Negative Topological Charge Research Articles

Antiferro skyrmion crystals consisting of skyrmions and anti-skyrmions on a bilayer square lattice

An antiferro-type skyrmion crystal consisting of skyrmions with a negative topological charge and antiskyrmions with a positive topological charge manifests itself in its peculiar topological magnetism. We theoretically investigate the emergence of such an antiferro-type skyrmion crystal, where the topological charge exists in each sublattice but vanishes in the whole system. By performing the simulated annealing for an effective spin model with competing exchange interactions and staggered Dzyaloshinskii-Moriya interaction in momentum space on a bilayer square lattice, we find that the synergy between the antiferromagnetic interlayer exchange interaction and high-harmonic wave-vector interaction in addition to the staggered Dzyaloshinskii-Moriya interaction results in the antiferro-type skyrmion crystal in an external magnetic field. We show that the antiferro-type skyrmion crystal turns into the ferro-type skyrmion crystal with the same topological charge for both layers when the magnitude of the external magnetic field is varied. We also demonstrate that the competing interactions between ordering wave-vector channels and their high-harmonic wave-vector channels are essential in stabilizing the antiferro-type skyrmion crystal. Our results provide important ingredients to realize the antiferro-type skyrmion crystal by the external magnetic field, which can be utilized for low-power and high-speed spintronic devices based on antiferromagnetic materials.

Clustering of negative topological charges precedes plastic failure in 3D glasses.

The deformation mechanism in amorphous solids subjected to external shear remains poorly understood because of the absence of well-defined topological defects mediating the plastic deformation. The notion of soft spots has emerged as a useful tool to characterize the onset of irreversible rearrangements and plastic flow, but these entities are not clearly defined in terms of geometry and topology. In this study, we unveil the phenomenology of recently discovered, precisely defined topological defects governing the microscopic mechanical and yielding behavior of a model 3D glass under shear deformation. We identify the existence of vortex-like and antivortex-like topological defects within the 3D nonaffine displacement field. The number density of these defects exhibits a significant anticorrelation with the plastic events, with defect proliferation-annihilation cycles matching the alternation of elastic-like segments and catastrophic plastic drops, respectively. Furthermore, we observe collective annihilation of these point-like defects via plastic events, with large local topological charge fluctuations in the vicinity of regions that feature strong nonaffine displacements. We reveal that plastic yielding is driven by several large sized clusters of net negative topological charge, the massive annihilation of which triggers the onset of plastic flow. These findings suggest a geometric and topological characterization of soft spots and pave the way for the mechanistic understanding of topological defects as mediators of plastic deformation in glassy materials.

Embedded Skyrmion Bags in Thin Films of Chiral Magnets.

Magnetic skyrmions are topologically nontrivial spin configurations that possess particle-like properties. Earlier research has mainly focused on a specific type of skyrmion with topological charge Q = -1. However, theoretical analyses of 2D chiral magnets have predicted the existence of skyrmion bags-solitons with arbitrary positive or negative topological charge. Although such spin textures are metastable states, recent experimental observations have confirmed the stability of isolated skyrmion bags in a limited range of applied magnetic fields. Here, by utilizing Lorentz transmission electron microscopy, the extraordinary stability of skyrmion bags in thin plates of B20-type FeGe is shown. In particular, it is shown that skyrmion bags embedded within a skyrmion lattice remain stable even in zero or inverted external magnetic fields. A robust protocol for nucleating such embedded skyrmion bags is provided. The results agree perfectly with micromagnetic simulations and establish thin plates of cubic chiral magnets as a powerful platform for exploring a broad spectrum of topological magneticsolitons.

Direct determination of topological charge of structured light via phase-shift interference

We present a straightforward theoretical approach for the direct observation of the orbital angular momentum (OAM) charge inherent in structured light. Our method involves utilizing phase-shift interference of beams to discern the sign and magnitude of the topological charge associated with Laguerre–Gaussian (LG) beams. Specifically, we demonstrate that the topological charge of an LG beam can be ascertained through the interference with a corresponding helical wavefront beam possessing an opposite charge due to the reflection in Mach–Zehnder-like interferometer. The determination of the topological charge magnitude is facilitated by examining the interference pattern’s half number of petals. Additionally, our study reveals that the petal-like interference pattern undergoes azimuthal shift, with the direction of rotation being contingent upon the sign of the topological charge of the beam. Notably, for a negative phase shift, a anti-clockwise azimuthal shift corresponds to a positive topological charge, while an clockwise rotation is associated with a negative topological charge. This work contributes to the advancement of methods for characterizing structured light based on OAM charge, with potential applications in diverse fields such as optics, telecommunications and topological photonics.

