Dynamics of coupled vortices in a pair of ferromagnetic disks

We here experimentally demonstrate that gyration modes of coupled vortices can be resonantly excited primarily by the ac current in a pair of ferromagnetic disks with variable separation. The sole gyration mode clearly splits into higher and lower frequency modes via dipolar interaction, where the main mode splitting is due to a chirality sensitive phase difference in gyrations of the coupled vortices, whereas the magnitude of the splitting is determined by their polarity configuration. These experimental results show that the coupled pair of vortices behaves similar to a diatomic molecule with bonding and antibonding states, implying a possibility for designing the magnonic band structure in a chain or an array of magnetic vortex oscillators.     

Collective motion of magnetization in two-dimensional arrays of square elements

The resonance in a two-dimensional array of square ferromagnetic elements has been experimentally investigated. The magnetization of the elements is shown to be in the vortex state. The resonance peak splitting in the array with increasing density of the elements has been established. The explanation of this phenomenon is proposed and eigenfrequencies of the collective modes are theoretically estimated. Different combinations of polarities and chiralities of the nearest elements in the array are examined.     

Freezing vortex rivers

We demonstrate experimentally and theoretically that the dissipative state at high current densities of superconducting samples with a periodic array of holes consist of flux rivers resulting from a short range attractive interaction between vortices. This dynamically induced vortex–vortex attraction results from the migration of quasiparticles out of the vortex core. We have directly visualized the formation of vortex chains by scanning Hall microscopy after freezing the dynamic state by a field cooling procedure at constant bias current. Similar experiments carried out in a sample without holes show no hint of flux river formation.     

Tunable optical vortex arrays using spontaneous periodic pattern formation in nematic liquid crystal cells

Controllable liquid crystal (LC) defects can provide an effective approach to creating tunable optical vortices. We develop a method to create tunable matter vortex arrays in an LC cell, in which +1 and −1 defects are periodically arranged in a square grid lattice. Spontaneous formation of the periodic defect array is achieved using a spontaneous standing pressure wave without using any patterned electrode or patterned alignment layer. The +1 and −1 defects in the array can induce optical vortices with opposite handedness, and the matter vortex array produces a periodic optical vortex array with orbital angular momenta of −2ℏ and +2ℏ in the same grid lattice. Because the pitch of the grid can be controlled, the method can provide a useful pathway to producing tunable optical vortex arrays for various applications such as advanced optical communication and quantum computation.     

Driving an individual vortex in the presence of a periodic pinning array

Recently it has been demonstrated experimentally that it is possible to manipulate an individual vortex in a type-II superconductor using a magnetic force microscope tip. Using numerical simulations, we investigate the dynamics of a single driven vortex in the presence of a periodic pinning array and other vortices. Remarkably, we find that the effective drag on the driven vortex is reduced at the matching fields, which is opposite from the behavior of the critical current when all the vortices are driven. We discuss this effect in the context of the type of dynamics that occur at matching and nonmatching fields.     

Generation of Circular Optical Vortex Array

We report on a novel optical vortex array named circular optical vortex array, which is generated by the superposition of two concentric perfect optical vortices. The circular optical vortex array has a constant topological charge of +1 or ?1, the number and sign of which are determined by the topological charges of the two perfect optical vortices. Moreover, the radius of the circular optical vortex array is easily adjusted by using the cone angle of an axicon. Furthermore, the circular optical vortex array and multiple circular optical vortex array can be rotated by changing the initial phase difference of the perfect optical vortices on demand. This work demonstrates a complex structured optical field, which is of significance for applications such as optical tweezers, micro‐particle manipulation, and optical imaging.     

Splitting times of doubly quantized vortices in dilute bose-einstein condensates

Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin, Phys. Rev. Lett. 93, 160406 (2004)10.1103/PhysRevLett.93.160406]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental setup. We show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments.     

Astigmatic telescopic transformation of a high-order optical vortex

Properties of an optical vortex light beam formed after the astigmatic telescopic transformation of a circular Laguerre-Gaussian mode are considered both theoretically and experimentally. The beam evolution is found to be in conformity with the general notions on the high-order optical vortex symmetry breakdown. Upon propagation, the asymmetric beam shows a sort of rotation of its transverse profile in accord with the energy circulation in the original circular mode; this process is described on the base of the beam intensity moments and the vortex and asymmetry components of its orbital angular momentum. An l-charged optical vortex converts into |l| secondary first-order vortices positioned on a straight line crossing the beam axis. Orientation of this straight line in the beam cross section and spatial separation of the secondary vortex cores depend on the propagation distance. Morphology (orientation and anisotropy) of all the secondary vortices is the same and depends on the propagation distance; the anisotropy can be characterized by the vortex component of the beam angular momentum. At certain distance, relative separation of secondary vortices with respect to the beam transverse size reaches its maximum that corresponds to the minimum anisotropy of the vortices. The results can be useful in the context of current research of the optical vortex arrays.     

