Single-charge Vortices Research Articles

Fractional angular momentum borne on rotating vortex solitons

We predict the existence of vortex solitons with one and two embedded off-centered phase singularities in competing media trapped in a rotating harmonic potential. The Coriolis force induced by the rotation of external potentials shifts the singularity of the single-charge vortex soliton from the origin to the periphery. In this process, the angular momentum carried by per photon varies continuously from 1 to 0. For vortex solitons with two separated opposite-charge singularities, the counterclockwise rotation leads to a variation of angular momentum per photon from 0 to −1, and vice versa. Particularly, for vortex solitons nesting two singularities of the same charge, two branches of vortices with symmetrical singularities and asymmetric singularities coexist when the rotation frequency exceeds a critical value. The angular momentum per photon still varies continuously with the rotation frequency. Linear stability analysis collaborated by direct propagation simulation demonstrates that rotating asymmetric vortex states carrying fractional angular momentum are extremely robust, provided that their power is high enough.

Vortex Dynamics and Structured Darkness of Laguerre-Gaussian Beams Transmitted Through Q-Plates Under Weak Axial-Asymmetric Incidence

We describe the rich vortex dynamics at normal and near-normal or off-centered Laguerre-Gaussian beam transmission through the q-plate – a waveplate capable of generating vortex beams from circularly polarized incident beams. First, we explore the basics of the spin-to-orbit angular momentum conversion and show the vortex constellations under normal incidence for the case of quarter-wave retardation. Second, we analyze the optical Gaussian and vortex beam profile transformations accompanying the giant beam shifts under axial-asymmetric incidence. Namely, we consider the near-normal (for the Fourier-space q-plate) and off-centered (for the real-space q-plate) incidence, when the incident angle becomes comparable with beam angular divergence and off-center distance becomes comparable with beam width, respectively. In this regime, one can control the positions of the single-charge vortices with the specified polarization components of the beam, including those residing in its structured darkness. All mentioned effects arise due to the extreme spin-orbit coupling. The results obtained form a novel platform for a plethora of optical vortex transformation and structured light phenomena.

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.

Periodic evolution of the out-of-phase dipole and the single-charged vortex solitons in periodic photonic moiré lattice with saturable self-focusing nonlinearity media.

We survey the propagation properties of the out-of-phase (OOP) dipole solitons and the single-charged vortex (SCV) soliton in a periodic photonic moiré lattice with θ=arctan⁡(3/4) under self-focusing nonlinearity media. Since the rotation angle, periodic photonic moiré lattices have peculiar energy band structures, with highly flat bands and the bandgaps being much more extensive, which is very favorable for the realization and stability of the solitons. When exciting a single point on-site with the OOP dipole beam, its evolution shows a periodic rollover around the lattice axis. Whereas, when exciting a single point on-site with the SCV beam, it transmits counterclockwise rotating periodically. Both the OOP dipole solitons and the SVC soliton maintain the local state, but their phase exhibits different variations. The phase of the OOP dipole solitons is flipped, while that of the SCV is rotated counterclockwise. Our work further complements the exploration of solitons in photonic moiré lattice with nonlinearity.

Exploring the ellipticity dependency on vector helical Ince-Gaussian beams and their focusing properties.

We present a numerical study of the intensity and polarization structure of vector helical Ince-Gaussian (VHIG) modes, which present a distinct subclass of vector Ince-Gaussian modes with defined parameter settings. The intensity profile of VHIG beams has an elliptic hollow structure, while the polarization distribution shows multiple single-charge polarization vortices arranged along a line. By selecting the mode order, phase factor and ellipticity of the VHIG beams, we can control the number of elliptic rings, the number of polarization vortices, and the topology of the vector singularity. Furthermore, we simulate the focusing properties of VHIG beams based on vector diffraction theory. Our results indicate that the ellipticity parameter of VHIG beams could be a valuable degree of freedom to generate attractive transverse profiles and longitudinal distributions under focusing, which may have implications for lithography, material processing, optical communication, and even optical trapping and manipulation.

Rotating optical vortex clusters in competing cubic-quintic media

We put forward a rich variety of optical vortex structures nested in a localized beam envelope supported by cubic-quintic media confined in a rotating harmonic trap. The globally linked vortex cluster comprises an even number of vortices with topological charges equaling 1 and $\ensuremath{-}1$ alternately. In the nonrotating frame, single-charged vortices reside evenly on a ring. Yet, the system rotation induces the Coriolis force, which in turn leads to a strong asymmetry of the vortex cluster. With the increase of rotation frequency, vortex clusters with a different number of vortices transform into rotating nonlinear states with different symmetries. Meanwhile, the beam envelope is deformed obviously. Nonrotating vortex clusters are stable provided that their power exceeds a certain critical value. Unstable rotating states are very robust and survive over thousands of diffraction lengths.

Dynamical evolution and decay of multi-charged quantum vortex in a Bose–Einstein condensate

We report the observation of the twisted decay of quadruply charged vortices taking place in an atomic Bose–Einstein condensate. Supporting numerical simulations show that the singly-charged vortices, which result from the decay of a multi-charged vortex, twist around intertwined in the shape of helical Kelvin waves.

