Topological Charge Research Articles

Topological classification of critical points for hairy black holes in Lovelock gravity

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, T=T(V,xi), as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Topological Classes of BTZ Black Holes

In a recent paper, black holes were viewed as topological thermodynamic defects using generalized off-shell free energy. The aforementioned work indicates that all black hole solutions in the pure Einstein–Maxwell gravity theory could be classified into three different topological classes for four and higher spacetime dimensions. In this paper, we investigate the topological number of BTZ black holes in distinct theories with different charges (Q) and rotational parameters (J). Using generalized free energy and Duan’s ϕ-mapping topological current theory, we found only two topological classes for BTZ spacetime. Particularly, for a BTZ black hole with rotation or in the Einstein–Power–Maxwell theory, there is only one zero point and the total topological number is 1. While for a BTZ black hole in new massive gravity, the global topological charge depends on the value of the specific parameter m, which provides a counter-example for the conjecture that the topological number is independent of the black hole’s parameters.

High‐Gain, High‐Order Vortex Air Lasing Generated by Plasma Amplification

AbstractVortex air lasing opens exciting perspectives for remote generation, amplification, and control of vortex beams in ambient air. By combining the advantages of air lasing and vortex beams, it holds great potential in some specific applications such as standoff detection of chiral molecules and rotating objects. However, it remains challenging to produce high‐order vortex air lasing and flexibly control its orbital angular momentum, hindered by the inhomogeneous distribution and instability of laser‐induced plasma. Herein, vortex lasing with a tunable vortex order from the first up to the tenth order is achieved through vortex seed amplification in plasma. The helical phase structure of the seed is well conserved in the amplification process. Each order vortex air lasing shows the same topological charge as the seed and a doughnut‐shaped profile. Moreover, the amplification factor is up to 104. Generation of high‐order, high‐gain vortex air lasing is attributed to the choice of an appropriate population‐inversion system, as well as the optimal control over spatial matching of pump and seed beams, gas pressures, and focusing conditions. This work facilitates the understanding of the gain mechanism of lasing and promises to extend the application scenarios of air‐lasing‐based spectroscopy.

Magnetic Hopfions: A Review

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented.

Selection of OAM signal constellations for atmospheric channels using optimal transport theory

We describe a method for determining optimal selections of orbital angular momentum (OAM) superpositions for OAM signal modulation in free-space optical communications using a measure of distance in the context of the Optimal Transport theory. Within the range of topological charges ℓ = −20 to ℓ = 20 we design OAM constellations using 16 to 128 symbols consisting of solos, duets, trios, and quartets of OAM modes. We propose a classification strategy requiring relatively low complexity to evaluate the performance of these constellations, achieving a classification error smaller than 1/1000 in weak to strong turbulence conditions for the 16-OAM constellation. We have found that the optimal set shows some dependence on the receiver’s architecture, so we offer results for optical detectors based on the conjugate projection, the mode sorter, and the Shack-Hartmann sensor.

Precision measurement of the topological charge of a fractional vortex beam based on angular-grating-diffraction OAM spectrum

Precision measurement of the topological charge of a fractional vortex beam based on angular-grating-diffraction OAM spectrum

Change in coherence properties of ovally Gaussian Schell-model vortex beam in non-Kolmogorov turbulence along an uplink path

Analytical expressions are obtained for the cross-spectral density (CSD) matrix elements of an ovally Gaussian Schell-model vortex (OGSMV) beam propagating in non-Kolmogorov turbulence along uplink path based on the extended Huygens-Fresnel principle, and its coherence properties such as spectral degree of coherence (SDOC), phase distributions and coherence vortices are investigated in detail. Results indicate that the profile of the SDOC of OGSMV beam in turbulence gradually degrades into a Gaussian-like profile, and OGSMV beam with smaller ovality, larger topological charge number and initial coherence lengths will slow down this process. Interestingly, it is clearer to observe the coherence rings of the SDOC for OGSMV beam by reducing the initial auto-correlation lengths. Furthermore, one also finds that the number of elliptical edge dislocation for phase distribution of OGSMV beam is equal to topological charge number. They can provide two effectively ways for measuring topological charge number. Lastly, we used the phase screen simulation to verify our theoretical predictions. Theoretical outcomes are in good agreement with the simulations. Our results will be of important reference for optical communication.

