Vortex Phase Research Articles

Three-dimensional imaging of topologically protected strings in a multiferroic nanocrystal

Multiferroic materials can host a plethora of intriguing phenomena due to the presence of multiple ferroic properties that break both spatial inversion symmetry and time reversal symmetry at an observable scale. Hexagonal manganite multiferroics are of particular interest as the properties of their symmetry-lowering phase transition can be described by a Mexican-hat-like potential energy surface. The early universe is proposed to have undergone a symmetry-lowering phase transition that is described by a similar Mexican-hat-like potential that gives rise to the formation of one-dimensional topologically protected defects known as cosmic strings. According to the Kibble-Zurek mechanism, hexagonal manganite multiferroics can host the crystallographic equivalent of cosmic strings and can therefore serve as a testing ground for exploration of concepts in cosmology. To date, however, direct imaging of 1D topological defects in a condensed matter material system has not been achieved. Here we report on robust three-dimensional imaging of topologically protected strings in a single hexagonal manganite nanocrystal, enabled by advances in experimental techniques. Our findings reveal multiferroic strings with a preferred phase vortex winding direction and average separation of ~93 nm.

Optical bottle beam transmit in polycyclic tornado mode

Light-field shaping technology is of significant importance for applications in particle trapping and optical communication. In this paper, we generate a new class of tunable polycyclic tornado Laguerre-Gaussian beams (TPTLGBs) experimentally and numerically by applying an annular spiral-zone phase (ASZP) with the second order chirped factor to Laguerre-Gaussian beams. By the parameters of the ASZP, we can modulate the focusing and diffraction of TPTLGBs along z-axis, controlling the number and quality of optical bottles (OBs) formed. In addition, it is possible to precisely control the direction of rotation of TPTLGBs during propagation. We further explore the specific effects of the ASZP and the central vortex phase on TPTLGBs. Adjusting the parameters of TPTLGBs, we obtain a high intensity focus. The multi-dimensional tunability and complex phase structure of TPTLGBs also provide new possibilities for further development of optical technology.

Flux jumps, cluster distribution model and vortex phase diagram of oxygenated YBa2Cu3-xAlxO6+δ single crystals for H|| ab

This work reports magnetic field direction dependent second magnetisation peak (SMP) anomaly in single crystals of oxygenated for ab. Detailed investigations on crystal A revealed the direction dependence of SMP anomaly at temperatures below 25 K, above which the direction dependence vanishes. The state of spatial order of the vortex lattice was found to be correlated to the vortex lattice symmetry that underwent a change at certain fields and was captured via single flux jumps observed in the third and fifth quadrant of magnetisation hysteresis loops. Bean’s critical state profiles drawn to explain the flux jumps required the presence of clusters of in the basal plane of with closely lying binding energies. Large full width at half maximum observed in Cu, O, Y and Ba photoelectron spectra confirmed the validity of the proposed cluster model. A vortex phase diagram incorporating all features in the magnetisation hysteresis loops has been made for oxygenated for || ab depicting various phases.

Unambiguous Detection of High-Energy Vortex States via the Superkick Effect.

Vortex states of photons, electrons, and other particles are freely propagating wave packets with helicoidal wave fronts winding around the axis of a phase vortex. A particle prepared in a vortex state carries a nonzero orbital angular momentum projection on the propagation direction, a quantum number that has never been exploited in experimental particle and nuclear physics. Low-energy vortex photons, electrons, neutrons, and helium atoms have been demonstrated in experiment and found numerous applications, and there exist proposals of boosting them to higher energies. However, verification that a high-energy particle is indeed in a vortex state will be a major challenge, since the low energy techniques become impractical at higher energies. Here, we propose a new diagnostic method based on the so-called superkick effect, which can unambiguously detect the presence of a phase vortex. A proof-of-principle experiment with vortex electrons can be done with existing technology, and its realization will also constitute the first observation of the superkick effect.

