Charged Vortices Research Articles

Multiply charged vortex states of polariton condensates

The existence of quantized vortices is a key feature of Bose–Einstein condensates. In equilibrium condensates, only quantum vortices of unit topological charge are stable, due to the dynamical instabilities of multiply charged defects, unless supported by strong external rotation. Due to immense interest in the physics of these topological excitations, a great deal of work has been done to understand how to force their stability. Here we show that in photonic Bose–Einstein condensates of exciton–polariton quasiparticles pumped in an annular geometry, not only do the constant particle fluxes intrinsic to the system naturally stabilize multiply charged vortex states, but that such states can indeed form spontaneously during the condensate formation through a dynamic symmetry breaking mechanism. We elucidate the properties of these states, notably finding that they radiate acoustically at topologically quantized frequencies. Finally, we show that the vorticity of these photonic fluids is limited by a quantum Kelvin–Helmholtz instability, and therefore by the condensate radius and pumping intensity. This reported instability in a quantum photonic fluid represents a fundamental result in fluid dynamics.

Topological polarization singularities in metaphotonics

AbstractPolarization singularities of vectorial electromagnetic fields locate at the positions where properties of polarization ellipses are not defined. First observed for conical diffraction in 1830s, polarization singularities have been studied systematically with the underlying concepts being reshaped and deepened by many pioneers of wave optics. Here we review the recent results on the generation and observation ofpolarization singularities in metaphotonics. We start with the discussion of polarization singularities in the Mie theory, where both electric and magnetic multipoles are explored from perspectives of local and global polarization properties. We then proceed with the discussion of various photonic-crystal structures, for which both near- and far-field patterns manifest diverse polarization singularities characterized by the integer Poincaré or more general half-integer Hopf indices (topological charges). Next, we review the most recent studies of conversions from polarization to phase singularities in scalar wave optics, demonstrating how bound states in the continuum can be exploited to generate directly optical vortices of various charges. Throughout our paper, we discuss and highlight several fundamental concepts and demonstrate their close connections and special links to metaphotonics. We believe polarization singularities can provide novel perspectives for light-matter manipulation for both fundamental studies and their practical applications.

Introduction of the vortex Hermite-Cosh-Gaussian beam and the analysis of its intensity pattern upon propagation

In this paper, a vortex-Hermite-cosh-Gaussian beam (vHChGB) is introduced as a general form of the vortex cosh-Gaussian and vortex Hermite-Gaussian beams. Based on the Huygens-Fresnel diffraction integral, a propagation formula of the vHChGB passing through a paraxial optical system is derived. The evolution of the intensity pattern of the propagated vHChGB as a function of the beam order, decentered parameter (b parameter) and topological vortex charge is discussed with numerical results. It is shown that the vHChGB shape in the source plane depends crucially on the decentered parameter. In far-field, the multi-lobe profile obtained for small b evolves into a four-petal-like beam. Whereas the initial four-lobe profile for large b, morphs into a multi-lobes pattern. The vHChGB shows specific intensity patterns depending on the beam order and the vortex charge. This study may be beneficial for applications involving beam shaping of hollow vortex beam, beam splitting techniques and optical communications.

Polarization interferometric prism: A versatile tool for generation of vector fields, measurement of topological charges, and implementation of a spin–orbit controlled-Not gate

Optical vortex and vector field are two important types of structured optical fields. Due to their wide applications and unique features in many scientific realms, the generation, manipulation, and measurement of such fields have attracted significant interest and become very important topics. However, most ways to generate vector fields have a trade-off among flexibility, efficiency, stability, and simplicity. Meanwhile, an easy and direct way to measure the topological charges, especially for a high order optical vortex, is still a challenge. Here we design and manufacture a prism: a polarization interferometric prism (PIP) as a single-element interferometer, which can conveniently convert an optical vortex to vector fields with high efficiency and be utilized to precisely measure the topological charge (both absolute value and sign) of an arbitrary optical vortex, even with a high order. Experimentally, we generate a variety of vector fields with global fidelity ranging from 0.963 to 0.993 and measure the topological charge of an optical vortex by counting the number of petals uniformly distributed over a ring on the output intensity patterns. As a versatile tool to generate, manipulate, and detect the spin-orbital state of single photons, PIP can also work in the single-photon regime for quantum information processing. In the experiment, the PIP is utilized as a spin–orbit controlled-Not gate on the generated 28 two-qubit states, achieving the state fidelities ranging from 0.966 to 0.995 and demonstrating the feasibility of the PIP for single photons.

Compound plasmonic vortex generation based on spiral nanoslits

In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre-Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for several examples confirm the effectiveness of the design principle. The discussions about the interference of vortex fields definite the generation condition for the structured vortex. This work provides a design methodology for generating new vortices using spiral nanoslits and the advanced radially structured plasmonic vortices is helpful for broadening the applications of vortex fields.

