Half-integer Topological Charge Research Articles

High-resolution three-dimensional imaging of topological textures in nanoscale single-diamond networks.

Topological defects-extended lattice deformations that are robust against local defects and annealing-have been exploited to engineer novel properties in both hard and soft materials. Yet, their formation kinetics and nanoscale three-dimensional structure are poorly understood, impeding their benefits for nanofabrication. We describe the fabrication of a pair of topological defects in the volume of a single-diamond network (space group Fd m) templated into gold from a triblock terpolymer crystal. Using X-ray nanotomography, we resolve the three-dimensional structure of nearly 70,000 individual single-diamond unit cells with a spatial resolution of 11.2 nm, allowing analysis of the long-range order of the network. The defects observed morphologically resemble the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals. Yet our analysis of strain in the network suggests typical hard matter behaviour. Our analysis approach does not require a priori knowledge of the expected positions of the nodes in three-dimensional nanostructured systems, allowing the identification of distorted morphologies and defects in large samples.

Bound states in the continuum in divided triangular hole metasurfaces

We investigate the bound states in the continuum (BICs) in dielectric metasurfaces consisting of a two-part divided triangular hole in the unit cell of a square lattice, with emphasis on the generation, splitting, and merging of BICs. At the smallest height ratio between the upper triangular and the lower trapezoidal holes, the accidental BIC with an extremely large quality factor emerges on an isolated dispersion band at the Brillouin zone center, which is recognized as a polarization singularity (V point) with an integer topological charge. As the height ratio increases, the accidental BIC is split into a pair of circularly polarized states, which are polarization singularities (C points) with half-integer topological charges. The two states depart from each other to a maximum distance, and then approach each other as the height ratio continues to change. They finally merge to another polarization singularity (V point) with an integer topological charge, which is identified as the Friedrich-Wintgen BIC that occurs near the avoided crossing between two interacting dispersion bands.

Perfect intrinsic and nonlinear chirality simultaneously driven by half-integer topological charge

Perfect intrinsic and nonlinear chirality simultaneously driven by half-integer topological charge

Non-Hermitian chiral degeneracy of gated graphene metasurfaces

Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction of an eigenspace dimensionality at the EP has been investigated mostly in a passive repetitive manner. Here, we propose an electrical and spectral way of resolving chiral EPs and clarifying the consequences of chiral mode collapsing of a non-Hermitian gated graphene metasurface. More specifically, the measured non-Hermitian Jones matrix in parameter space enables the quantification of nonorthogonality of polarisation eigenstates and half-integer topological charges associated with a chiral EP. Interestingly, the output polarisation state can be made orthogonal to the coalesced polarisation eigenstate of the metasurface, revealing the missing dimension at the chiral EP. In addition, the maximal nonorthogonality at the chiral EP leads to a blocking of one of the cross-polarised transmission pathways and, consequently, the observation of enhanced asymmetric polarisation conversion. We anticipate that electrically controllable non-Hermitian metasurface platforms can serve as an interesting framework for the investigation of rich non-Hermitian polarisation dynamics around chiral EPs.

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.

Multi-meron interactions and statistics in two-dimensional materials

As a fundamental type of topological spin textures in two-dimensional (2D) magnets, a magnetic meron carries half-integer topological charge and forms a pair with its antithesis to keep the stability in materials. However, it is challenging to quantitatively calculate merons and their dynamics by using the widely used continuum model because of the characteristic highly inhomogeneous spin textures. In this work, we develop a discrete method to address the concentrated spin structures around the core of merons. We reveal a logarithmic-scale interaction between merons when their distance is larger than twice their core size and obtain subsequent statistics of meron gas. The model also predicts how these properties of single and paired merons evolve with magnetic exchange interactions, and the results are in excellent agreement with the Monte Carlo simulations using the parameters of real 2D van der Waals magnetic materials. This discrete approach not only shows equilibrium static statistics of meron systems but also is useful to further explore the dynamic properties of merons through the quantified pairing interactions.

Precise measurement of trapping and manipulation properties of focused fractional vortex beams.