Second-order statistical characteristics of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase in a turbulent atmosphere

Abstract Based on the extended Huygens-Fresnel integral method, we have derived analytical formulae for the cross-spectral density matrix of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase (i.e., partially coherent radially polarized elliptical vortex (PCRPEV) beam) propagating through atmospheric turbulence, and have investigated the evolution laws of statistical characteristics such as the average intensity, degree of coherence (DOC), and degree of polarization (DOP) of the PCRPEV beam in turbulence. The results indicate that atmospheric turbulence causes the average intensity distribution of the PCRPEV beam to split and rotate during propagation, ultimately degenerating into a Gaussian-like distribution. Moreover, the PCRPEV beam with lower ellipticity, larger coherence length, and higher topological charge degenerates into a Gaussian-like beam at a slower rate in turbulence. Additionally, we also find that DOC distribution is related to topological charge, meaning that it can provide a new way to measure topological charge. In addition, we simulate the propagation of the PCRPEV beam through atmospheric turbulence using the complex screen and the multi-phase screens methods to verify the theoretical results. The research indicates that the simulation results are essentially consistent with the theoretical findings. These outcomes hold significant relevance for the advancement of free-space optical communication and remote sensing technologies.

Polarization-Independent Focusing Vortex Beam Generation Based on Ultra-Thin Spiral Diffractive Lens on Fiber End-Facet

An ultra-thin spiral diffractive lens (SDL) was fabricated by using focused ion beam milling on a fiber end-facet coated with a 100 nm thick Au film. Focusing vortex beams (FVBs) were successfully excited by the SDLs due to the coherent superposition of diffracted waves and their azimuth dependence of the phase accumulated from the spiral aperture to the beam axis. The polarization and phase characteristics of the FVBs were experimentally investigated. Results show that the input beams with various polarization states were converted to FVBs, whose polarization states were the same as those of the input beams. Furthermore, the focal length of the SDL and the in-tensity and phase distribution at the focus spot of the FVBs were numerically simulated by the FDTD method in the ultra-wide near-infrared waveband from 1300 nm to 1800 nm. The focal length was tuned from 21.8 μm to 14.7 μm, the intensity profiles exhibited a doughnut-like shape, and the vortex phase was converted throughout the broadband range. The devices are expected to be candidates for widespread applications including optical communications, optical imaging, and optical tweezers.

Achromatizing photolithographically patterned metasurfaces with arbitrary, variable unit cell size

In recent years, across many fields, a large emphasis has been placed on the development of optical materials that can realize arbitrary control over the phase, transmission, and polarization of light, particularly across a broad wavelength range. Metasurface optics, or arrays of subwavelength structures with highly tailorable geometry and composition on a thin substrate, have emerged as a promising contender to fulfill these needs. Several methods for the achromatization of metasurfaces have been demonstrated, including the use of amorphous nanopost shapes as well as multiple, simple nanopost shapes. We present what we believe to be a novel technique that can be used separately or in conjunction with these techniques to provide achromatic phase control: arbitrary aperiodicity. By varying the period, or spacing between adjacent nanoposts, metasurfaces can be demonstrated that achieve desirable phase behavior and high transmission over a relatively large bandwidth. We detail the design and fabrication of such a device, in the form of a 1 cm diameter polarization insensitive metasurface with a vortex phase profile that exhibits achromatic behavior over a ∼12% bandwidth centered at 1650 nm. We demonstrate simulated phase residuals below 0.4 rad and transmission above 85% for this bandwidth, as well as measured phase residuals below 0.6 rad and transmission above 88% for this bandwidth. By showing that we can create such a device with deep-UV photolithographic fabrication techniques, we make clear the fidelity of our aperiodic technique in realizing mass-manufactureable, large-area achromatic metasurfaces for the near-infrared.