Topological Floquet engineering of a three-band optical lattice with dual-mode resonant driving

We present a Floquet framework for controlling topological features of a one-dimensional optical lattice system with dual-mode resonant driving, in which both the amplitude and phase of the lattice potential are modulated simultaneously. We investigate a three-band model consisting of the three lowest orbitals and elucidate the formation of a crosslinked two-leg ladder through an indirect interband coupling via an off-resonant band. We numerically demonstrate the emergence of topologically nontrivial bands within the driven system, and a topological charge pumping phenomenon with cyclic parameter changes in the dual-mode resonant driving. Finally, we show that the band topology in the driven three-band system is protected by parity-time reversal symmetry. Published by the American Physical Society 2024

MEMS-tunable topological bilayer metasurfaces for reconfigurable dual-state phase control

Tunable optical metasurfaces (MSs) have demonstrated exceptional capabilities in actively manipulating light fields. However, most existing tunable MSs are limited to controlling only one functionality. Here, by combining a MEMS mirror with a plasmonic bilayer MS (BMS), we develop an electrically driven MEMS-BMS platform enabling complete reflection phase transformation and switching between two encoded functionalities by actuating the MEMS mirror. This capability stems from different optical responses of each MS layer at distinct MEMS-BMS separations, due to evolving topological singularities in a defined parameter space. With this tunable topological MEMS-BMS platform, we demonstrate polarization-independent MEMS-BMS for reconfigurable diffraction gratings, achieving ∼25% efficiency, ∼0.75 contrast at 850-nm wavelength, and fast response (∼5µs). The MEMS-BMS arrangement for generating vortex beams with switchable topological charges of ±1 is also demonstrated, evidenced by distinct near- and far-field interferograms. Our work expands the scope of tunable MSs by exploiting dynamic topological phases in the MEMS-BMS arrangement, paving the way for multifunctional tunable meta-optics.

Spin angular momentum and optical chirality of Poincaré vector vortex beams

Abstract The optical chirality and spin angular momentum of structured scalar vortex beams has been intensively studied in recent years. The pseudoscalar topological charge ℓ of these beams is responsible for their unique properties. Constructed from a superposition of scalar vortex beams with topological charges ℓ A and ℓ B , cylindrical vector vortex beams are higher-order Poincaré modes which possess a spatially inhomogeneous polarization distribution. Here we highlight the highly tailorable and exotic spatial distributions of the optical spin and chirality densities of these higher-order structured beams under both paraxial (weak focusing) and non-paraxial (tight focusing) conditions. Our analytical theory can yield the spin angular momentum and optical chirality of each point on any higher-order or hybrid-order Poincaré sphere. It is shown that the tunable Pancharatnam topological charge ℓ P = ( ℓ A + ℓ B ) / 2 and polarization index m = ( ℓ B − ℓ A ) / 2 of the vector vortex beam plays a decisive role in customizing their spin and chirality spatial distributions. We also provide the correct analytical equations to describe a focused, non-paraxial scalar Bessel beam.

Merging bound states in the continuum-driven ultrahigh sensing figure of merit in all-dielectric metasurfaces.

Radiation-free photonic bound states in the continuum (BIC) in metasurfaces allow ultrahigh quality (Q) factor and strongly confined mode volume, which are extremely advantageous in the development of ultrasensitive microcavity sensors. However, the conventional isolated BICs are susceptible to failure due to symmetry breaking caused by fabrication imperfection and nonzero incident angle. Here, we propose a silicon nitride-based metasurface with multiple BIC merging. The merging of accidental BIC and symmetry-protected BIC can increase the Q-factor near the Brillouin zone Γ point and thus robustly induces a figure of merit (FOM) of refractive index sensing at small incident angles two orders of magnitude higher than that in isolated BIC configuration. Specifically, the FOM in merging BIC reaches 108 at a 2° incident angle. The BIC merging can be universally achieved in square lattices with C4 symmetry, and slower decay of Q-factor and higher FOM can further occur in hexagonal lattices benefiting from higher-order topological charges. The advantage of merging BIC is also maintained when considering in-plane and out-of-plane symmetry breaking. These results offer a unique design path for high-performance metasurface sensors and can be extended to other high-Q applications such as low-threshold lasers, nonlinear frequency conversion, and low-loss waveguides.