Polarized vortex Smith-Purcell radiation with cascaded metasurfaces.

We introduce the concept of polarized vortex Smith-Purcell radiation by the interaction of an electron beam and cascaded metasurfaces. The spin and orbital angular momenta of Smith-Purcell radiation are determined by the cascaded metasurface that consists of a grating and a phase gradient metasurface. The grating converts the electron beam radiation into the desired polarized light, while the phase gradient metasurface generates the vortex light. Furthermore, the vortex Smith-Purcell radiation with linear and circular polarizations can be achieved by the various cascaded metasurfaces. In particular, the conversion of chirality in the Smith-Purcell radiation carrying circular polarization is accompanied by the alteration of positive and negative topological charges. This work paves the way for generating polarized vortex electron radiation and is beneficial to promote the development of free-electron-driven devices.

Reconfigurable perfect vortex beam generator based on a liquid crystal spiral phase plate.

A transmissive adaptable optical setup to generate a range of perfect vortex beams (PVBs) carrying different topological charges (TC) without using moving parts is presented. The setup is composed of an ad hoc transparent reconfigurable liquid crystal (LC) spiral phase plate (SPP), a refractive axicon and a convergent refractive lens. The LC SPP electrodes are manufactured ablating indium-tin oxide (ITO) glass substrates using direct laser writing (DLW) resulting in a very high fill factor device. In-house tailored electronics drive the 72 LC SPP electrodes giving rise to 72 different configurations with orbital angular momentum. In this work, the generation of PVBs with 36 positive or 36 negative TCs using this optical setup is accomplished.

Topology of nonlinearly charged black hole chemistry via massive gravity

The classification of critical points of charged topological black holes (TBHs) in anti-de Sitter spacetime (AdS) under the Power Maxwell Invariant (PMI)-massive gravity is accomplished within the framework of black hole chemistry (BHC). Considering the grand canonical ensemble (GCE), we show that d=4 black hole have only one topological class, whereas dge 5 black holes belong to two different topology classes. Furthermore, the conventional critical point characterized by negative topological charge coincides with the maximum extreme point of temperature; and the novel critical point featuring opposite topological charge corresponds to the minimum extreme point of temperature. With increasing pressure, new phases emerge at the novel critical point while disappear from the conventional one. Moreover, a atypical van der Waals (vdW) behavior is found in dge 6 dimensions, and the anomaly disappears at the traditional critical point. In the limit of nonlinearity parameter srightarrow 1, different topology classes are only obtained in the GCE and they may not exist within the canonical ensemble. With the absence of electric potential Phi , the neutral TBHs share the same topological classification results as the charged TBHs in the GCE of Maxwell-massive gravity.

Scalar vortex beams produced by Pancharatnam-Berry phase optical elements that utilize polarization holography.

We discuss the appearance of the Pancharatnam-Berry phase in polarization holography, and confirm the possibility of generating scalar vortex beams by using the Pancharatnam-Berry phase. The polarization holograms used to generate scalar vortex beams are produced in phenanthrenequinone-doped polymethylmethacrylate (PQ/PMMA), where each radial direction consists of an equivalent half-wave plate hologram with gradually changing directions. The spin angular momentum carried by a circular polarization reading wave is converted into orbital angular momentum in a reconstruction process, resulting in the formation of scalar vortex beams with positive and negative topological charges controlled by the reading polarization.

Topological defects in silicene

Using the molecular dynamic simulations a new class of topological defects in silicene is investigated. Si atoms in silicene belong to two triangular sublattices shifted one with respect to the other by h along the direction normal to the sheet. Silicene can have two energetically equivalent structures when the first or second sublattice is above the other. Topological defects appear at the junctions of the domains of these two structures. Domain walls can be rectilinear or curvilinear. Such defects cannot disappear from the structure except as a result of the annihilation of defects with positive and negative topological charges. Structure and energy of the topological defects are calculated. The effect of temperature is shown. Similar defects inevitably exist in other group IVA elemental 2D materials with buckled structure, such as germanene, stanene, and plumbene. As a result of the work, the problem of experimental detection of such defects and the question of how they affect the physicochemical and mechanical properties of materials, in particular, toxicity or sensory properties, is posed.