LED-based chromatic and white-light vortices of fractional topological charges

Based on an LED light source, we present an experimental scheme to produce chromatic and white-light optical vortices carrying fractional topological charges. In theory, we develop a general formula to simulate the propagation dynamics of such fractional chromatic and white-light vortices based on the eigenmode decomposition of orbital angular momentum within the Gaussian–Schell model. In the experiment, for the generation of the chromatic and white-light optical vortices, we use a phase-only spatial light modulator to prepare the desired holographic gratings and a prism to compensate for the dispersion for three primary colors (red, green, and blue). The experimental observations, e.g., the seal-healing effect of dislocation lines, are in good agreement with the simulation results. The present work extends the studies of fractional optical vortices not only from highly coherent to partially coherent region but also from monochromatic to chromatic (white-light) source, which may find potential applications in LED-based visible light communication and optical displaying.

On some configurations of oppositely charged trapped vortices in the plane

Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. The use of invariants and symmetries enables deducing a set of equations in elementary symmetric polynomials, which can then be fully solved via computational algebra packages. We retrieve a number of previously identified configurations, including collinear ones and polygonal (e.g. quadrupolar and hexagonal) ones. However, importantly, we also retrieve a configuration with 4 positive charges and 2 negative ones, which is unprecedented, to the best of our knowledge, in BEC studies. We corroborate these predictions via numerical computations in the fully two-dimensional PDE system of the Gross-Pitaevskii type which characterizes the BEC at the mean-field level.

Spiral phase plate with multiple singularity centers

We investigate a multispiral phase plate (MSPP) with multiple centers of phase singularity arbitrarily located in the MSPP plane. Equations to describe the topological charge of an optical vortex in the initial plane immediately behind the MSPP and orbital angular momentum (OAM) normalized relative to the beam power are derived. The topological charge in the initial plane is found as a sum of the topological charges of all singularities if their centers are located inside a finite-radius circular aperture. If the phase singularity centers are partially located on the boundary of a circular diaphragm limiting the MSPP, the total topological charge is found as the sum of all singularities divided by 2. Total OAM that the vortex carries depends on the location of the singularity centers: the farther from the center of the plate the singularity center is located, the smaller is its contribution to the OAM. If all singularity centers are located on the boundary of the diaphragm limiting MSPP, then the OAM of the vortex beam equals zero, although in this case the topological charge of the beam is nonzero.

Zeroth- and first-order long range non-diffracting Gauss\u2013Bessel beams generated by annihilating multiple-charged optical vortices

We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss–Bessel beams (GBBs). Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The developed analytical model reproduces the experimental data. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories.

Experimental investigation on a novel agglomeration device based on charged ultrasonic spray and vortex generators for improving the removal of fine particles

Multi-field synergistic agglomeration is a promising pretreatment technology for improving the control and removal of fine particles. In this work, a novel agglomerator coupling with plasma charged ultrasonic spray and turbulent vortex generator was put forward, which has three agglomeration modes, namely turbulent agglomeration, atomized turbulent agglomeration and charged atomized turbulent agglomeration. As a pretreatment device, the agglomerator was combined with a fabric filter for the experimental investigation. The result indicated that the agglomeration efficiencies of the PM1 for the three agglomeration modes were 21.8%, 53.2% and 68.9%, respectively; and the removal efficiencies of the PM1 for the only fabric filter and the fabric filter combined with the three agglomeration modes were 66.5%, 83.9%, 86.8% and 89.7%, respectively. The characteristic experiment of the designed electrode showed that the stable voltage was about 19–38 kV and the charge-to-mass ratio was in the range of 1–5 mC kg−1. The optimization study of the two important parameters showed that the atomization quantity was recommended in the range of 1.6–2.7 kg∙h−1 and the inlet flue gas velocity should be as small as possible and close to 4.8 m/s to ensure the agglomeration effect.

The effect of Ni–Zn ferrite doping on the superconductivity of Y3Ba5Cu8O18 nanocomposite materials

Nanocomposite materials of the Y3Ba5Cu8O18/(Ni0.5Zn0.5Fe2O4)x type, where x = 0.00 wt. %, 0.03 wt. %, 0.10 wt. %, and 0.50 wt. %, are synthesized by the improvement of the solid-state reaction technique. The prepared samples have been characterized by x-ray diffraction (XRD), scanning electron microscopy, x-ray energy dispersion, infra-red spectroscopy, thermo-gravimetric analysis, four probe DC resistance, and current–voltage (I–V) measurements. It was found that the prepared samples have an orthorhombic structure with unit cell parameters (a = 3.9557 Å, b = 3.8197 Å, and c = 30.2460 Å) for pure Y358, and the unit cell volume decreases by the addition of (Ni0.5Zn0.5Fe2O4) nanoparticles into the Y358 compound. The crystallite size (D) was evaluated from XRD patterns by Scherrer’s method. The crystallite size (D) is decreased from 40 nm for pure Y358 to 18 nm for Y358 doped by the Ni–Zn nanoferrite content of 0.50 wt. %. The critical current density Jc and I–V characteristics for superconductor/nanoferrite (Y358/Ni–Zn) composite materials are explained according to Bean’s critical state model and the charge–vortex duality in the Y358 high-Tc mixed-state.

