Topological Charge Number Research Articles

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 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 orbital angular momentum remains a challenge for most existing technologies. In this paper, a new method for generating coherent high-power THz vortices with tunable orbital angular momentum 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.

Eliminating Skyrmion Hall Effect in Ferromagnetic Skyrmions.

Skyrmion Hall effect (SkHE) remains an obstacle for the application of magnetic skyrmions. While methods have been established to cancel or compensate SkHE in artificial antiferromagnets and ferrimagnets, eliminating intrinsic SkHE in ferromagnets is still a big challenge. Here, we propose a strategy to eliminate SkHE by intercalating nonmagnetic elements into van der Waals bilayer ferromagnets featuring in-plane ferromagnetism. The in-plane magnetism, along with a delicate balance among exchange interactions, Dzyaloshinskii-Moriya interactions (DMI), and magnetocrystalline anisotropy, creates interlayer bimerons/quadmerons, whose polarity can be controlled by DMI. Opposite DMI in the upper and lower layers results in opposite polarity and topological charge number Q-locking of topological spin texture, therefore, eliminating the SkHE. By intercalating Sr (Ba) in bilayer VSe2, we identify ten topological magnetic structures with zero topological charge number. Furthermore, we present a phase diagram illustrating diverse magnetic configurations achievable within the bimagnetic atomic layer, offering valuable guidance for future investigations.

Thermodynamic topology of quantum corrected AdS-Reissner-Nordstrom black holes in Kiselev spacetime

In this paper, we consider the intricate thermodynamic topology of quantum-corrected Anti-de Sitter-Reissner-Nordstrm (AdS-RN) black holes within the framework of Kiselev spacetime. By employing the generalized off-shell Helmholtz free energy approach, we meticulously compute the thermodynamic topology of these selected black holes. Furthermore, we establish their topological classifications. Our findings reveal that quantum correction terms influence the topological charges of black holes in Kiselev spacetime, leading to novel insights into topological classifications. Our research findings elucidate that, in contrast to the scenario in which ω = 0 and a = 0.7 with total topological charge W = 0 and ω = –4/3 with total topological charge W = –1, in other cases, the total topological charge for the black hole under consideration predominantly stabilizes at +1. This stabilization occurs with the significant influence of the parameters a, c, and ω on the number of topological charges. Specifically, when ω assumes the values of ω = –1/3, ω = –2/3, and ω = –1, the total topological charge will consistently be W = +1.

Multi‐Concentric Generalized Perfect Vortex Beams by Hybrid Phase Metasurfaces

AbstractMetasurface‐based vortex beams are expected to overcome the current communication challenges of massive data and limited bandwidth by their theoretical infinite and mutually orthogonal states. However, limited by the spatial extension of array vortices, only finite orbital angular momentum (OAM) eigenstates are available, of which the expansion will boost the bandwidth toward an inexhaustible stage. In this manuscript, multi‐concentric generalized perfect vortex beams (G‐PVBs) are experimentally generated by the fabricated hybrid phase metasurfaces integrating generalized focusing phases and circular domain function into vortex phases. Diverse vortex shapes and helical lobes within beam patterns and spiral interferograms are both arranged in a non‐overlapping concentric manner instead of spatial arrays, respectively, breaking the limitation of symmetric shape while avoiding inter‐modal cross‐talk. The vortex shape, topological charge and vortex number are decoupled mutually in orthogonal polarization states, realizing both space and polarization multiplexing. Furthermore, shaped into anomalous profiles with asymmetric states of polarization, multi‐concentric vector G‐PVBs are experimentally generated to transmit parallelly stable order information with high robustness in turbulence environments. The proposed multi‐concentric G‐PVBs simultaneously expanded the novel vortex dimension by anomalous shapes and information channels of multi‐concentric OAM modes, providing potential application in high‐capacity vortex optical communication and information encryption.

A distributed reception based method for identifying vortex beams

After the vortex beam is transmitted in the space laser communication scene for hundreds of kilometers, the spot diameter will expand to several meters or even tens of meters, and the existing detection methods that require receiving the whole spot are no longer applicable. In order to address this problem, a distributed detection scheme is proposed in this paper for demultiplexing two L-G beams. We choose two specific points on the light spot to receive two optical signals. Then the two optical signals are interfered with a designed optical fiber path which use the cross-coupling of the coupler. Then the demultiplexing is achieved according to the interference results at two ports. This scheme is suitable for demultiplexing intensity-modulated optical signals. The feasibility of this scheme is theoretically analyzed, and the demultiplexing of L-G beams with multiple combinations of topological charge numbers is realized.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.