Fundamental and vortex gap solitons in quasiperiodic photonic lattices.

We address the existence and stability of fundamental, single-charged vortex, and double-charged vortex gap solitons in two-dimensional quasiperiodic photonic lattices imprinted in a Kerr-type medium. Fundamental and vortex gap solitons can bifurcate from linear localized states or their combination supported by quasiperiodic lattices for both defocusing and focusing nonlinearities. We find that the three types of solitons mentioned above are stable in the entire existence domain for defocusing nonlinearities, and that they can also be stable at a lower power level for focusing nonlinearities. At higher power, unstable solitons are characterized by a ring-shaped symmetry-breaking distribution, and the unique spot profile formed is repeatedly observed with changes in propagation distance.

Stable vortex in Bose-Einstein condensate dark matter

The nature of dark matter (DM) is one of the most fascinating unresolved challenges of modern physics. One of the perspective hypotheses suggests that DM consists of ultralight bosonic particles in the state of Bose–Einstein condensate (BEC). The superfluid nature of BEC must dramatically affect the properties of DM including quantization of the angular momentum. Angular momentum quantum in the form of a vortex line is expected to produce a considerable impact on the luminous matter in galaxies including density distribution and rotation curves. We investigate the evolution of spinning DM cloud with typical galactic halo mass and radius. Analytically and numerically stationary vortex soliton states with different topological charges have been analyzed. It has been shown that while all multi-charged vortex states are unstable, a single-charged vortex soliton is extremely robust and survives during the lifetime of the Universe.

Rotation and oscillation of gap vortex solitons in optically induced square photonic lattices with a self-focusing nonlinearity

We demonstrate the rotation and oscillation of the single-charged vortex (SCV) and double-charged vortex (DCV) in two-dimensional (2D) optically induced square photonic lattices under single-site excitation with appropriate self-focusing nonlinearity conditions. Numerical analysis shows that the SCV can self-trap into a localized gap vortex soliton mode that resides in the first Bragg reflection gap, for which a vortex is nested centrally in the rotating square-shaped optical envelope and four peaks always appear at four corners. Whereas DCV tends to evolve into a dynamical rotating quasi-vortex gap soliton formed in the second Bragg reflection gap, employing an out-of-phase quadrupole-like beam as a transition state to reverse the topological charge and the direction of rotation periodically. Our findings may provide insights into the experimental feasibility of observing such phenomena.

Periodic Evolution of the Out-of-Phase Dipole and the Single-Charged Vortex Solitons in Periodic Photonic Moiré Lattice with Saturable Self-Focusing Nonlinearity Media

Periodic Evolution of the Out-of-Phase Dipole and the Single-Charged Vortex Solitons in Periodic Photonic Moiré Lattice with Saturable Self-Focusing Nonlinearity Media

Transformation of the singular skeleton in optical-vortex beams diffracted by a rectilinear phase step

Based on the Kirchhoff–Fresnel approximation, we numerically analyze spatial characteristics of the light field formed after a circular Laguerre–Gaussian beam with a single-charged optical vortex (OV) passes the transparent screen with a rectilinear phase step. The main attention is paid to the localization and interactions of the OVs, which form the singular skeleton of the transformed field. The phase-step influence depends on its value and position with respect to the beam axis. Upon ‘weak perturbation’ (low phase step), the main effect is that the OV is shifted from the initial axial position and describes a closed loop when the phase step is monotonously translated across the beam. The ‘strong perturbation’ (the phase step is close to π) induces topological reactions with emergence and annihilation of additional singularities in the near-axial region of the diffracted beam cross section. These features are interpreted based on the 3D OV trajectories that show an intricate behavior with kinks and ‘retrograde’ segments. The details of the OV migration and singular skeleton transformations reveal the fundamental helical nature and transverse energy circulation in the OV beams. The numerical results obtained in this paper show possibilities for the purposeful control of the singular skeleton characteristics within the transformed beam, and can be useful for the OV diagnostics, OV metrology and micromanipulation techniques.

Higher-charge vortex solitons and vector vortex solitons in strongly nonlocal media.

We report, to the best of our knowledge, the first experimental observation of higher-charge vortex solitons and vector vortex solitons in lead glass with strongly thermal nonlocal nonlinearity. A higher-charge vortex soliton with a topological charge of l=4 and a vector vortex soliton consisting of two orthogonally polarized vortex components, with charges l1=1 and l2=4, were observed at several times of diffraction length. We show that the ring profiles and the carried topological charges of the two incoherently coupled vortex components can be preserved. We also numerically find that the stability of the higher-charge vortex can be enhanced by co-propagating a stable, single-charge vortex.