Fractional vortex beams (FVBs) were believed to be hard to rotate microparticles at a half-integer topological charge due to the unique radial opening (low-intensity gap) in their intensity ring. However, recent research discovered more symmetric intensity structures with less intensity inhomogeneity of practical FVBs at the focal plane. Here, we experimentally demonstrated the manipulation of trapped microparticles and precisely measured their rotation periods at the focal plane of practical FVBs by using a high-speed camera. We verified that the measured orbital angular momentum (OAM) derived from the collective microparticle rotation is roughly proportional to the fractional OAM of practical FVBs. Furthermore, we also experimentally obtained the trapped microparticles' power spectra under the illumination of FVBs, from which we achieved the average trap stiffness to evaluate the two-dimensional trapping strength of the practical focused FVB intensity ring. Our results provide a new insight and an efficient tool on finely trapping and rotating microparticles and bio-cells by using fractional vortex beams.

Polaritonic Vortices with a Half-Integer Charge.

Topological spin textures are field arrangements that cannot be continuously deformed to a fully polarized state. In particular, merons are topological textures characterized by half-integer topological charge ±1/2 and vortex-like swirling patterns at large distances. Merons have been studied previously in the context of cosmology, fluid dynamics, condensed matter physics and plasmonics. Here, we visualized optical spin angular momentum of phonon polaritons that resembles nanoscale meron spin textures. Phonon polaritons, hybrids of infrared photons and phonons in hexagonal boron nitride, were excited by circularly polarized light incident on a ring-shaped antenna and imaged using infrared near-field techniques. The polariton field reveals a half-integer topological charge determined by the handedness of the incident beam. Our phonon polaritonic platform opens up new pathways to create, control, and visualize topological textures.

Conservation of the half-integer topological charge on propagation of a superposition of two Bessel-Gaussian beams

We theoretically show that by continuously varying the amplitude of a constituent beam in the superposition of two Bessel-Gaussian (BG) beams with topological charges (TCs) $m$ and $n$ the TC of the entire superposition can be controlled. Between the constituent beams, there is a topological competition. For some parameters of the BG beams, TC of the superposition equals $n$, while for other parameters, it is equal to $m$. In the center of such a superposition (on the optical axis), there is an $m$-fold degenerate intensity null (optical vortex with the TC of $m<n$), whereas $n--m$ optical vortices with the unitary TC are in the beam periphery. We demonstrate that when the amplitudes of the constituent beams tend to be equal, peripheral vortices ``move'' to infinity. In this case, superposition of two BG beams has a half-integer TC, and this TC is conserved on propagation in space. The fractional part of the TC is, however, ``hidden'' in the infinity (``hidden'' phase). Conservation of the half-integer TC of an optical vortex on propagation is shown.

Exceptional topology in ordinary soft matter.

Hydrodynamics is shown to induce non-Hermitian topological phenomena in ordinary, passive soft matter. This is demonstrated by subjecting a two-dimensional elastic lattice to a low-Reynolds viscous flow. The interplay of hydrodynamics and elasticity splits Dirac cones into bulk Fermi arcs, pairing exceptional points with opposite half-integer topological charges. The bulk Fermi arc is a generic hallmark of the system exhibited in all lattice and flow symmetries. An analytic model and simulations explain how the emergent singularities shape the spectral bands and give rise to a web of van Hove singularity lines in the density of states. The present findings suggest that non-Hermitian physics can be explored in a broad class of ordinary soft matter, living and artificial alike, opening avenues for topology-based technology in this regime.

Configurational entropy of skyrmions and half-skyrmions in planar magnetic elements

This works deals with the presence of localized planar structures in magnetic materials that admit integer or half-integer topological charge. We study models in which the internal disposition of magnetization is driven by a single parameter, that controls the topological charge density of the magnetic structure. In particular, we focus mainly on the configurational entropy of these skyrmions and half-skyrmions and show how to increase or diminish their informational capabilities.

Topological defects promote layer formation in Myxococcus xanthus colonies

The soil bacterium Myxococcus xanthus lives in densely packed groups that form dynamic three-dimensional patterns in response to environmental changes, such as droplet-like fruiting bodies during starvation. The development of these multicellular structures begins with the sequential formation of cell layers in a process that is poorly understood. Using confocal three-dimensional imaging, we find that motile rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal. Cell alignment is nearly perfect throughout the population except at point defects that carry half-integer topological charge. We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes preferentially open at -1/2 defects. To explain these findings, we model the bacterial colony as an extensile active nematic fluid with anisotropic friction. In agreement with our experimental measurements, this model predicts an influx of cells toward +1/2 defects, and an outflux of cells from -1/2 defects. Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to promote the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus.