Defect self-propulsion in active nematic films with spatially varying activity.

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

A new family of two-dimensional Laguerre beams

We found a new family of non-diffracting Laguerre beams, which are constructed by the associated Laguerre polynomials and trigonometric functions, and described by different radial mode numbers and negative topological charges. Surprisingly, the description with negative topological charges is very different from the description of the general non-diffracting Laguerre beams with positive topological charges. The evolution laws for the new family of non-diffracting beams with the negative topological charges is depicted graphically, and the excitation mechanism of this new family is revealed, which might be helpful in improving the understanding of two-dimensional non-diffracting solutions of the paraxial wave equation.

Optical Vortex Beams with a Symmetric OAM Spectrum beyond a Sector Aperture

In this work, we theoretically and numerically show that in the superposition of optical Gaussian vortices with a symmetric OAM spectrum, the normalized orbital angular momentum (OAM) carried by the beam and the topological charge (TC) equal TC of the middle constituent vortex. We also show that after passing a sector-shaped aperture, the symmetric superposition preserves the OAM carried, with the TC becoming fractional and proportional to the angle of the sector aperture. As it further propagates in free space after the sector aperture, the TC of the superposition becomes an integer, albeit indefinite, thanks to the aperture edges generating a multitude of extra optical vortices with positive and negative unit TC, irregularly arranged across the beam.

Identification and Measurement of Positive and Negative Topological Charges of LG Beams for Medical Care

A medical care system’s security, high-capacity information transfer, and communication are all dependent on OAM-based quantum key distribution, namely on the measurement of OAM’s topological charges (TCs). The intensity patterns of interference between the vortex beam and its conjugate beam are analyzed to detect and evaluate positive and negative TCs of Laguerre-Gaussian (LG) vortex beams in a novel manner. An upgraded Mach–Zehnder (M-Z) interferometer is used to establish the order of positive, negative, integer, and half-integer TCs. Deciphering the order of integer TCs and half-integer TCs may be accomplished by measuring the interference bright petals as well as half of the total numbers of bright petals. The integer and half-integer TCs (VPP) may be modulated by the use of light path rotational with a vortex stage plate. Using the interferometer as mentioned earlier, the positive and negative of integer and half-integer TCs are acquired. Quantitatively, the order and sign of integer and half-integer TCs are measured in this manner. And this method is straightforward and less susceptible to the influence of parasitic interference. This can provide comprehensive security protection for the medical monitoring system, better reduce medical risks and protect patient privacy.

Diffraction of an off-axis vector-beam by a tilted aperture

Manifestations of orbital angular momentum induced effects in the diffraction of a radially polarized vector beam by an off-axis tilted aperture are studied both experimentally and theoretically. Experiments were carried out to extract the degree of circular polarization, which was shown to be proportional to the on-axis component of the spin angular momentum density. We report a clear separation of the regions of dominance of the right and left circular polarizations associated with positive and negative topological charges respectively, which is reminiscent of the standard vortex-induced transverse shift, albeit in the diffraction scenario. The experimental results are supported by model simulations and the agreement is quite satisfactory. The results are useful to appreciate the orbit-orbit related effects due to unavoidable misalignment problems (especially for vortex beams).

Low-loss and helical-phase-dependent selective excitation of high-order orbital angular momentum modes in a twisted ring-core fiber

We propose a method for the selective generation of high-order orbital angular momentum (OAM) modes by twisting a ring-core fiber (RCF). Theoretically, 22 OAM modes can be generated in the twisted RCF with effective mode separation. We experimentally demonstrate the excitation of OAM modes up to the fourth order. The positive or negative topological charge is determined by the clockwise or counterclockwise twist direction, indicating that the helical phase of the OAM can be controlled by the twist orientation. Compared with other fiber-based methods, the high-order OAM modes generated by our approach have the characteristics of low loss (minimum 0.3 dB), high mode purity (maximum 98%), and simple fabrication. This has potential applications in high-resolution imaging, high-capacity fiber-optics communication, vortex-optics sensing, and other fields.

