Canonical Vortex Research Articles

Noncanonical vortex states and dynamics in Bose-Einstein condensates

Vortex excitations triggered by nonlinear interactions in Bose-Einstein condensates have attracted interest in the study of ultracold atoms. However, most studies focus on canonical vortex states with integer topological charges. In this paper, we study the dynamic properties of noncanonical vortex condensates with three phase distributions: power-exponent, new type power-exponent and oscillation type. The results show that the noncanonical vortices are dynamic unstable and their density distributions obviously depend on the phase parameters of the initial optical phase masks. Different noncanonical vortices decay into canonical clusters with diverse configurations showing rich topological excitation patterns. In particular, a new power exponential noncanonical vortex state decays into a stable canonical polygonal vortex cluster structure. Because the phase structures of the noncanonical optical vortices destroy the rotational symmetry of the condensate, the angular momentum of the condensate is no longer quantized, and its value changes with the power of the azimuthal angle of the optical field or the oscillation frequency, which is obviously different from the evolution of the corresponding noncanonical vortex optical field itself. In the dynamical process, the center-of-mass trajectory of noncanonical vortex condensates with the new type of power exponent phase is always a point, while for the noncanonical vortex condensates with power exponent and oscillating phase, the center-of-mass trajectories are ellipses centering at the origin of coordinates.

Manipulation of Energy Flow with X-Type Vortex

In this study, a new method for manipulating energy flow in a 3D vector field is proposed. In this method, an azimuthally-polarized beam with a noncanonical vortex, the X-type vortex, is focused in a high-numerical aperture system. It is found that, instead of the invariance of the energy flow which is characteristic of the traditional vortex (i.e., canonical vortex), both the longitudinal and the transverse energy flows in virtue of the X-type vortex rotate around the beam center as the beam propagates, and this rotational behavior (including the maxima location and the rotational angle) can be adjusted by the anisotropic parameter and the order the X-type vortex. Through defining a complex transverse Poynting field and applying the equivalence principle, the transverse energy flow and its topological reactions are discussed in the focal plane. Our result shows that, by changing the anisotropic parameter of the X-type vortex, rich topological reactions will occur, resulting in various distribution patterns of the energy flow, such as multi vortex-type singularities around the beam center. Our research demonstrates newly-observed features of the X-type vortex and also provides a simple method to manipulate energy flows both along longitudinal and transverse directions, which will be useful in optical manipulations.

Topological structures in a noncanonical perturbative dynamic of a cuscutonlike model

In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by the perturbative approach, we investigate the existence of topological structures in the cuscuton-like model. The structures we study are, first, kink-like configurations in two dimensional spacetime, second, vortex solutions in three dimensional one with gauge field ruled by the Maxwell term. In fact, to show the existence of kink solutions it is needed to introduce a standard dynamics term in the cuscuton-like model. Then, a numerical approach (interpolation method) is used and the solution of the scalar field is presented. On the other hand, for the study of topological vortices, we reorganized the energy density to obtain, for convenience, equations similar to those canonical vortex structures, namely, the Maxwell-Higgs model. In fact, even for this particular case, we observed the existence of structures with localized energy and quantized magnetic flux in a given topological sector. We also show that when the model does not spontaneously break the symmetry, the $(2+1)D$ model only admits the so-called non-topological field solutions.

X-type vortex and its effect on beam shaping

In this article we propose a new type of optical vortex, the X-type vortex. This vortex inherits and develops the conventional noncanonical vortex, i.e. it no longer has a constant phase gradient around the center, while the intensity keeps invariant azimuthally. The strongly focusing properties of the X-type vortex and its effect on the beam shaping in three-dimensional (3D) fields are analyzed. The interesting phenomena, which cannot be seen in canonical vortices, are observed, for instance the ‘switch effect’ which shows that the intensity pattern can switch from one transverse axis to another in the focal plane by controlling the phase gradient parameter. It is shown that by adjusting the phase gradient of this vortex, the focal field can have marvelous patterns, from the doughnut shape to the shapes with different lobes, and the beam along propagation direction will form a twisting shape in 3D space with controllable rotation direction and location. The physical mechanisms underlying the rule of the beam shaping are also discussed, which generally say that the phase gradient of the X-type vortex, the orbital angular momentum, the polarization and the ‘nongeneric’ characteristic contribute differently in shaping fields. This new type of vortex may supply a new freedom for tailoring 3D optical fields, and our work will pave a way for exploration of new vortices and their applications.

Comparison of microparticle manipulating characteristics of canonical vortex beam and power-exponent-phase vortex beam

We have experimentally studied the stable trapping and rotation of silica microspheres using canonical vortex (CV) beam and power-exponent-phase vortex (PEPV) beam. Numerical simulation was carried out to characterize the focusing property of these two types of beams. The dynamics of the microspheres in the two types of beams with various topological charges was investigated in detail. It shows that the precise control of microspheres in one direction can be realized. Furthermore, by optical trapping and moving the microspheres in the focus of the PEPV beam, it is proven that the velocity of the microspheres does not increase with the increase in the power order of the spiral phase and constant topological charge. We demonstrate the advantages and flexibility of PEPV beam for optical trapping applications. Optical manipulation technology based on PEPV beam may be used beneficially in optical tweezers and in applications for guiding microparticles.