Aperture partitioning holographic metasurface for the generation of a directional vortex beam

In this paper, what we believe to be a new aperture partitioning holographic metasurface is designed to effectively generate a directional vortex beam with mixed orbital angular momentum (OAM) modes. The proposed holographic metasurface consists of four adjacent doughnut-shaped regions, and a monopole probe is set in the center for feeding. These four well-designed regions generate four different OAM mode numbers of -1, -2, -3, and -4 respectively, and thus realize a directional vortex beam with mixed OAM modes. The proposed holographic metasurface operating at 10 GHz is simulated, fabricated, and measured. The measurement results agree well with the simulation results. The realized directional vortex beam contains both beam directionality and rich vortex phase vibrations property, which makes it useful in improving vortex beam transmission distance and applications in Multiple-Input Multiple-Output (MIMO) communication systems.

Rotating windmill array beam with adjustable wing angle.

In this study, we introduce a method for adjusting the wing angles of windmill beams. After varying the phase parameters, the sector strengths with different wing angles were generated, and they exhibited a self-rotating property in free-space propagation. This phase was obtained by performing an elliptical operation on the stretching vortex phase. The angle between the wings of the beam varied with the ellipticity. Accordingly, array windmill beams with adjustable wing angles were designed. Finally, we analyzed the evolution of the wing angle and self-rotating properties of the beam in detail. The experimental results were consistent with those of simulations. This operational method can be applied to optical cropping techniques, and the beam can be used in optical manipulation and imaging applications.

Competition of vortex core structures in superfluid He3−B

Among vortex structures identified so far in superfluid He3−B, the most common are the A-phase-core and double-core vortices. According to earlier numerical calculations, the double-core vortex is energetically favored nearly everywhere in the p−T phase diagram. Nevertheless, in experiments, the A-phase-core vortex has been observed down to temperatures of 0.6Tc at high pressures. We use the Ginzburg-Landau formalism to calculate the energies of the two vortex structures in the experimentally relevant magnetic field as well as the energy barrier for the transition between the two structures. Assigning vanishing barrier as the boundary of the metastability region of the A-phase-core vortex, we reproduce the experimentally measured vortex phase diagram and provide an explanation for the reappearance of the double-core vortex near the critical temperature Tc at low pressures: the difference in Zeeman energy between the two vortex structures becomes relatively more important close to Tc, and the A-phase-core vortex becomes unstable. In contrast to the equilibrium vortex structures, we suggest that the vortex nucleation process favors the A-phase-core vortex over the double-core vortex. Our approach can be used to analyze competition between different vortex structures in other unconventional superfluids and superconductors. Published by the American Physical Society 2024

Observation of vortices in a dipolar supersolid.

Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance owing to the appearance of a crystal structure and phase invariance owing to phase locking of single-particle wavefunctions, responsible for superfluid phenomena. Although originally predicted to be present in solid helium1-5, ultracold quantum gases provided a first platform to observe supersolids6-10, with particular success coming from dipolar atoms8-12. Phase locking in dipolar supersolids has been investigated through, for example, measurements of the phase coherence8-10 and gapless Goldstone modes13, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases14,15 and supersolids with two-dimensional crystalline order11,16,17, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase (SSP). Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with numerous spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars18.

Poincaré tornados.

We show that Poincaré polarization singularities, spiraling like a tornado, can be generated by superimposing two orthogonally polarized, abruptly auto-focusing ring-Airy beams that carry orbital angular momentum (OAM). Seeded by phase vortices of the same helicity, which are adapted to the high-intensity rings of one of the superimposing beams, these polarization singularities follow trajectories that twist and shrink in an accelerating fashion along their propagation. Reaching angular acceleration that exceeds 120 rad/mm2, these Poincaré tornados can find application in singular optics, wavefront shaping, polarization engineering, and imaging through complex media.