Topology-optimized terahertz real-time reconfigurable multifunctional liquid-crystal-coding metasurface

In this paper, a reflective terahertz reconfigurable multifunctional coding metasurface based on topology optimization using liquid crystal (LC) is presented. First, the LC metasurface unit is topologically optimized using the NSGA-II multi-objective optimization algorithm. By applying the bias voltage to dynamically adjust the dielectric constant of the LC, the metasurface unit is capable of 2-bit coding at the frequency of 0.67 THz. Then, based on the designed metasurface unit, the array arrangements of the coding metasurface are reversely designed, which makes the metasurface realize flexible control and dynamic switching between beam assignment and vortex beam generation. The results show that for the beam assignment, the single-beam and multi-beam control can be realized with the reflected electromagnetic waves at continuous arbitrary angles in the range of elevation angle of 40° and azimuth angle of 360°. Moreover, the elevation angle and azimuth angle of each beam in the multi-beam can be controlled independently. Using the Fourier convolution addition operation, the control range of the single-beam elevation angle can be expanded. For the vortex beam, the single vortex beam and the multi-vortex beam can be generated in the range of elevation angle of 40° and azimuth angle of 360° with topological charges l=±1, ±2, ±3 at arbitrary angles. This provides flexibility and diversity in the generation of vortex beams. Therefore, the proposed terahertz LC metasurface can realize flexible control of reconfigurable functions and has certain application prospects in terahertz communication, phased array radar, and vortex radar.

Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems.

We study the Kondo lattice model of multipolar magnetic moments interacting with conduction electrons on a triangular lattice. Bond-dependent electron hoppings induce a compasslike anisotropy in the effective Ruderman-Kittel-Kasuya-Yosida interaction between multipolar moments. This unique anisotropy stabilizes multipolar skyrmion crystals at zero magnetic field. In a unit cell, the skyrmion fractionalizes into meron composites subject to the conservation of total topological charge. Diverse multipolar phases in the phase diagram give rise to novel spontaneous Hall response of conduction electrons.

Dynamical friction in rotating ultralight dark matter galactic cores

Abstract Dynamical friction and stellar orbital motion in spiral galaxies with dark matter composed of ultralight bosons in the state of rotating Bose–Einstein condensate (BEC) are studied. It is found that the dynamical friction force is significantly affected by the topological charge of the vortex structure of the BEC core with the strongest effect at distances near the galactic center. It is also shown that the ultralight dark matter self-interaction plays an important role in studying the dynamical friction.

High topological charge lasing in quasicrystals.

Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry-higher order charges require symmetries not compatible with any two-dimensional Bravais lattice. Here, we experimentally demonstrate lasing with topological charges as high as -5, +7, -17 and +19 in quasicrystals. We discover rich ordered structures of increasing topological charges in the reciprocal space. Our quasicrystal design utilizes group theory in determining electromagnetic field nodes, where lossy plasmonic nanoparticles are positioned to maximize gain. Our results open a new path for fundamental studies of higher-order topological defects, coherent light beams of high topological charge, and realizations of omni-directional, flat-band-like lasing.