Vortex structures in photodetachment by few-cycle circularly polarized pulses

Generation of electron vortices in photodetachment of ${\mathrm{H}}^{\ensuremath{-}}$ by circularly polarized laser pulses is analyzed by means of strong-field approximation and by numerically solving the time-dependent Schr\"odinger equation. A very good agreement is shown for the magnitude and the phase of the probability amplitude of photodetachment from both approaches. We demonstrate that spiral-like patterns in the probability amplitude of detachment, observed for a pair of counter-rotating circularly polarized laser pulses, cannot be associated with nonvanishing topological charge vortices. The latter can be generated, on the other hand, by a circularly polarized laser pulse or a sequence of such pulses with corotating polarizations. Such interpretation of our results follows from the hydrodynamical formulation of quantum mechanics and its generalization to arbitrary parametric spaces.

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations. The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

Stability of topological properties of optical vortices after diffraction on a phase screen

It is theoretically shown that the distribution of the average intensity of Gaussian optical vortex in the focal plane of a spherical lens scattered by random phase screen has the form of a ring with non-zero value on the optical axis. The radius of the ring depends on the topological charge of the optical vortex and the scattering power of the diffuser. Therefore the topological charge cannot be determined only by the radius of the formed ring. However, it can be determined by the number of points with phase singularity for which detection Shack–Hartmann sensor is used. It is also shown that when using a linear combination of two optical vortices than the distribution of the average intensity will have local maxima the quantity of which is equal to the difference of their topological charges. The number of these maxima does not depend on the degree of diffusion and can serve as an indicator for identifying an optical vortex. Numerical simulation and experiment confirm the theoretical conclusions.

Polarization singular patterns in modal fields of few-mode optical fiber

Structured light with isolated complex π -symmetric polarization singular topologies such as lemon, star, and monstar is experimentally generated using few-mode optical fiber (FMF). These singularities, popularly known as C-points, are generated in the fiber modal field as a result of an inherent combination of orthogonally polarized Gaussian and vortex modes, excited simultaneously in FMF and controlled by input coupling conditions. The vortex charge, the state of polarization of the combining modes, and the relative phase difference between them are analyzed using Stokes polarimetry. Further, modal fields consisting of two opposite/similar index C-points are also generated, and the possible mode combinations that are responsible for such complex patterns are discussed. The helicity and index conservations in formation of dipoles also are discussed.

Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function

The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam.

Periodic Maxwell–Chern–Simons vortices with concentrating property

In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS) model with respect to the Chern-Simons parameter without any restriction on either a particular class of solutions or the number of vortex points. The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by [Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to establish the existence of periodic Maxwell-Chern-Simons vortices satisfying the concentrating property of the density of superconductive electron pairs. Furthermore, we expect that the (CS) limit analysis in this paper would help to study the stability, multiplicity, and bubbling phenomena for solutions of the (MCS) model.

Birth of optical vortices in propagating fields with an original fractional topological charge

In contrast to the orbital angular momentum (OAM), which is conserved on free space propagation, the topological charge (TC) of a paraxial optical vortex (OV) is not conserved in the general case. Here, we investigate a Gaussian beam with a fractional TC in the original plane and demonstrate both theoretically and numerically how the TC changes in the course of propagation. Depending on the proximity of the topological charge to an even or odd integer number, an optical vortex with the original fractional TC is shown to behave in a number of different ways. For simple OVs (Laguerre-Gaussian or Bessel-Gaussian modes), TC is conserved both in propagation and after weak phase distortions. An experiment shows that when scattered by a random phase screen, the integer TC of an OV is conserved right up to a random phase variation of π. Therefore, in the case of weak turbulences, it is expedient to measure a discretely varying TC instead of a continuously varying OAM.

Ergoregion instabilities in rotating two-dimensional Bose-Einstein condensates: Perspectives on the stability of quantized vortices

We investigate the stability of vortices in two-dimensional Bose--Einstein condensates. In analogy with rotating spacetimes and with a careful account of boundary conditions, we show that the dynamical instability of multiply quantized vortices in trapped condensates persists in untrapped, spatially homogeneous geometries and has an ergoregion nature with some modification due to the peculiar dispersion of Bogoliubov sound. Our results open new perspectives to the physics of vortices in trapped condensates, where multiply quantized vortices can be stabilized by interference effects and singly charged vortices can become unstable in suitably designed trap potentials. We show how superradiant scattering can be observed also in the short-time dynamics of dynamically unstable systems, providing an alternative point of view on dynamical (in)stability phenomena in spatially finite systems.

Measuring the topological charges of acoustic vortices by apertures.

The acoustic vortex wave has exhibited high-potential applications such as communication. In this work, the authors propose an efficient method for quantitatively measuring the topological charge of an acoustic vortex through two kinds of annular apertures: an annular triangle aperture and an annular ellipse aperture. It is found that the characteristics of the diffraction pattern in the far-field are well related with the shape of apertures and the topological charges of the acoustic vortex wave. Therefore, the topological charge of acoustic vortex beams can be determined from the diffraction patterns, which provide an effective method for measuring the topological charge of acoustic vortex beams.