Vortex Phase Diagram and Pinning Mechanisms of Air‐Annealed FeTe0.8S0.2 Single Crystals

The vortex phase diagram and superconducting properties of air‐annealed FeTe0.8S0.2 single crystals are investigated. The annealed samples exhibit a superconducting transition, as confirmed by temperature‐dependent resistivity measurements. The thermally activated energy is calculated from the magnetotransport measurements, and the analysis shows that as the magnetic field increases, there is a crossover from single to collective vortex pinning. The vortex phase diagrams have been determined by analyzing magnetic field‐dependent resistivity, revealing the transitions from an unpinned vortex liquid region to a pinned vortex liquid state and further transition from this pinned state to a vortex glass state. Temperature‐dependent magnetization measurement determines the superconducting volume fraction. The critical current densities, as a function of the magnetic field (JC(H)), have been estimated from the magnetization versus magnetic field loops measured at various temperatures. Bean's critical state model estimates the JC values, and for an optimized annealed crystal, the self‐field JC at 2 K is . The normalized pinning force density in the samples is determined using the Dew Hughes model to identify the pinning mechanisms. The temperature‐dependent JC data analysis indicates the presence of ‐pinning in the samples. Theoretical models analyze experimental observations to understand the vortex pinning mechanisms.

Revealing the vortex phases and second magnetization peaks in SmBCO superconductors

Revealing the vortex phases and second magnetization peaks in SmBCO superconductors

Switchable phase modulation and multifunctional metasurface with vanadium dioxide layer

Abstract Metasurface, comprising subwavelength unit cells, offers a flexible modulation of the optical phase. However, traditional metasurfaces are typically engineered to function solely in one mode, limiting their efficiency and adaptability. In this study, we proposed a switchable metasurface consisting of gold bars deposited on polyimide and vanadium dioxide (VO2) layer. Upon the phase transition of VO2, this switchable metasurface exhibits functionality in both transmissive and reflective modes. Specifically, it efficiently converts left circularly polarized (LCP) light into right circularly polarized (RCP) light. For the dielectric (metallic) phases of VO2, the design behaves as metalens with a focal length of 1000 (906) μm at working frequency of 1.2 THz, respectively. Furthermore, the vortex phase can be effectively manipulated with topological number from 1 to 4 through the analysis of the electric field distribution. A directional emission from 12.9° to 42.2° is obtained in the reflective mode and Airy beam paths way can also be well regulated at 1.49 THz. The phase modulation is further achieved by varying the inter-mediums and its thickness. Finally, the sensing ability is explored with different covered solution. Consequently, this multifunctional and adaptable metasurface offers valuable insights for the development of reflectors, modulators, lenses and sensors.

A Review: Phase Measurement Techniques Based on Metasurfaces

Phase carries crucial information about the light propagation process, and the visualization and quantitative measurement of phase have important applications, ranging from ultra-precision metrology to biomedical imaging. Traditional phase measurement techniques typically require large and complex optical systems, limiting their applicability in various scenarios. Optical metasurfaces, as flat optical elements, offer a novel approach to phase measurement by manipulating light at the nanoscale through light-matter interactions. Metasurfaces are advantageous due to their lightweight, multifunctional, and easy-to-integrate nature, providing new possibilities for simplifying traditional phase measurement methods. This review categorizes phase measurement techniques into quantitative and non-quantitative methods and reviews the advancements in metasurface-based phase measurement technologies. Detailed discussions are provided on several methods, including vortex phase contrast, holographic interferometry, shearing interferometry, the Transport of Intensity Equation (TIE), and wavefront sensing. The advantages and limitations of metasurfaces in phase measurement are highlighted, and future research directions are explored.

Collective behavior of active filaments with homogeneous and heterogeneous stiffness.

