Charged Vortices Research Articles

Efficient generation of tunable magnetic and optical vortices using plasmas

Plasma is an attractive medium for generating strong microscopic magnetic structures and tunable electromagnetic radiation with predictable topologies due to its extraordinary ability to sustain and manipulate high currents and strong fields. Here, using theory and simulations, we show efficient generation of multimegagauss magnetic and tunable optical vortices when a sharp relativistic ionization front (IF) passes through a relatively long wavelength Laguerre-Gaussian (LG) laser pulse with orbital angular momentum (OAM). The optical vortex is frequency upshifted within a wide spectral range simply by changing the plasma density and is compressed in duration. The topological charges of both vortices can be manipulated by controlling the OAM mode of the incident LG laser and/or by controlling the topology and density of the IF. For relatively high (low) plasma densities, most of the energy of the incident LG laser pulse is converted into the magnetic (optical) vortex, with conversion efficiency approaching ∼90% for an ideal IF.Received 13 April 2022Revised 11 August 2022Accepted 2 January 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L012011Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLaser-plasma interactionsMagnetic field generation & plasma dynamoOptical vorticesX-ray generation in plasmasPlasma PhysicsAccelerators & BeamsAtomic, Molecular & Optical

Tight focusing of orthogonal C-point polarization states

Recently it is shown that spatially varying polarization distribution embedded with polarization singularity can be used to form an orthogonal basis pair. In this paper we show tight focusing of orthogonal basis pairs of bright and dark C-points. We observe that unlike orthogonal basis pairs of homogeneous polarization distribution, the orthogonal basis pairs of spatially varying polarization distributions embedded with C-points, show same intensity distribution at the focal plane upon tight focusing. We show that the focal plane intensity distribution is depend upon the intensity distribution of the beam under tight focusing. The longitudinal and transverse field components are hosted with phase vortices of charge ±1. Though the position of phase singularities remains same in a given orthogonal C-point pair, but the sign of phase vortices undergo reversal. The current study may reveal various other fundamental concepts related to polarization singularities.

Amplitude structure of optical vortices determines annihilation dynamics.

We show that annihilation dynamics between oppositely charged optical vortex pairs can be manipulated by the initial size of the vortex cores, consistent with hydrodynamics. When sufficiently close together, vortices with strongly overlapped cores annihilate more quickly than vortices with smaller cores that must wait for diffraction to cause meaningful core overlap. Numerical simulations and experimental measurements for vortices with hyperbolic tangent cores of various initial sizes show that hydrodynamics governs their motion, and reveal distinct phases of vortex recombination; decreasing the core size of an annihilating pair can prevent the annihilation event.

Giant vortex in a fast rotating holographic superfluid

In a holographic superfluid disk, when the rotational velocity is large enough, we find a giant vortex will form in the center of the system by merging several single charge vortices at some specific rotational velocity, with a phase stratification phenomenon for the order parameter. The formation of a giant vortex can be explained as there is not enough space for a standard vortex lattice. Keep increasing the rotational velocity the giant vortex will disappear and there will be an appearance of a superfluid ring. In the giant vortex region, the number of vortices measured from winding number and rotational velocity always satisfies the linear Feynman relation. However, when the superfluid ring starts to appear, the number of vortices in the disk will decrease though the rotational velocity is increasing, where most of the order parameter is suppressed.

Scalar optical hopfions

Hopfions are three-dimensional (3D) topological states discovered in field theory, magnetics, and hydrodynamics that resemble particle-like objects in physical space. Hopfions inherit the topological features of the Hopf fibration, a homotopic mapping from unit sphere in 4D space to unit sphere in 3D space. Here we design and demonstrate dynamic scalar optical hopfions in the shape of a toroidal vortex and expressed as an approximate solution to Maxwell’s equations. Equiphase lines correspond to disjoint and interlinked loops forming complete ring tori in 3D space. The Hopf invariant, product of two winding numbers, is determined by the topological charge of the poloidal spatiotemporal vortices and toroidal spatial vortices in toroidal coordinates. Optical hopfions provide a photonic testbed for studying topological states and may be utilized as high-dimensional information carriers.