Study on the Generation of 1.9 μm Mode Superposition Conversion Laser by Double-End Off-Axis Pumping

In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, l1=l2, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, l1=−l2, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition.

Breaking the symmetric spiral spectrum distribution of a Laguerre-Gaussian beam propagating in moderate-to-strong isotropic atmospheric turbulence.

We demonstrate that the spiral spectrum (also known as orbital angular momentum spectrum) of a Laguerre-Gaussian (LG) beam with topological charge (TC) l is asymmetrically broadened propagating through moderate-to-strong atmospheric turbulence, even the statistics of turbulence is isotropic. This phenomenon is quite different from that predicted in weak turbulence where the spiral spectrum of a disturbed LG beam is symmetric with respect to its TC number l. An explicit analytical expression of the spiral spectrum of the LG beam with l = 1 is derived based on the extend Huygens-Fresnel integral and quadratic approximation, which is used to illustrate the transition scenarios of the spiral spectrum from symmetry to asymmetry in weak-to-strong turbulence. The physical mechanism for the asymmetric spiral spectrum in moderate-to-strong turbulence is thoroughly discussed. Our results are confirmed by the multi-phase screen numerical simulations and are consistent with the experimental results reported in Phys. Rev. A105, 053513 (2022)10.1103/PhysRevA.105.053513 and Opt. Lett.38, 4062 (2013)10.1364/OL.38.004062.

Multiparameter multiplexing applied in an OAM holography via moiré metalens phase encoding

Orbital angular momentum(OAM) holography has attracted wide attention from researchers in high-security encryption field. In this manuscript, the moiré phase modulation is introduced in multiplexing holography to achieve information encryption. The modulated parameters of the moiré metalens phase(MMP) plate, namely the topological charge (TC) number, the moiré constant, the azimuthal displacement factor, the segment modes and the displacement amount on the structure of the moiré phase plate can be used as encoding and decoding keys in OAM holography. The feasibility of the proposed scheme with the above parameters is verified by numerical simulations and experiments. The advantage is that this technique is of higher design freedom and security compared to the existed orbital angular momentum multiplexed holography techniques. The flexibility of the MMP plate promotes the encrypted channel diversity and shows a new perspective.

Tight Focusing of Circular Partially Coherent Radially Polarized Circular Airy Vortex Beam

The tight focusing properties of circular partially coherent radially polarized circular Airy vortex beams (CPCRPCAVBs) are theoretically studied in this paper. After deriving the cross-spectral density matrix of CPCRPCAVBs in the focal region of a high-NA objective, numerical calculations were performed to indicate the influence of the topological charge of the vortex phase on intensity distribution, degree of coherence and degree of polarization of the tightly focused beam. An intensity profile along the propagation axis shows that a super-length optical needle (~15 λ) can be obtained with a topological charge of 1, and a super-length dark channel (~15 λ) is observed with a topological charge of 2 or 3. In the focal plane, the rise in the number of topological charge does not distort the shapes of the coherence distribution pattern and the polarization distribution pattern, but enlarges their sizes.

Single-celled metasurface for labeled vortex beam generator

Vortex light is a unique beam characterized by a spiral phase as it propagates. A fundamental parameter of vortex light is the topological charge, which determines the amount of angular momentum and plays a crucial role in tailoring its behavior. However, conventional measurement methods for determining the topological charge, such as those based on interference and phase modulation, tend to be intricate and complex. In this regard, a labeled vortex beam generator is proposed, composed of a metasurface with a single-celled configuration. When the metasurface is illuminated by light of the designed wavelength, the outgoing light exhibits a vortex structure. Furthermore, the topological charge numbers can be directly observed with distinct labeled patterns when the metasurface is placed in an orthogonal-polarized optical path. With advantages such as ultra-compactness, high robustness, and exceptional precision, the proposed metasurface exhibits significant potential for applications in optical communication, light manipulation, optical sensing, etc.