Evolution of vortex and quadrupole solitons in the complex potentials with saturable nonlinearity

We investigate the evolution of vortex and quadrupole solitons in the parity-time (PT)-symmetric optical lattices with self-focusing saturable nonlinearity. It is found that the saturable parameter plays a significant role on the existence and stability of vortex solitons. There exists a threshold for saturable parameter, above which the single-charged vortex solitons can be stable. The strength of gain–loss component of the PT-symmetric potential can affect the existence and stability of vortex solitons dramatically. We find that the single-charged vortex solitons can exist even at the phase transition point of the PT-symmetric potential, but diffuse fast during propagation. In addition, it is also found that the direction of the angular momentum has little effect on the properties of vortex solitons. Dramatically, the stable regions of out-of-phase quadrupole solitons are broader than that of the single-charged vortex solitons, while the stable regions of in-phase quadrupole solitons are narrower than that of the single-charged vortex solitons.

Vortices in self-bound dipolar droplets

Quantized vortices have been observed in a variety of superfluid systems, from $^4$He to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized vortex lines in dilute dipolar self-bound droplets. We first discuss the energetic stability region of dipolar vortex excitations within a variational ansatz in the generalized nonlocal Gross-Pitaevskii functional that includes quantum fluctuation corrections. We find a wide region where stationary solutions corresponding to axially-symmetric vortex states exist. However, these singly-charged vortex states are shown to be unstable, either by splitting the droplet in two fragments or by vortex-line instabilities developed from Kelvin-wave excitations. These observations are the results of large-scale fully three-dimensional simulations in real time. We conclude with some experimental considerations for the observation of such states and suggest possible extensions of this work.

Ultrashort vortex from a Gaussian pulse \u2013 An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ωλ with correlated linear phase (ϕ0 ≥ 0.025 λ) and lateral shear (y0 ≥ 0.05 ωλ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Collectively induced many-vortices topology via rotatory Dicke quantum phase transition

We examine the superradiance of a Bose–Einstein condensate pumped with a Laguerre–Gaussian laser of high winding number, e.g., . The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ-fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ-fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ-fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.

Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer

We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre–Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.

Density Dependence of Charge-4 Vortex Splitting in Bose–Einstein Condensates

We studied the axial-direction density dependence of the splitting of a charge-4 vortex created in 87Rb Bose–Einstein condensates. Vortices were generated by topological phase imprinting, and the axial density of the condensates was controlled by an optical potential. Linear and triangular arrangements of four single-charged vortices that emerged through the charge-4 vortex collapse were observed. The splitting of the charge-4 vortices was suppressed by maintaining the density outside the l = 2 unstable mode regions where linear arrangements were formed. In addition, we studied vortex dynamics in a high density region for which investigations have not been previously performed.

Fractional Fourier transform of astigmatic sine-Gaussian beams and generation of dark hollow light beams with elliptic geometry

In this work, we develop a novel method of creating dark hollow beam with vortex by converting a sine-Gaussian beam (SeGB) with edge-dislocation and astigmatism through using fractional Fourier transform (FrFT) optical system. On the basis of the definition of the FrFT, an analytical transformation formula is derived for an astigmatic SeGB passing through such a transform system. By use of the derived formulae, the changes of the intensity distribution and the corresponding phase properties associated with the transforming astigmatic SeGBs are analytically discussed in detail. It is found that for an input SeGB without astigmatism, there is still a dark line or an edge dislocation associated with the intensity distribution of the FrFT beam along the initial dislocation line, similar to that of the input SeGB. However, when the input SeGB astigmatically passes through an FrFT optical system, the dark line of the intensity distribution of the input SeGB can be converted into a solitary zero point, or in other words, a dark hollow beam with a single-charge vortex can be produced by SeGB with an edge dislocation. The results reveal that the astigmatism plays a critical role in transforming a SeGB into a dark hollow one through the FrFT optical system. Furthermore, some numerical calculation results based on the derived formula are presented and discussed graphically. It is shown that for appropriate beam parameters and carefully adjusting the transform angle of FrFT, dark hollow beams with single-charge vortex and elongated elliptic geometry can be realized with astigmatic SeGBs. The influences of the beam parameters and the transform angle of FrFT optical system on the generation of perfect dark hollow beams are also investigated. The results demonstrate that the linear eccentricity of the dark hollow beam, which is roughly defined as the ratio of semi-minor axis to semi-major one of the intensity pattern, mainly depends on the Fresnel number. And the optimal linear eccentricity may be relatively large under carefully selecting the beam and optical system parameters. Moreover, optimal parameter values corresponding to perfect dark hollow beam configurations which can be experimentally accessed are presented. As is well known, there are two types of pure phase defects or dislocations in the optical fields:one is screw dislocation or vortex and the other is edge-dislocation. Due to their important applications, the propagation dynamics of optical vortices or edge dislocations are extensively studied both theoretically and experimentally. The vortex-edge dislocation interaction is investigated in detail. However, there are fewer reports on the direct conversion between a single edge dislocation and a vortex. Therefore, the results obtained in this paper represent a significant step forward in understanding the transformation dynamics between beams with pure edge dislocation and vortex, and also opens possibilities for their potential applications, e.g., in generating dark hollow beams with elliptic geometry using FrFT systems.