Effect of polymer solutions on the propagation and structure of freely translating vortex rings

We experimentally study the propagation of vortex rings in aqueous solutions of polyethylene oxide (PEO400) and hydrolysed polyacrylamide (PAMH25). We study the canonical vortex ring as a caricature problem to the phenomenon of turbulent polymer drag reduction. PAMH25 has a similar infinite shear viscosity, ten times the zero shear viscosity and a thousand times the relaxation time of PEO400. We study the vortex rings generated by the trapezoidal motion of a piston-cylinder mechanism using PIV and PLIF at constant impulse. We see that PAMH25 drastically affects the propagation properties and the structure of the vortex ring, while PEO400 shows a behaviour similar to water. We conclude that PAMH25 retards the roll-up process of the ring, due to both the large range of plateau viscosities and large relaxation time. We surmise that the behaviour of the vortex ring observed might be used to unravel the mechanism of polymer drag reduction.

Patterns for efficient propulsion during the energy evolution of vortex rings

Compared with steady-jet propulsion, pulsed-jet propulsion can exhibit more efficient by manipulating the unsteady formation of vortex rings in the near wake. That is, energy is much better transferred and used in the form of vortices to generate propulsive force rather than a steady jet. This study is aimed at analyzing the energy evolution of vortex rings and revealing the patterns for efficient propulsion during the energy evolution. Of particular importance to the energy evolution of vortex rings is the pinch-off mechanism, which is owing to the limiting effects of energy and causes that vortex rings cannot grow indefinitely. Canonical vortex rings are generated by using a piston–cylinder apparatus and their time-dependent flow fields are measured using digital particle image velocimetry. During the energy evolution of vortex rings, overpressure and fluid flux at the exit plane are found to significantly contribute to their energy. Moreover, overpressure is the dominant pattern contributing to the energy of vortex rings and has a greater contribution than fluid flux at the early evolution stage, whereas the contribution of overpressure nearly disappears once vortex rings pinch off. By contrast, fluid flux continuously contributes to the energy of vortex rings until they physically separate from the trailing vortices. Based on the hyperbolic LCSs, distinguishable flow patterns are detected to correspond to the energy evolution of vortex ring. The appearance of a newly disconnected LCS in the trailing jet indicates the initial roll-up of a trailing vortex and the onset of pinch-off, which coincides with the end of overpressure contribution to the energy of vortex rings. A LCS barrier behind the vortex rings appears and prevents any fluid flux from entering the vortex rings, thereby indicating the end of pinch-off and corresponding to the end of fluid-flux contribution. Moreover, it is suggested that transferring or using energy by pressure is a more efficient pattern than fluid flux to generate hydrodynamic force, and enlarging the energy contribution to vortices can further enhance propulsive performance.

Comment on “Symmetries and Interaction Coefficients of Kelvin waves” by Lebedev and L’vov

We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L'vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kinetics---not only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w(z) = x(z) + iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expressions.

The transformation of canonical vortices embedded in a general elliptical Gaussian beam to noncanonical vortices

Based on the generalized Collins integral, the transformation of canonical vortices embedded in a general elliptical Gaussian beam to noncanonical ones in free space and through a misaligned optical system is studied, and the effect of the beam parameters on the evolution behavior of noncanonical vortices is addressed. It is shown that in comparison with Gaussian background vortex beams there are richer dynamic features in the evolution of elliptical Gaussian background vortex beams, and for the latter case the noncanonical vortex transformation takes place both in free space and through a misaligned lens. In the evolution process the topological charge is not always conserved. The results are illustrated by numerical examples.

Coupling of noncanonical optical vortices

When canonical vortices with different topological charges coexist in an optical beam, they inevitably become noncanonical during propagation. The noncanonical nature of optical vortices can be expressed in terms of morphological parameters, which can be represented in terms of a spinor, similar to the Jones vectors for polarization. This allows one to express the prefactor for a Gaussian beam containing two arbitrary vortices in terms of two terms. One is a product of two linearly propagating vortices. The other one, which is called the coupling term, represents the interaction between the vortices. The coupling term is independent of the vortex positions but depends on their initial morphological parameters. There are two situations where the interaction is zero. One is when the vortices are canonical with the same topological charge, and the other is when the vortices have the same anisotropy but with orthogonal orientations. The former situation is well known. The noninteraction of the latter situation is confirmed by a numerical simulation.

Trajectory of an optical vortex: canonical vs. non-canonical

We produce a canonical vortex using a computer generated hologram which is then converted to a non-canonical vortex by passing it through a cylindrical lens (CL). We study the trajectories of both canonical and non-canonical vortices in free space experimentally. We also obtained an analytical expression for the same. The computed trajectories and shapes of the vortices agree quite well with our experimental results. Theory as well as experiments show that canonical and non-canonical vortices follow quite different paths in free space.

Short wavelength spectrum and Hamiltonian stability of vortex rings.

We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength because the canonical vortex Hamiltonian is unbounded from below for these modes. To explicitly demonstrate this behavior, we derive the oscillation spectrum of vortex rings in incompressible, inviscid fluids within a geometrical cutoff procedure for the core. The spectrum develops an anomalous branch of negative group velocity and approaches the zero of energy for wavelengths that are about six times the core diameter. We show the consequences of this dispersion relation for the thermodynamics of vortex rings in superfluid 4He at low temperatures.