Terahertz quasi-perfect vortex beam with integer-order and fractional-order generated by a spiral spherical harmonic axicon

Abstract We have proposed a new method to generate terahertz perfect vortex beam with integer-order and fractional-order. A new optical diffractive element which is composed of the phase combination of a spherical harmonic axicon and a spiral phase plate is designed, and called spiral spherical harmonic axicon. A terahertz Gaussian beam passes through the spiral spherical harmonic axicon to generate a terahertz vortex beam. When only increasing the number of topological charges carried by spiral spherical harmonic axicon, the ring radius of terahertz vortex beam increases slightly, so it is a terahertz quasi-perfect vortex beam. Importantly, the terahertz quasi-perfect vortex beam can carry not only integer-order but also fractional-order topological charges. This is the first time that vortex beam and quasi-perfect vortex beam with fractional-order has been successfully realized in terahertz domain and experiment.

Focusing characteristics of chirped phase-modulated Lorentz-Gaussian vortex beams.

This work presents a thorough investigation of the focusing characteristic of chirped phase modulated Lorentz-Gaussian (LG) vortex beams based on the vector diffraction theory. The results show that changing the first-order chirp parameter c 1 can effectively adjust the size of the focusing spot, and the distance between focusing spots can also be controlled. The second-order chirp parameter c 2 can control the up-and-down movement of the optical chain in the focusing region. Simultaneously, the length of the focusing spots can be accurately changed by modulating the waist width ω. In addition, the influence of integer topological charge number m on controlling the size of an optical dark trap is discussed in detail. And fractional topological charge number m can control the rotation of focus peak and the number of optical dark traps. Potential applications of these findings include optical shape and capture, optical particle transmission, and contemporary medical care.

Dynamics of skyrmion bags driven by spin wave

Skyrmion bags are spin textures with arbitrary integer topological charge numbers, holding promise for utilization in high-density racetrack memory devices. In this study, we investigate the dynamics of skyrmion bags driven by propagating spin waves in a magnetic nanostrip, employing micromagnetic simulations. Our findings reveal that propagating spin waves can induce a stable movement of skyrmion bags, irrespective of their topological charge numbers. The amplitude and frequency of the spin wave, alongside material parameters such as damping constant and saturation magnetization, exhibit discernible effects on the behavior of skyrmion bags. These outcomes have the potential to advance the development of racetrack memory based on skyrmion bags.

Polarization characteristics of partially coherent radially and azimuthally polarized beams with vortex phase propagating through atmospheric turbulence

Analytical formulas for the normalized spectral Stokes parameters of the partially coherent radially and azimuthally polarized beams with vortex phase (i.e., PCRPV and PCAPV beams) propagating through the turbulent atmosphere are derived. The polarization properties of PCRPV and PCAPV beams in atmospheric turbulence have been studied in detail. Our findings show that different correlation lengths induce nonuniform distribution to degree of polarization (DOP) and the normalized spectral Stokes parameters. And different correlation lengths also cause the polarization singularity splitting. Besides, we find also that the vortex phase will lead to the rotation of distributions of orientation angles and the normalized spectral Stokes parameters of PCRPV and PCAPV beams in turbulence, and the rotation degree will become obvious with increasing topological charge number. It can be found also that larger topological charge number can reduce the speed of polarization singularities destroyed by atmospheric turbulence, meaning that PCRPV and PCAPV beams with a larger topological charge has a stronger ability to resist atmospheric turbulence. Our studies could be important for free-space optical communications and polarization lidar system.

Experimental study of the transport characteristics of fractional-order vortex beams in a turbulent atmosphere simulator

Fractional vortex beams have attracted increasing attention due to their complex yet intriguing physical properties, such as radial notch intensity distribution and higher degrees of modulation in orbital angular momentum. In this study, we experimentally investigated and compared the beam spread and beam wander characteristics of fractional-order vortex beams with those of integer-order vortex beams after passing through a turbulent atmosphere simulator with varying turbulence intensities. Our results revealed that the beam spread of both fractional-order and integer-order vortex beams increased in a stepwise manner with the topological charge number, indicating that a larger topological charge number resulted in more severe beam spread. Interestingly, we observed that the beam radius of fractional-order vortex beams between two adjacent integer orders initially grew slowly and then rapidly before finally stabilizing into a curvilinear growth trend. This is in contrast to the linear growth trend exhibited by the beam radius of integer-order vortex beams. Furthermore, we found that the growth of the beam radius of half-integer-order vortex beams followed the linear growth trend of the beam radius of integer-order vortex beams. When the integer part of the topological charge was fixed, we observed that stronger turbulence resulted in more severe beam wander for both integer-order and fractional-order vortex beams, with the variance of the center-of-mass drift following the same growth curve. However, when the turbulence intensity is constant, both integer-order and fractional-order vortex beams exhibit a weaker beam wander effect with increasing topological charge. Our findings may provide valuable insights for applications such as optical communication and optical measurement using fractional-order vortex beams.

