Array Of Vortices Research Articles

Vortex phase diagram of rotating superfluid He3−B

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of $^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^3$He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\,\mbox{G}$ parallel to the rotation axis, $\vec{H}\parallel\vec{\Omega}$, are reported, as well as the supercooling transition line, $T^{*}_ {v} (p,H)$. In zero field the vortex phases of $^3$He-B are separated by a first-order phase transition line $T_ {v} (p)$ that terminates on the bulk critical line $T_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T^{*}_ {v} (p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\,\mbox{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^3$He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^3$He-B.

Orientation-selective elliptic optical vortex array

We propose an orientation-selective elliptic optical vortex array (OS-EOVA). Using multicoordinate (namely, polar, Cartesian, and elliptic) transformations, three kinds of operations applied on optical vortex elements (including location, rotation, and stretching) were executed to obtain the desired orientation in the observed plane. Then, exploiting the reverse design technique, the above-mentioned operations were mapped onto the initial execution plane via Fourier transform. Based on this, 1D and 2D OS-EOVAs were generated experimentally and the existence of optical vortices was verified. Specific OS-EOVAs were designed, possessing antenna array orientation as well as radial and azimuthal orientation. Compared to existing OVAs, the OS-EOVA provides an additional modulated dimension, i.e., orientation. This technique will open up some potential applications, such as complex manipulation of multiparticle systems and fabrication of micromaterials with orientation.

Three-dimensional polarization vortex configuration evolution in compressed BaTiO3/SrTiO3 superlattice

The molecular dynamics method based on the shell model was used to investigate the polarization configuration evolution in a ferroelectric superlattice under a compressive strain that increases at a constant rate. The polarization curl was used to render the polarization configurations. The evolution of vortex domains in location, shape, and size as well as their relative movement and annihilation was observed in three dimensions. It was found that two clockwise-anticlockwise vortex arrays occur in different material layers simultaneously at a compressive strain of −0.05%. With increasing compressive strain, the vortexes continually change their locations, shapes, and sizes and possibly walk across the bimaterial interface. Their lengths could be shortened through being split in the middle or partially annihilating from both ends. Different from the single material case, there are three ways for polarization vortex annihilation to occur in ferroelectric superlattice structures. Vortexes neighboring the material interface or boundaries are inclined to annihilate first, and then the others inside the material annihilate by combining with their neighboring antivortexes. These observations are very helpful for extending applications of ferroelectric superlattices.

Exotic Transverse-Vortex Magnetic Configurations in CoNi Nanowires.

The magnetic configurations of cylindrical Co-rich CoNi nanowires have been quantitatively analyzed at the nanoscale by electron holography and correlated to local structural and chemical properties. The nanowires display grains of both face-centered cubic (fcc) and hexagonal close packed (hcp) crystal structures, with grain boundaries parallel to the nanowire axis direction. Electron holography evidences the existence of a complex exotic magnetic configuration characterized by two distinctly different types of magnetic configurations within a single nanowire: an array of periodical vortices separating small transverse domains in hcp-rich regions with perpendicular easy axis orientation and a mostly axial configuration parallel to the nanowire axis in regions with fcc grains. These vastly different domains are found to be caused by local variations in the chemical composition modifying the crystalline orientation and/or structure, which give rise to change in magnetic anisotropies. Micromagnetic simulations, including the structural properties that have been experimentally determined, allow for a deeper understanding of the complex magnetic states observed by electron holography.

Generation of a vortex and helix with square arrays with high-efficiency by the use of a 2D binary phase mask

In this paper, we designed a binary phase mask (PM) with specific phase modulation characteristic and analyzed the spatial spectrum of the beam passing through the PM. In the case where the difference of phase modulation between two lattices of the binary PM is not equal to π, we found the spatial spectrum has the central spot (direct current component, DC component) except for the central eight strong symmetrical spots and many outer weak symmetrical spots. Based on the multiple-beam interference, the propagation-invariant vortex with a square array can be realized by interference of the eight plane waves with the same wave vectors along the optical axis from the central eight symmetrical spots via the modulated phase values of the central eight symmetric spots. The vortex arrays have two kinds of vortex with an opposite topological charge of l=±1. The helix can be formed with a square array by the interference of the vortex array and the plane wave along the optical axis from the DC component. The helix with outstanding helical intensity distributions have two screw directions, which coincide with the phase distribution of the optical vortex with the square array. The energy efficiency of this method can reach more than 80%. The simulation results demonstrate the feasibility of this method.