Vortex emission accompanies the advection of optical localized structures

We show that the advection of optical localized structures is accompanied by the emission of vortices, with phase singularities appearing in the wake of the drifting structure. Localized structures are obtained in a light-valve experiment and made to drift by a mirror tilt in the feedback loop. Pairs of oppositely charged vortices are detected for small drifts, whereas for large drifts a vortex array develops. Observations are supported by numerical simulations and linear stability analysis of the system equations and are expected to be generic for a large class of translated optical patterns.     

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.     

Rectified vortex motion in an Nb film with a spacing-graded array of holes

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.     

Generation of optical vortex array based on the fractional Talbot effect

A phase-only diffractive optical element (DOE) for generating array of optical vortices with high compression ratio is presented. Since it is designed according to the fractional Talbot effect, we name the DOE optical vortex Talbot array illuminator (OVTAI). As an example, an OVTAI for generating a hexagonal array of optical vortices is designed, and demonstrated through displaying the OVTAI on a programmable liquid crystal spatial light modulator. The diffraction properties of the vortex array generated by the OVTAI are observed and analyzed, and an optimal distance for generating sharp ringed vortex arrays is given.     

Reversible magnetization of a thin superconducting film with radiation defects

The thermodynamic potential of a system of Peierls vortices in a thin superconducting film, containing radiation defects, in a perpendicular external magnetic field is calculated. The equilibrium temperature dependences of the densities of free vortices and vortices trapped by defects are found in the mean-field approximation for various magnitudes of the external field. It is shown that the equilibrium magnetization of a thin superconducting film exhibits the same features that were observed experimentally in the reversible magnetization of high-temperature superconductors. An asymptotic expression is obtained for the difference of the magnetizations of perfect and irradiated films. According to this expression, the difference depends on the pinning energy of a vortex on a defect and the density of defects.     

Natural shaping of the cylindrically polarized beams

We have experimentally and theoretically shown that the circularly polarized beam bearing a singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in the vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs.     

Pauli paramagnetic effects on vortices in superconducting TmNi2B2C

The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.     

Quantum tunneling of a vortex between two pinning potentials

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.     

Dressed Airy Vortex Beam in a Hot Atomic Medium

Introducing vortices into an Airy beam by the interference between the lobes of the Airy beam for the first time, the modulation of Airy vortices is experimentally and theoretically investigated by electromagnetically induced transparency (EIT) effect and changing the number of side lobes of the Airy beam. The formation and disappearance of vortices in Airy beams can be caused by changing the number of side lobes. The EIT effect can induce the movement of vortex phase singularity by regulating the intensities of lobes in Airy beams. However, changing the number of side lobes can change the energy distribution of the lobes through the energy flow due to the self-healing of Airy beams, thus causing the displacement of vortex phase singularity. In addition, the simulation of the Poynting vector shows that the less the side lobes are blocked, the more energy can be retained in the main lobe and the unblocked side lobes, so that the overall shape of the Airy beam can be better maintained. Such studies provide a new method to acquire and adjust Airy vortex beams and can be applied in the realm of optical micromanipulation.     

Detecting the topological charge of vortex beams using an annular triangle aperture

The Fraunhofer diffraction pattern of a vortex beam by an annular triangle aperture is analyzed theoretically and experimentally. It is found that the pattern of the far-field diffraction intensity distribution exhibits a triangular lattice array, which becomes much clearer with the increase of the ratio of the inner to the outer side of the annular triangle aperture. The number of spot points of any external side of the triangular lattice array minus one is just equal to the topological charge value of the measured optical vortex. For the vortex beam with negative topological charge, the triangular diffraction pattern after the annular triangle aperture will be rotated by 180° in relation to the case of the positive topological charge. Based on the above properties, we propose a simple and feasible method to determine the magnitude and sign of the topological charge of an optical vortex beam.     

Vortex lattice generation using interferometric techniques based on lateral shearing

Interferometric techniques that use lateral shearing for generation of a regular network of optical vortices are reported. These techniques are simple, robust, and less sensitive to vibrations compared to the existing interferometric methods of vortex lattice generation. Vortex lattice is created using three-wave interference of plane as well as spherical waves. Theory of vortex lattice formation using phasor approach is provided. The location of vortices in the interference field is described in terms of spatial frequencies of the interfering waves. The presence of the vortices in the interference field is confirmed experimentally by producing fork fringes, as vortex signatures. Results of simulation studies are presented to support experimentally recorded interferograms.     

Splitting and rotating of optical vortices due to non-circular symmetry in amplitude and phase distributions of host beams

Discussed is the dynamics of optical vortices carrying multi-topological charges, which are nested in optical envelopes with non-circular symmetric amplitudes and phases. As a result of the non-circular symmetry either in amplitudes or in phases, the vortices can split in pairs from the centers of the host beams. During the splitting process of every constituent vortex, its carried integer charges evolve into fractional ones. Furthermore, the overall rotations of the host optical envelopes are found to happen in the splitting process. The theoretical results may find potential applications in beam shaping and engineering.