The peripheral vortex biome of confined quantum fluids and its influence on vortex dipole annihilation

The self-annihilation of a pair of oppositely charged optical vortices (vortex dipole) in a quantum fluid is hindered by nonlinearity and promoted by radial confinement, resulting in rich life-cycle dynamics of such pairs. The competing effects generate a biome of peripheral vortices that can directly interact with the original pair to produce a sequence of surrogation events. Numerical simulation is used to elucidate the role of the vortex biome as a function of nonlinearity strength and the initial spacing between the engineered vortices. The results apply directly to other nonlinear quantum fluids as well and may be useful in the control of complex condensates in which vortex dynamics produce topologically protected phases.

Determining the topological charge of optical vortex by intensity distribution of a quasi-Airy vortex beam

Determining the orbital angular momentum state or the topological charge (TC) of a vortex beam is important in exploiting its applications. By analyzing the intensity distribution of the quasi-Airy vortex beam (QAVB) in far field, we find that the number of forked fringes is equal to the TCs of the vortex beam, and the direction of the forked fringes is related to the sign of TCs. Based on this property, a method of measuring the TC of optical vortex by the intensity distribution of QAVB is proposed. The range of initial topological angle (from 0 to 73°) for determining the TC of optical vortex is obtained as well as the relationship between the optimal propagation position and the initial topological angle to observe the forked fringes. In addition, the characteristics of QAVB embedded with multiple optical vortices at different locations would provide a new possibility for improving the confidentiality and the information capacity in free space optical communication.

Evolution of an accelerated charged vortex particle in an inhomogeneous magnetic lens

We present a detailed analysis of the capture and acceleration of a nonrelativistic charged vortex particle (electron, positron, proton, etc.) with an orbital angular momentum in the field of an axisymmetric electromagnetic lens, typical for a linear accelerator. We account for the acceleration and the inhomogeneity of both electric and magnetic fields that may arise from real-life imperfections. We establish the conditions for this wave packet to be captured and successfully transported through the lens. We describe the transition process and explain how a free Laguerre-Gaussian packet can be captured into the Landau state of the lens and how its structure is preserved for all moments in time. We illustrate the developed formalism with several representative examples.

No general relation between phase vortices and orbital angular momentum

Simple superpositions of Laguerre–Gauss beams illustrate, counterintuitively, the difference between two quantities that are commonly conflated: the component of orbital angular momentum ⟨l⟩ in the propagation direction z, and the total topological charge S, which is the algebraic sum of the charges of vortices piercing any plane perpendicular to z. The examples illustrate two contrasting situations: ⟨l⟩ = 0, S ≠ 0, and ⟨l⟩ ≠ 0, S = 0. In the second situation, not only is the total charge zero but also there are no vortices in the infinite half-space beyond the beam waist plane z = 0.

Constraints on the detection of topological charge of optical vortices using self-reference interferometry

In this paper we investigate the self-reference interferometry of optical vortices using a Michelson interferometer. It is found that the detection of topological charge (TC) for optical vortices is constrained by some physical conditions. We present these conditions through theoretical analyses, numerical simulation and experimental results. The maximal detectable TCs are different for different parameters, which is helpful for the measurement of TC in practical applications. Within the range allowed by the constrained conditions, we also study the detection of TC using the interference pattern of a two-way optical vortex, by changing the inclined angle of one mirror of the Michelson interferometer.

Observation of a triangular-lattice pattern in nonlinear wave mixing with optical vortices

Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.