Phase-field model of topological charge interaction force in nematic liquid crystals

ABSTRACT Nematic liquid crystals (LCs) normally contain both integer and half-integer topological charges. In this work, we investigate topological charge evolution dynamics in nematic LCs by the phase-field model. We observe the annihilation of the topological charge, and the total number of charges decreases to two cores with time evolution in a disk. A significant decrease in charges is observed during the initial evolution. The positive topological charge and negative topological charge annihilate depending on the distance between two charges, which can be treated as the interaction force. The form of interaction force is similar to Coulomb’s law, but the force is inversely the distance of defects instead of the square of the distance in Coulomb’s law. Therefore, the present study contributes to the understanding of topological charge evolution dynamics and provides guidance for experiments to design in nematic LCs.

Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an {{rm{N}}}_{2}^{+}-implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Transmission of fractional topological charges via circular arrays of anisotropic fibers.

We demonstrate that in circular arrays of anisotropic fibers at certain distribution of anisotropy directors robust transmission of optical fields with half-integer topological charges is possible. We show that this is possible because the supermodes of such arrays may contain in their circularly polarized components half-integer topological charges of opposite values. We also study the structure of singularities in these supermodes.

High-order topological charges measurement of LG vortex beams with a modified Mach–Zehnder interferometer

We present a new method to measure the high-order topological charges (TCs) of Laguerre–Gaussian (LG) vortex beams by using a modified Mach–Zehnder interferometer. Counting the number of interference bright fringes between the LG beam and its conjugate beam determines integer and half-integer TCs through half of the bright fringe number. The proposed method can measure the order of the integer TC up to 90, which is higher than that achieved by previous methods. This technique opens up new applications for LG vortex beams.

Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges

Orbital angular momentum associated with the helical phase-front of optical beams provides an unbounded “space” for both classical and quantum communications. Among the different approaches to generate and manipulate orbital angular momentum states of light, coupling between spin and orbital angular momentum allows a faster manipulation of orbital angular momentum states because it depends on manipulating the polarisation state of light, which is simpler and generally faster than manipulating conventional orbital angular momentum generators. In this work, we design and fabricate an ultra-thin spin-to-orbital angular momentum converter, based on plasmonic nano-antennas and operating in the visible wavelength range that is capable of converting spin to an arbitrary value of orbital angular momentum ℓ. The nano-antennas are arranged in an array with a well-defined geometry in the transverse plane of the beam, possessing a specific integer or half-integer topological charge q. When a circularly polarised light beam traverses this metasurface, the output beam polarisation switches handedness and the orbital angular momentum changes in value by ℓ=±2qℏ per photon. We experimentally demonstrate ℓ values ranging from ±1 to ±25 with conversion efficiencies of 8.6% ± 0.4%. Our ultra-thin devices are integratable and thus suitable for applications in quantum communications, quantum computations, and nano-scale sensing.

Handedness control in a 2-μm optical vortex parametric oscillator

We present the first handedness control of an optical vortex output from a vortex-pumped optical parametric oscillator. The handedness of the optical vortex was identical to that of the pump vortex beam. Over 2 mJ, 2-μm optical vortex with a topological charge of ± 1 was achieved. We found that the handedness of a fractional vortex with a half integer topological charge can also be selectively controlled.

Optical vortex pumped mid-infrared optical parametric oscillator

The first demonstration of a mid-infrared optical parametric oscillator pumped by 1-μm optical vortex pulses is presented. A 0.5-mJ 2-μm fractional vortex pulse having half-integer topological charge is generated. Using this system, 0.24-mJ vortex pulses with a topological charge of 1 can be created. The topological charges of the mid-infrared vortex pulses are observed by an interferometric technique in combination with second-harmonic frequency conversion.

SPIN CHAIN SIMULATIONS WITH A MERON CLUSTER ALGORITHM

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is powerful enough to provide precise results for the model with a θ-term — it is therefore one of the rare examples, where a system with a complex action can be solved numerically. In particular we measure the correlation length, as well as the topological and magnetic susceptibility. We discuss the algorithmic efficiency in view of the critical slowing down. Due to the excellent performance that we observe, it is strongly motivated to work on new applications of meron cluster algorithms in higher dimensions.