Raman Laser with an Astigmatic Mode Convertor

Broadband vortex arrays distributed in 2D n × n vortices are extremely needed for multiple microparticle manipulation, high‐capacity optical communication, and quantum information. Vortex arrays are usually generated with spatial light modulators, metamaterials; it is a big challenge to improve beam quality and output power. Herein, crisscross 2D n × n vortex arrays are converted from petal‐like Raman lasers with an astigmatic mode convertor. Efficient petal‐like lasers in the form of the Laguerre–Gaussian mode with zero radial index and l azimuthal index (LG0,l ) are irradiated in a Raman microchip laser (RML) by adjusting optimal beam waist and locating the position of focus spot of the annular pump beam. High‐beam‐quality LG0,9 petal‐like Raman laser oscillating at broadband wavelength (bandwidth: 16.2 nm) is generated with power of 773 mW and an efficiency of 10.6%. The conversion efficiency from petal‐like laser to crisscross vortex array is as high as 90%. The vortex array with 5 × 5 vortices operating around 1078 nm is generated with a power of 693 mW and an optical efficiency of 9.5%. Taking advantages of the broad emission spectrum of ytterbium‐doped laser materials and stimulated Raman scattering effect, RMLs are potential sources for generating flexible vortex arrays with desired 2D n × n vortices oscillating in Raman wavelengths.

Design of the Polarization-Independent Wavelength Multiplexing Holographic Metasurface

Metasurface regulates the polarization, phase, amplitude, frequency, and other characteristics of electromagnetic waves through the subwavelength microstructure. By using its polarization characteristics, it can realize the functions of optical rotation and vector beam generation. It is the most widely used method of regulation. However, parallel optical manipulation, imaging, and communication usually require polarization-insensitive focused (or vortex) arrays of beams, so polarization-independent wavelength multiplexing optical systems need to be considered. In this paper, the genetic algorithm combined with the computer-generated hologram (CGH) is used to control the transmission phase of the structure itself, and on the basis of wavelength multiplexing, the corresponding array of focused or vortex beams without the polarization selection property is realized. The simulation software results show that the method has a huge application prospect in optical communication and optical manipulation.

Gibbs–Wulff optical vortex array

Optical vortex array (OVA) containing multiple optical vortices is an optimal candidate for applications of optical communications, complex manipulation of multi-particle systems, and mass-synchronous fabrication. However, the existing OVAs have not been constructed to respond to the application requirements, particularly for micro-/nanomaterial fabrication where the boundary, size, and stability need to be carefully considered. To address this issue, we propose a Gibbs–Wulff OVA (GWOVA) by analogizing the Gibbs–Wulff theorem in solid-state physics. Herein, the Gibbs–Wulff theorem is first generalized to OVA's generation as the condition to confine its growth boundary. The GWOVA, which possesses versatile structures and arrangement modes (simple- and close-packed modes), is successfully generated and grown. It exhibits high stability and perfect symmetry during growth and rotation, which satisfies the symmetric group of D2s. Owing to its stable structure and growth boundary conditions, the GWOVA has great potential for a wide range of applications, particularly in micro-/nanomaterial fabrication.

Generation of Square Optical Vortex Array and Optical Helix Array by Periodic Orthogonal Binary Phase Plate

Generation of Square Optical Vortex Array and Optical Helix Array by Periodic Orthogonal Binary Phase Plate

Spatial correlated vortex arrays.

Spatial correlated vortex arrays may form in the same beam when a random source contains multiple helical phase structures. We introduced two types of partially coherent sources with Cartesian and polar symmetric helical phase structure and reveal the characteristics of their radiated fields, respectively. It is demonstrated that far fields generated by these families of sources carry interesting features through the joint regulation of coherence and topological charge, being lattice-like vortex patterns with adjustable dimension and shape.

Vortex Pinning in Neutron Stars, Slipstick Dynamics, and the Origin of Spin Glitches

We study pinning and unpinning of superfluid vortices in the inner crust of a neutron star using three-dimensional dynamical simulations. Strong pinning occurs for certain lattice orientations of an idealized, body-centered-cubic lattice and occurs generally in an amorphous or impure nuclear lattice. The pinning force per unit length is ∼1016 dyn cm−1 for a vortex–nucleus interaction that is repulsive and ∼1017 dyn cm−1 for an attractive interaction. The pinning force is strong enough to account for observed spin jumps (glitches). Vortices forced through the lattice move with a slipstick character; for a range of superfluid velocities, the vortex can be in either a cold, pinned state or a hot, unpinned state, with strong excitation of Kelvin waves on the vortex. This two-state nature of vortex motion sets the stage for large-scale vortex movement that creates an observable spin glitch. We argue that the vortex array is likely to become tangled as a result of repeated unpinnings and repinnings. We conjecture that during a glitch, the Kelvin-wave excitation spreads rapidly along the direction of the mean superfluid vorticity and slower in the direction perpendicular to it, akin to an anisotropic deflagration.