Hydrodynamical instabilities in the superfluid interior of neutron stars with background flows between the components

The interiors of mature neutron stars are expected to be superfluid. Superfluidity of matter on the microscopic scale can have a number of large scale, potentially observable consequences, as the superfluid component of the star can now flow relative to the `normal' component that is tracked by electromagnetic emission. The most spectacular of such phenomena are pulsar glitches, sudden spin-ups observed in many pulsars. A background flow of a normal-fluid component with respect to the superfluid is also known to lead to a number of instabilities in laboratory superfluids, possibly leading to turbulence and modifying the nature of the mutual friction coupling between the two fluids. In this paper we consider modes of oscillation in the crust and core of a superfluid neutron star, by conducting a plane-wave analysis. We explicitly account for a background flow between the two components (as would be expected in the presence of pinning) and the entrainment, and we consider both standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutual friction. We find that for standard mutual friction there are families of unstable inertial and sound waves both in the case of a counter-flow along the superfluid vortex axis and for counterflow perpendicular to the vortex axis and find that entrainment leads to a quantitative difference between instabilities in the crust and core of the star. For isotropic mutual friction we find no unstable modes, and speculate that instabilities in a straight vortex array may be linked to glitching behaviour, which then ceases until the turbulence has decayed.

Measurement of vortex spectrum in a purely degenerate vortices array

The article presents a new method for determining the basic characteristics (square of amplitude and initial phase) of purely degenerate arrays of optical vortices using intensity moments. Under purely degenerate arrays, a complex beam is assumed, in which the magnitude of the square of the amplitude of the vortices, opposite in sign of the charge, is equal, and the phases take only two values 0 and π. When the frequency parameter changes in hundredths of decimal places, the internal structure of the complex beam can be significantly changed, which is well reflected by the results obtained.

Roughness measurement with nanoscale resolution by symmetric array of optical vortices

In present report we review the principles and applications of interference vortex method for the real time determination of polished optical surface roughness for transparent and reflecting materials with using of symmetric Laguerre-Gaussian array as a probe beams and reference beams with low topological charge. High spatial resolution caused by interference of vortices and their phase sensitivity, which is automatically analyzable to retrieve the 2D and 3D shape of micro- and nanostructured surfaces is applicable for non-destructive roughness testing of thin films and solid microstructures. The longitudinal and transverse resolution down to 1.75 nm and 7 nm respectively for visible light sources is achieved by the proposed method. The dependence of the rotational angle of the resulting interference pattern in form of two-petal laser beams on the optical path difference and sample thickness for two singular beams superposition is considered in detail.

Gauge-potential-induced vortices in spin-1 Bose–Einstein condensates with spin–orbit coupling

We investigate the vortex states generated by the gauge-potential-induced rotation in spin-1 Bose–Einstein condensates with spin–orbit coupling. An external magnetic field coupling with spin equivalently imprints a non-zero gauge angular momentum, which induces an equivalent canonical angular momentum in the opposite direction, accompanied by the generation of quantized vortices. The competition between interatomic interactions, spin–orbit coupling and magnetic field leads to a variety of vortex structures. In the weakly interatomic interacting regime, as the increase of SO coupling strength, the condensate with a weak magnetic field gradient experiences the transition from polar-core vortex to Mermin–Ho vortex then to vortex cluster , and the three-vortex structures are found in the vortex cluster. As the SO coupling increases further, the condensate presents symmetrical density domains separated by radial vortex arrays. With the increase of magnetic field gradient, the number of density domains increases, and the condensate eventually turns into a giant vortex. In the relatively strong interatomic interacting regime, vortex sheets are formed when the magnetic field gradient is weak, and the increasing of magnetic field gradient makes the vortex arrangement orderly. Compared with the cases of weak interatomic interacting regime, density domain structures are broken because of the strong interatomic interactions, and the vortices are arranged in coaxial annular arrays.