The collective dynamics of active biopolymers is crucial for many processes in life, such as cellular motility, intracellular transport, and division. Recent experiments revealed fascinating self-organized patterns of diverse active filaments, while an explicit parameter control strategy remains an open problem. Moreover, theoretical studies so far mostly dealt with active chains with uniform stiffness, which are inadequate in describing the more complicated class of polymers with varying stiffness along the backbone. Here, using Langevin dynamics simulations, we investigate the collective behavior of active chains with homogeneous and heterogeneous stiffness in a comparative manner. We map a detailed non-equilibrium phase diagram in activity and stiffness parameter space. A wide range of phase states, including melt, cluster, spiral, polar, and vortex, are demonstrated. The appropriate parameter combination for large-scale polar and vortex formation is identified. In addition, we find that stiffness heterogeneity can substantially modulate the phase behaviors of the system. It has an evident destructive effect on the long-ranged polar structure but benefits the stability of the vortex pattern. Intriguingly, we unravel a novel polar-vortex transition in both homogeneous and heterogeneous systems, which is closely related to the local alignment mechanism. Overall, we achieve new insights into how the interplay among activity, stiffness, and heterogeneity affects the collective dynamics of active filament systems.

High contrast computational imaging with vortex phase diversity

Abstract Optical imaging systems employing spatially incoherent illumination are widely used in routine imaging applications like photography and bright-field microscopy. We describe an incoherent computational imaging system that uses an open aperture as well as a vortex phase aperture for recording the same scene. The two raw recorded images provide a diversity of information that can be effectively combined using the generalized Wiener filter. For the specific choice of aperture functions used here, the two corresponding generalized Wiener filters have nearly opposing polarity. This property leads to an effective computational PSF whose central lobe is $0.6$ times smaller compared to the diffraction-limited PSF and has a super-oscillatory character with side-lobes. The resultant computational imaging system provides images with significantly improved contrast. While our methodology requires two image records, the enhanced point spread function (PSF) with super-oscillatory character is obtained by employing bulk off-the-shelf optical elements instead of sub-wavelength structured masks. The vortex phase diversity concept along with computational image reconstructions are illustrated with both simulation and experimental data. The proposed imaging methodology may be used to improve imaging performance for wide ranging imaging systems without changing their form factor.

Flux dynamics, anisotropy in Jc and vortex phase diagram of H+-intercalated FeSe single crystal

This paper investigates the superconductivity, pinning, and vortex dynamics of FeSe before and after protonation. The study shows that, after being protonated, FeSe's superconducting critical temperature Tc has been increased to more than 40 K and the critical current density Jc has also been increased from 2.1 × 104 A/cm2 to 1.2 × 106 A/cm2, with significantly larger magnetic relaxation rates (Q). Meanwhile, the critical current density anisotropy (γ) decreases substantially while the upper critical field Hc2 increases from 13 T to 91 T after protonation. In addition, the reasons for the absence of the second peak effect in Hx-FeSe were explored. This investigation also reveals the existence of the vortex phase transition associated with the pinning behavior in protonated FeSe, demonstrated by the foot-like characteristics of resistivity. Based on these results, the vortex phase diagrams of FeSe before and after protonation were established. These findings provide important insights for exploring new high-temperature superconductors and their magnetic flux dynamics through protonation.

Angularly Selective Enhanced Vortex Screening in Extremely Layered Superconductors with Tilted Columnar Defects

We report on two mechanisms of angularly selective enhanced screening in the solid vortex phase of extremely layered superconductors with tilted columnar defects (CDs). We study Bi2Sr2CaCu2O8+δ samples with different densities of CD tilted 45° from the c-axis, and conduct local ac Hall magnetometry measurements, probing the sustainable current of the vortex system. We reveal two types of maxima in sustainable current for particular directions, detected as dips in the magnetic transmittivity of the vortex system. First, for a smaller number of vortices than of defects, an enhancement of screening is detected at an angular location Θdip1∼45° for H applied close to the direction of CD. For a larger number of vortices than of CD, Θdip1 decreases towards the ab-plane direction upon warming. Second, a pair of additional dips in transmittivity are detected at angles Θdip2 closer to, and quite symmetric with, the ab-plane. These two types of angularly selective enhanced screening reveal the effective pinning by tilted CD even for the composite vortex lattices nucleated in tilted fields in Bi2Sr2CaCu2O8+δ.