Optical Vortices with A Quadratic Azimuthal Phase Dependence

AbstractThe light diffraction on fork‐shaped binary phase holograms (BPHs) with quadratic azimuthal phase term is considered. The distribution of intensity and phase, including positions of singularities and their number on the value of the quadratic term is revealed and analyzed. A simple analytical expression for the total topological charge (TC) of optical vortices (OVs) is derived for arbitrary power of azimuthal phase dependence. In order to visualize the phase distributions and phase singularities, interference measurements are carried out. The results of analytical and numerical calculations are confirmed by experimental data. These results may provide new possibilities for optical trapping and manipulation.

Focusing properties and focal shift of vortex Hermite-cosh-Gaussian beams

In this work, we investigate the focusing properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a converging lens system. The analytical propagation equation as well as the beam width expression of a focused vHChGB is derived based on the Huygens-Fresnel diffraction principle. From the obtained formulae, the effects of the Gaussian Fresnel number NF and the initial beam parameters, namely the beam order, the decentered parameter b, and the vortex charge number m, on the structure of the light intensity distribution and the beam spot size in the focal region are analyzed numerically. It is shown that the focal shift, which is determined from the minimum beam spot width criterion, is strongly dependent on the Fresnel number NF. And it is affected by the parameter b and the vortex charge m but is nearly insensitive to the beam order n. For a fixed value of NF, the focal shift is smaller when b or m is larger. The focal shift decreases monotonously with the increase of NF until it vanishes asymptotically for large values of NF. The obtained results may be useful for the applications of vHChGB in beam shaping and beam focusing.

Brownian motion theory of the two-dimensional quantum vortex gas.

A theory of Brownian motion is presented for an assembly of vortices. The attempt is motivated by a realization of Dyson's Coulomb gas in the context of quantum condensates. By starting with the time-dependent Landau-Ginzburg (LG) theory, the dynamics of the vortex gas is constructed, which is governed by the canonical equationof motion. The dynamics of point vortices is converted to the Langevin equation, which results in the generalized Fokker-Planck (GFP) (or Smolkovski) equationusing the functional integral on the ansatz of the Gaussian white noise. The GFP, which possesses a non-Hermitian property, is characterized by two regimes called the overdamping and the underdamping regimes. In the overdamping regime, where the dissipation is much larger that the vortex strength, the GFP becomes the standard Fokker-Planck equation, which is transformed into the two-dimensional many-particle system. Several specific applications are given of the Fokker-Planck equation. An asymptotic limit of small diffusion is also discussed for the two-vortices system. The underdamping limit, for which the vortex charge is much larger than the dissipation, is briefly discussed.

Analysis of practical fractional vortex beams at far field

The subject of calculating the topological charge (TC) or vortex strength of optical vortices has generated divided opinions among scientists. This is due to the fact that proper analytical results are hard to support from the experimental point of view, leading to different results and conclusions. In this work we will present numerical data that shows the limits of TC measurements for practical fractional vortices and the possible challenges that high order measurements may pose. By analyzing the far field phase and the behavior of the transitions we have shown that they follow specific curves that depend not only on the TC but also on the beam waist. This leads us to present a new “strength staircase” for practical vortices. Our aim is to give some insight in practical scenarios that have not been taken into account in previous results.

Propagation Characteristics of Circular Airy Vortex Beams in a Uniaxial Crystal along the Optical Axis

Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB’s profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane.

The propagation properties of a Laguerre–Gaussian beam in nonlinear plasma

The self-focusing properties of the Laguerre–Gaussian beams in nonlinear plasma, characterized by significant collisional or ponderomotive nonlinearity have been explored. The second-order differential equation of the beam width is established from Maxwell’s equations with Wentzel–Kramers–Brillouin and paraxial like approximation. The effect of the vortex charge number, intensity parameter and plasma temperature on the self-focusing properties of the Laguerre–Gaussian beam has been investigated.