Generation and Propagation of Optical Superoscillatory Vortex Arrays

AbstractSuperoscillation is an intriguing wave phenomenon which enables subwavelength features propagating into far field and hence has potential applications in super‐resolution microscopy as well as particle trapping and manipulation. While previous demonstrations mostly concentrate on designing complicated nanostructures for generating uncontrollable superoscillatory functions, here a new technique which allows for creating polynomially shaped superoscillatory functions that contain phase singularity arrays is demonstrated both theoretically and experimentally. Such a technique is implemented in optical experiments for the first time and controllable superoscillatory lobes with feature much below the diffraction limit is achieved. More importantly, a general theoretical framework, which, to our knowledge, has not been reported before, is developed to show how the created superoscillations propagate to a distance of many Rayleigh ranges and eventually disappear when the distance is sufficiently larger. The validity of the model is confirmed by the experiments. The results may trigger further studies in light field shaping and manipulations in subwavelength scale.

Controlling an optical vortex array from a vortex phase plate, mode converter, and spatial light modulator.

In this Letter, we propose a convenient method of generating an optical vortex (OV) array, in which the size and quantity can be controlled by employing vortex phase plates, a mode converter, and a spatial light modulator into a simple optical system. Different sizes of OV arrays are generated from the superposition of crossed Hermite-Gaussian (HG) modes possessing equal or unequal orders and mutually orthogonal circular polarizations. We experimentally and theoretically demonstrate a series of vector superposed optical fields. Here the sizes of the OV arrays, as well as the quantities of OVs, are defined in terms of specific sets of HG bases. Our results indicate that a simple setup can be used to effectively generate and control OVs and OV arrays.

Beyond the Horizon: Magneto-Optical Imaging Studies of the Kibble–Zurek Scenario in Superconductors

The Kibble–Zurek (Kibble in J Phys A 9:1387–1398, 1976; Zurek in Nature 317:505–508, 1985) scenario predicts that the outcome of a second-order phase transition from a disordered system into an ordered one depends on the quench rate. The emerging order parameter in the ordered state is not spatially uniform, containing topological defects. The faster the transition, the larger the density of defects. In the case of a conductor–superconductor transition, these defects are flux quanta (vortices). To investigate this scenario, we developed a high-resolution magneto-optical imaging system capable of resolving single flux quanta. Using this system, we imaged arrays of spontaneously created vortices in a Nb film. These vortices were formed after the film was rapidly cooled into the superconducting state at rates around 109 K/s. The internal correlations within the vortex array are important in order to differentiate between competing models. In the Kibble–Zurek scenario, neighboring vortices should have a different polarity, while in Hindmarsh–Rajantie (Hindmarsh and Rajantie in Phys Rev Lett 85:4660–4663, 2000) model the polarity should be the same. Our results favor the Kibble–Zurek scenario.

Precision Measurement of Fractional Orbital Angular Momentum

Optical vortices bearing orbital angular momentum (OAM) with fractional topological charge have many applications in particle guiding and transport, anisotropic edge enhancement, high-dimensional quantum entanglement, and free-space optical communication. A fractional optical vortex (FOV) breaks OAM orthogonality, though, making precise measurement complex and difficult. This article shows how to measure the charge of a FOV by using a two-dimensional multifocal array of vortices with different integer charges. With an error of FOV detection below 2.5%, this technique is sufficient for a wide range of real-time requirements for using FOV in optical manipulation, imaging, or quantum optics.

Quasiperiodic boundary conditions for three-dimensional superfluids

We derive boundary conditions that allow a three-dimensional periodic array of superfluid vortices to be modeled in a Cartesian domain. The method is applicable to vortices in the Gross-Pitaevskii description of a superfluid and to fluxtubes in the Ginzburg-Landau description of a superconductor. Unlike standard methods for modeling infinite arrays of vortices, the boundary conditions can be used to study the three-dimensional tangling and reconnection of vortex lines expected in superfluid turbulence. In the two-dimensional case, the boundary conditions include two parameters that determine the lattice offset, which for a single superfluid is essentially arbitrary. In the three-dimensional case the boundary conditions include three parameters that must satisfy a particular linear relationship. We present an algorithm for finding all vortex lattice states within a given domain. We demonstrate the utility of the boundary conditions in two specific problems with imperfect or tangled lattices.