False vacuum Skyrmions revisited

We consider the classical static soliton solutions of the Skyrme model with false vacuum potential. We make use of fully three-dimensional relaxation calculations to construct global energy minimizers in the sectors of topological degrees from $Q=1$ to $Q=6$. These solutions may be metastable, they contain a domain of true vacuum inside the core. Further, we explore small regions of negative topological charge density which appear for the Skyrmions of degrees $Q=3$, 5, 6.

Experimental realization of tunable finite square optical arrays

Recently optical lattices containing optical vortices (OVs), which carry phase singularities and possess exotic optical properties, have attracted increasing attention due to their potential applications in optical trapping or light-matter interaction systems. Here, we propose a kind of arbitrary order alternated OV lattices with positive and negative topological charges ±n, which are named as the nth-order alternated OV lattices (NAOVLs), and we experimentally demonstrate their propagation properties. We find that such NAOVLs can generate finite square optical arrays with interesting patterns or defects near the focal plane or far-field Fraunhofer region. We further find a general law (although with some exceptions) about the number N of bright spots in finite optical arrays as the value n increases. The interference experiments confirm optical properties of such finite arrays close to the focal plane. Our results may have potential applications in particle trapping and experimental realizations of novel optical arrays for the interaction between special optical lattices and atoms (or molecules, ions, micro- or nano-particles).

Transformations of structurally stable states of spiral beams subjected to sector perturbations

We investigated conditions for the violation of the structural stability of a spiral beam subject to sector perturbations. Based on the method of computer simulation and measurement of mode spectra, we have shown that a spiral vortex beam has a characteristic caustic surface, the intersection of which sharply changes the shape of the Poynting vector streamlines and the total topological charge of the beam. Sector beam perturbation does not almost change the streamline structure up to scale and rotation. We found that perturbation of the beam causes a change in the direction of circulation of streamlines in the region of perturbation, which is caused by the appearance of vortices with negative topological charges. Their contribution to the total energy flow is fractions of a percent. However, such perturbations do not cause changing the OAM in the beam, despite an increase in the number of vortex modes. Nevertheless, the perturbed beam remains only conditionally structurally stable due to the presence of a small fraction of optical currents with opposite circulations.

Generation and Propagation of Partially Coherent Power-Exponent-Phase Vortex Beam

We report on a partially coherent power-exponent-phase vortex beam (PC-PEPV), whose spatial coherence is controllable and the initial phase exhibits a periodic power exponential change. The PC-PEPV beam was generated experimentally with various spatial coherence widths, and its propagation properties were studied both numerically and experimentally. By modulating the topological charge (TC) and power order of the PC-PEPV beam, the structure of the vortex beam can be adjusted from circular to elliptic, triangular, quadrangle, and pentagon. When the power order is odd, the PC-PEPV beam with a negative TC can be generated, and the profiles of the PC-PEPV beam can be precisely controlled via adjusting the value of the power order. For the case of high spatial coherence width, the number of the dark cores in the polygonal intensity array of the PC-PEPV beam equals the magnitude of the TC. However, when decreasing the spatial coherence width, the dark cores vanish and the intensity gradually transforms into a polygonal light spot. Fortunately, from the modulus and phase distributions of the cross-spectral density (CSD), both the magnitude and sign of the TC can be determined. In the experiment, the modulus and phase distribution of the CSD are verified by the phase perturbation method. This study has potential applications in beam shaping, micro-particle trapping, and optical tweezers.

On-chip orbital angular momentum detection using a catenary grating metasurface

Vortex lights with optical orbital angular momentum have shown great promise in the areas of optical communication, optical manipulation and quantum optics. However, traditional methods for detecting the topological charge of vortex beams, such as interference and diffraction, are still challenging in miniaturization of the detection system and perfect matching of wave vectors. Here, a detection approach is proposed for measuring the topological charge of Laguerre–Gaussian (LG) vortex beams based on a catenary grating metasurface. According to the wave vector matching principle, the LG vortex beam can be coupled into surface plasmon polariton (SPP) waves propagating in different directions by using the well-designed catenary grating structure. The positive and negative topological charges can be distinguished by different arrangement of the catenary gratings. Additionally, the propagation angle of the launched SPP waves increases with the value of the topological charge. We believe that the proposed device would have broad application prospects in high compact photonic integrated circuits.