Synthesizing Structured Optical Vortices

AbstractA noniterative approach to generation of binary phase holograms is applied for synthesizing complex optical vortex arrays. This approach does not use inverse Fourier analysis and allows one to obtain arbitrary optical vortex arrays with specified topological charges, which cannot be obtained using conventional fork‐shaped gratings. A topological charge of individual optical vortices generated using binary phase holograms can be specified at a given spatial frequency, so that the equidistant array of optical vortices can be generated via illuminating a hologram by a beam with the zero topological charge. The results of the calculation are consistent with the experimental data, including those of the interferometric measurements. The approach also makes it possible to synthesize superimposed optical vortices, where an optical field represents well‐ordered circular arrays of optical singularities. An unusual behavior of phase dislocations in superimposed structures is found. For two optical vortices of same reciprocal lattice vectors, but different topological charges, spatial distribution of singularities are reconfigured in a such manner that a couple of concentric circular arrays of singularities appear. The proposed binary phase holograms offer new opportunities for synthesizing the complex optical vortex light fields, which can find light–matter interaction‐based applications.

Influence of optical "dipoles" on the topological charge of a field with a fractional initial charge.

In this work, using the Rayleigh-Sommerfeld integral and Berry formula, a topological charge (TC) of a Gaussian optical vortex with an initial fractional TC in the far field was calculated. It was found that, for diverse fractional parts of the TC, the beam contained different numbers of screw dislocations, which determined the TC of the entire beam. If a fractional part of the TC was small, the beam consisted of the main optical vortex centered on the optical axis, with the TC equal to the nearest integer (say n>0) and two edge dislocations located on the vertical axis (one above and the other below the center). When the fractional part of the initial TC increased, a "dipole" was formed from the upper edge dislocation, consisting of two vortices with TCs equal to +1 and -1. With a further increase in the fractional part, the additional vortex with TC=+1 moved to the center of the beam, and the vortex with TC=-1 moved to the periphery. When the fractional part of the TC increased further, another "dipole" was formed from the lower edge dislocation, in which, on the contrary, the vortex with TC=-1 was displaced to the optical axis (to the center of the beam) and the vortex with TC=+1 moved to the beam periphery. When the fractional part of the TC became equal to 1/2, the lower vortex with a TC=-1, which was earlier displaced to the center of the beam, began to shift to the periphery, and the upper vortex with a TC=+1 moved closer and closer to the center of the beam, eventually merging with the main vortex when the fractional part approached 1. Such dynamics of additional vortices with TCs above +1 and below -1 determined which whole TC the beam would have (n or n+1) for different values of the fractional part from the segment [n,n+1]. Our analysis has shown that, for any value of the fractional part of the initial topological charge, the TC of the beam in the far field will not be determined. Since, with an increase in the radius of the circle in the beam section on which the TC is calculated, more optical "dipoles" will appear, and the TC will be either n or n+1.

Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"

In this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, which determine the TС of the entire beam. With a small fractional part of the TС, the beam consists of the main optical vortex centered on the optical axis with the TС equal to the nearest integer (let be n), and two edge dislocations located on the vertical axis (above and below the center). With an increase in the fractional part of the initial TC, a "dipole" is formed from the upper edge dislocation, consisting of two vortices with TC+1 and –1. With a further increase in the fractional part, the additional vortex with TC+1 is displaced to the center of the beam, and the vortex with TC–1 is displaced to the periphery. With a further increase in the fractional part of the TC, another "dipole" is formed from the lower edge dislocation, in which, on the contrary, the vortex with TC–1 is displaced to the optical axis (to the center of the beam), and the vortex with TC+1 is displaced to the beam periphery. When the fractional part of the TC becomes equal to 1/2, the "lower" vortex with TC–1, which was displaced to the center of the beam, begins to shift to the periphery, and the "upper" vortex with TC+1 moves closer and closer to the center of the beam and merges with the main vortex when the fractional part approaches 1. Such dynamics of additional vortices with upper TC+1 and lower TC–1 determine the whole TC the beam have (n or n+1) for different values of the fractional part from the segment [n, n+1].