Scale setting and hadronic properties in the light quark sector with ( 2+1 )-flavor Wilson fermions at the physical point

We report scale setting and hadronic properties for our new lattice QCD gauge configuration set (HAL-conf-2023). We employ (2+1)-flavor nonperturbatively improved Wilson fermions with stout smearing and the Iwasaki gauge action on a 964 lattice, and generate configurations of 8000 trajectories at the physical point. We show the basic properties of the configurations such as the plaquette value, topological charge distribution and their autocorrelation times. The scale setting is performed by detailed analyses of the Ω baryon mass. We calculate the physical results of quark masses, decay constants of pseudoscalar mesons and single hadron spectra in light quark sector. The masses of the stable hadrons are found to agree with the experimental values within a subpercent level. Published by the American Physical Society 2024

Optomechanical motions of gold dimer’s spin, rotation and revolution manipulated by bessel beam

The optomechanical motion of a gold nanoparticle (GNP) dimer—a pair of optically bound GNPs—in fluid, manipulated by a Bessel beam, is theoretically studied using the multiple multipole (MMP) method. Since a Bessel beam possesses orbital angular momentum (OAM) and spin angular momentum (SAM) simultaneously, complicated rigid-body motions of the dimer can be induced. The mechanism involves the equilibrium between the optical force with the reactive drag force exerted by the fluid. Our results demonstrate that the dimer rotates around its center of mass (COM), while the COM performs an orbital revolution around the optical axis. Additionally, each individual GNP undergoes spinning. The directions of the GNPs’ spin and the orbital revolution of COM depend on the handedness and the order (topological charge) of Bessel beam, respectively. Nevertheless, the rotation direction of the dimer depends on the size of GNP. In the case of a smaller dimer, the direction of dimer’s rotation with respect to the COM is consistent with the handedness of the light. Conversely, a larger dimer performs a reverse rotation, accompanied by a precession during the orbital revolution. There are multiple turning points in the radius of the GNP for the alternating rotation of the dimer caused by positive or negative optical torque. Our finding may provide an insight to the optomechanical manipulation of optical vortexes on the motions of GNP clusters.

Skyrmion Hall Effect in Altermagnets.

It is widely believed that the skyrmion Hall effect is absent in antiferromagnets because of the vanishing topological charge. However, the Aharonov-Casher theory indicates the possibility of topological effects for neutral particles. In this Letter, we predict the skyrmion Hall effect in emerging altermagnets with zero net magnetization and zero skyrmion charge. We first show that the neutral skyrmion manifests as a magnetic quadrupole in altermagnets. We reveal a hidden gauge field from the magnetic quadrupole, which induces the skyrmion Hall effect when driven by spin transfer torque. Interestingly, we identify a sign change of the Hall angle when one swaps the anisotropic exchange couplings in altermagnets. Furthermore, we demonstrate that both the velocity and Hall angle of altermagnetic skyrmions sensitively depend on the current direction. Our findings real the critical role of magnetic quadrupole in driving the skyrmion Hall effect with vanishing charge, and pave the way to discovering new Hall effect of neutral quasiparticles beyond magnetic skyrmions.

Detecting topological charge and phase of the vortex beam embedded into the low coherence background

We propose and experimentally demonstrate a single-path interferometric approach to quantify the higher-order topological charge (TC) and phase structure of a vortex beam embedded into a low-coherence background. The topological charge is determined by an in-line and common path configuration for superposing the fluctuating coherent beams loaded with vortex and non-vortex features. Ensemble average of the intensities of the superimposed fluctuating fields generates petal structure, and the number of petals infers the absolute value of the topological charge of the vortex beam. Furthermore, a three-step phase-shifting method along with a single-path interferometer is utilized to recover the phase and spectra of the TCs in the beams embedded into a low-coherence background. The results of our experiment demonstrate successful measurement of vortex beam with TCs up to 150. We believe that such petal patterns with incoherent light will be useful in sensing the rotation and motion of optically rough objects.

Coherent high-power terahertz vortex generation with tunable orbital angular momentum based on transverse phase mask shaping

Abstract Terahertz (THz) radiation has become a significant tool in cutting-edge research due to its superior properties. THz vortices with tunable orbital angular momentum (OAM) are particularly attractive to the scientific community due to their well-defined discrete azimuthal phase around the propagation axis. However, the generation of high-power THz radiation with OAM remains a challenge for most existing technologies. In this paper, a new method for generating coherent high-power THz vortices with tunable OAM and frequency is proposed by combining frequency beating and transverse phase mask shaping techniques. Theoretical analyses and numerical simulations indicate that this method can generate coherent THz vortices with peak powers in the tens of megawatts and tunable topological charge numbers.