Topological steering of light by nematic vortices and analogy to cosmic strings.

Liquid crystals are widely known for their technological uses in displays, electro-optics, photonics and nonlinear optics, but these applications typically rely on defining and switching non-topological spatial patterns of the optical axis. Here, we demonstrate how a liquid crystal's optical axis patterns with singular vortex lines can robustly steer beams of light. External stimuli, including an electric field and light itself, allow us to reconfigure these unusual light-matter interactions. Periodic arrays of vortices obtained by photo-patterning enable the vortex-mediated fission of optical solitons, yielding their lightning-like propagation patterns. Predesigned patterns and spatial trajectories of vortex lines in high-birefringence liquid crystals can steer light into closed loops or even knots. Our vortex lattices might find technological uses in beam steering, telecommunications, virtual reality implementations and anticounterfeiting, as well as possibly offering a model system for probing the interaction of light with defects, including the theoretically predicted, imagination-capturing light-steering action of cosmic strings, elusive defects in cosmology.

Can the radial number of vortex modes control the orbital angular momentum?

In general, a standard Laguerre–Gauss (LG) beam, whose state is given by two quantum numbers (n, 𝓁): the radial number n and the azimuthal number 𝓁 (or the topological charge (TС) of the vortex carried by the LG beam), is unstable with respect to weak perturbations. This is not difficult to see if we decompose the complex amplitude of the LG beam in terms of Hermite–Gauss modes (HG), with the total number of HG modes being equal to N = 2n +𝓁 + 1. If we now slightly change the amplitudes and phases of each HG mode, then the structure of the LG beam radically changes. Such a combination of modes is called a structured LG beam (sLG), which can carry large additional arrays of information embedded in the sLG beam by encoding the amplitudes and phases of the HG modes (excitation of modes). But as soon as a perturbation is inserted into the LG beam, its orbital angular momentum (OAM) can change dramatically in such a way that the value of the OAM changes in the interval (–𝓁, 𝓁), and the total TC – in the interval (–2n – 𝓁, 2n + 𝓁). At n = 0, the OAM changes smoothly in the interval (–𝓁, 𝓁), however it is worth "turning on" the radial number n, as the OAM oscillations occur. The number of minima (maxima) of the oscillations is equal to the radial number n in the interval θ = (0, π) and θ = (π, 2π), with their amplitude nonlinearly depending on the difference 𝓁 – n, except for the point θ = π, where the structured beam becomes degenerate. If 𝓁 = 0, then the OAM is zero, so that in the sLG beam structure, we observe either a symmetrical array of vortices with opposite-sign TCs or a pattern of edge dislocations, the number of which is equal to the radial number n. We also found that, despite the fast oscillations of the OAM, the absolute value of the total TC of the sLG beam does not change with variation of both the amplitude ε and phase θ parameters, but depends solely on the initial state (n, 𝓁) of the LG beam and modulo (2n + 𝓁).

Controlling spacing of double-ring perfect optical vortex using the Fourier transform of Bessel beam with axicon phase

The perfect optical vortex (POV) has additional potential uses in optical trapping and optical communication, due to its diameter being independent of its topological charge. In this study, we demonstrate a double-ring vortex beam with adjustable spacing between the two rings; its size is also only minimally affected by the change of topological charge. To our knowledge, the beam satisfies the double-ring POV concept. The Fourier transform of a Bessel beam embedded with an axicon phase can theoretically produce such a beam. The experimental findings support the numerical results, demonstrating that the ring spacing between two rings can be modulated via the conical parameter, expanding the superposition of double-ring beams and that the two rings always keep the same topological charge value. We also consider the vortex array created by the double-ring beam, as well as the beam’s shape. Optical trapping, orbital angular momentum multiplexing, and optical communication could all benefit from the changeable ring spacing of a double-ring vortex beam.