High-dimensional vortex beam encoding/decoding for high-speed free-space optical communication

The development of communication technologies has led to an ever-increasing demand for higher dimension and higher speed of optical coding technology. The orbital angular momentum (OAM) of vortex beams provides a new degree of freedom for optical coding in recent years. In this paper, we propose a novel high-dimensional vortex beam encoding/decoding scheme for high-speed free-space communication. An off-axis 4f-configuration with a digital micromirror device (DMD) and a MIP-based pattern formation algorithm are employed to generate fast switchable, accurate vortex beams (arrays) that can be used for encoding. Interference is introduced to efficiently decode data information. We experimentally demonstrate a high-quality communication link based on 64-ary vortex beam encoding/decoding and zero bit error rate is observed, which shows the validity of the proposed high-dimensional scheme. Owing to enhancement of encoding dimension and employment of high-speed DMDs, the proposed scheme enjoys a higher transfer rate exceeding other communication technologies. What is more, the data transfer rate can be further improved by introducing vortex arrays, which is demonstrated by the rapid transmission of a 24-bit true color bitmap.

Enhancement of Autofocusing Performance for Circular Arrayed‐Airy Vortex Beams

AbstractNumerically and experimentally circular arrayed‐Airy vortex beams (CAAVBs) are demonstrated, of which propagation dynamics and autofocusing performance are investigated. In contrast to the classical circular Airy beams, the focal intensity of CAAVBs can be abruptly enhanced several orders of magnitude by introducing vortex arrays (VAs) and increasing Airy arrays number, and the autofocusing performance markedly increases in the focal plane due to introducing VAs. The position of the focal point can be readily controlled by varying the circular arrayed Airy radius is also demonstrated. Experimental results agree with the numerical calculations. These advantages could be beneficial for potential applications in optical trapping, the generation of high intensity laser, medical treatment, and nonlinear effect.

Annular arrayed-Airy beams carrying vortex arrays

We propose and experimentally demonstrate annular arrayed-Airy beams (AAABs) carrying vortex arrays by combining multiple beams. The propagation dynamics and abrupt autofocusing property are studied. The focal intensity can be greatly increased by two orders of magnitude by increasing vortex array number. Furthermore, the autofocusing property is also enhanced significantly. This tightly autofocusing property would be advantageous for the generation of high intensity laser, optical manipulation, medical treatments, and nonlinear effects.

Constant spacing in filament bundles

Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to the distance of closest approach between the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. In this paper, we consider two distinct notions of constant spacing in multi-filament packings in : equidistance, where the distance of closest approach is constant along the length of filament pairs; and isometry, where the distances of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in . The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while non-equidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three ‘almost equidistant’ ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness.

First-order pinning interaction in type-II superconductors with Ginzburg–Landau descriptions

The spontaneous magneto-elastic (ME) interaction dictates the coupling between vortex arrays and crystal lattice, triggered by the spontaneous vortex nucleation in mixed state. In Ginzburg–Landau theory, the pinning interaction is ascribed to the interaction energy of first-order defect strain field and spontaneous elastic field. The pinning force is therefore estimated as the force on a dislocation imposed by the spontaneous stress field. Subsequently, the first-order pinning is compared with the weak collective pinning quantitively. The magnetization contribution by the first-order pinning is a parabolic dependence with field H , while the magnetization of the collective pinning shows a severe suppression at high fields as H −3 . The difference in magnetization is attributed to the energy characterization in pinning mechanisms. As for the critical current density, the combination of first-order and collective pinning generally reproduces the experimental data of Ba0.75 K0.25 Fe2 As2 sample where the second magnetization peak (SMP) disappears. In this view, the elasticity effect in mixed state is sufficient to cause the vanishment of SMP, especially in samples with high pressure dependence of T c .

Seeing infrared optical vortex arrays with a nonlinear spiral phase filter.

We demonstrate a new method to detect infrared optical vortex arrays efficiently, which is based on simultaneous up-conversion imaging and spiral phase contrast via second-harmonic generation (SHG) in the Fourier domain. In our experiment, we use a spatial light modulator to prepare a variety of 1064nm structured vortex arrays and employ a vortex phase plate of different topological charges to serve as the nonlinear orbital angular momentum (OAM) filter. The SHG is done by mixing the Fourier spectra of input-structured vortices with a single OAM beam in a type-II potassium titanyl phosphate crystal. Then we can convert the input invisible vortex arrays into the visible SHG light fields, and the vortex cores are mapped and seen by bright Gaussian spots, revealing both their positions and topological charges. Our work has potential in the field of infrared imaging and monitoring.