Optical image conversion and encryption based on structured light illumination and a diffractive neural network.

In this paper, an optical image encryption method is proposed based on structured light illumination and a diffractive neural network (DNN), which can realize conversion between different images. With the use of the structured phase mask (SPM) in the iterative phase retrieval algorithm, a plaintext image is encoded into a DNN composed of multiple phase-only masks (POMs) and ciphertext. It is worth noting that ciphertext is a visible image such that the conversion of one image to another is achieved, leading to high concealment of the proposed optical image encryption method. In addition, the wavelength of the illuminating light, all Fresnel diffraction distances, the optical parameters of the adopted SPM such as focal length and topological charge number, as well as all POMs in the DNN are all considered as security keys in the decryption process, contributing to a large key space and high level of security. Numerical simulations are performed to demonstrate the feasibility of the proposed method, and simulation results show that it exhibits high feasibility and safety as well as strong robustness.

Dynamic control of hybrid grafted perfect vector vortex beams

Perfect vector vortex beams (PVVBs) have attracted considerable interest due to their peculiar optical features. PVVBs are typically generated through the superposition of perfect vortex beams, which suffer from the limited number of topological charges (TCs). Furthermore, dynamic control of PVVBs is desirable and has not been reported. We propose and experimentally demonstrate hybrid grafted perfect vector vortex beams (GPVVBs) and their dynamic control. Hybrid GPVVBs are generated through the superposition of grafted perfect vortex beams with a multifunctional metasurface. The generated hybrid GPVVBs possess spatially variant rates of polarization change due to the involvement of more TCs. Each hybrid GPVVB includes different GPVVBs in the same beam, adding more design flexibility. Moreover, these beams are dynamically controlled with a rotating half waveplate. The generated dynamic GPVVBs may find applications in the fields where dynamic control is in high demand, including optical encryption, dense data communication, and multiple particle manipulation.

Focusing pattern of the Laguerre-Gaussian beam with polarization mixing helical-conical phase modulation.

This paper focuses on the focusing pattern of the Laguerre-Gaussian (LG) beam with polarization mixing helical-conical phase modulation, which is based on the vector diffraction theory. The results show that the topological charge number l can sensitively control the intensity of the intensity peaks. The focal spot will split along the optical axis under different polarization parameters P. When l=1, the spot position and the peak intensity can be modulated by changing the polarization parameter P. The truncation parameter β makes the focusing spot form an optical trap. By adjusting the eccentricity parameter K, the opening direction of the optical trap can be well controlled. These results may be helpful in optical applications such as optical manipulation, optical focusing, and optical information transmission.

Ideal unconventional charge-2 Dirac fermions in an ultralightweight chiral crystal

When topology meets chirality, it is of great interest to search for possible topological properties in chiral crystals, thereby achieving the effect of making $1+1$ greater than 2. Here, we accomplish a complete list of topological charge-2 (C-2) Dirac fermions based on 65 S\"ohncke space groups. Such emergent fermions occurring in chiral crystals enjoy a higher topological charge number and exhibit more unique characteristics compared to C-0 cases, including multiple Fermi arcs extending to most of the Brillouin zone. For material realization, we propose that an ultralightweight chiral crystal ${\mathrm{N}}_{4}\mathrm{Cl}$ is a high-quality C-2 Dirac semimetal, where the seductive nodal points reside at the Fermi level and exhibit a large linear energy range to overcome the interruption of irrelevant bands. More interestingly, the doubly degenerate Landau levels are described by a Kramers-like degeneracy in such a C-2 Dirac fermion, featuring a doubly degenerate zero mode. Furthermore, the topological phase transitions from Dirac to Weyl states of ${\mathrm{N}}_{4}\mathrm{Cl}$ can be manipulated by applying shear strains. These fascinating findings will certainly evoke continued exploration of unconventional Dirac semimetals, in turn leading to extensive application prospects and uncommon insights.