Topological Charge Number Research Articles

Dielectric metasurfaces enabling twisted light generation/detection/(de)multiplexing for data information transfer.

We propose, design, fabricate and demonstrate nanophotonic all-dielectric metasurfaces enabling the generation, detection and (de)multiplexing of twisted light having helical phase structure and carrying orbital angular momentum (OAM). The designed metasurfaces are based on dielectric elliptical resonators on standard silicon-on-insulator (SOI) platform. One can achieve full-phase control of 0-2π and flexible amplitude adjustment by properly changing the geometric dimensions (long axis, short axis) and orientation of dielectric elliptical resonator based on the Mie resonance effect. Using the designed and fabricated all-dielectric metasurfaces, we demonstrate the generation and detection of OAM beams with topological charge number from l = -4 to 4. The crosstalk matrix of generated OAM beams is also characterized showing -16 dB crosstalk. We further demonstrate the (de)multiplexing of two OAM beams (OAM+1 & OAM+4 or OAM+2 & OAM+3) each carrying a binary image ("A" & "B" or "HUST" & "WNLO"). The obtained results show error-free data information transfer with favorable performance. The presented alternative approach of all-dielectric metasurfaces shows distinct features of easy fabrication process and easy chip-scale integration facilitating ultrathin optical applications. The demonstrations may open a door to find more interesting applications in all-dielectric metasurfaces enabled spatial light manipulation and optical communications and interconnects.

Direct Measurement of the Topological Charge in Elliptical Beams Using Diffraction by a Triangular Aperture

We introduce a simple method to characterize the topological charge associated with the orbital angular momentum of a m-order elliptic light beam. This method consists in the observation of the far field pattern of the beam carrying orbital angular momentum, diffracted from a triangular aperture. We show numerically and experimentally, for Mathieu, Ince–Gaussian, and vortex Hermite–Gaussian beams, that only isosceles triangular apertures allow us to determine in a precise and direct way, the magnitude m of the order and the number and sign of unitary topological charges of isolated vortices inside the core of these beams.

Transmission characteristics of Bessel–Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel–Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

Theoretical Analysis of a 750-nm Bandwidth Hollow-Core Ring Photonic Crystal Fiber With a Graded Structure for Transporting 38 Orbital Angular Momentum Modes

In this paper, a novel hollow-core ring photonic crystal fiber (HR-PCF) is proposed based on As2S3. It supports the transmission of up to 38 orbital angular momentum (OAM) modes. It is composed of a concentric ring cladding of air holes gradually increasing in diameter. In addition, the center also has a large circular air hole. A numerical simulation is accomplished using the finite-element method. Different geometrical parameters of the proposed HR-PCF include the number of air hole rings in the cladding and the background material. These parameters are varied to determine the optimal structure. The properties of the synthesized OAM vector modes are simulated and analyzed systematically and theoretically. Through the simulation of different parameters, we show that the optical fiber structure based on a three-ring cladding and As2S3 material can support 38 OAM modes. This configuration also has better eigenmode characteristics, such as the effective refractive index difference between vector modes with the same topological charge number. This difference can exceed 10−4, preventing these modes from coupling to linear polarization modes. In addition, the vector mode dispersion curve becomes smoother with increasing wavelength, and the confinement loss remains low, ranging from 10−10–10−9dB/m. Moreover, we also discuss effective mode area and nonlinear coefficients and their applications. We also investigated that various effects on the dispersions by details of the proposed HR-PCF, such as air hole spacing between adjacent rings and the diameter of the center circular air hole. This system offers some promising applications for short-distance, high-volume communications due to the increased number of OAM transfer modes.

Topological charge number multiplexing for JTC multiple-image encryption

We propose a method of topological charge number multiplexing based on the JTC encryption system to achieve multiple-image encryption. Using this method, multi-image can be encrypted into single ciphertext, and the original images can be recovered according to the authority level. The number of encrypted images is increased, moreover, the quality of decrypted images is improved. Results of computer simulation and initial experiment identify the validity of our proposed method.

Propagation and spatiotemporal coupling characteristics of ultra-short Gaussian vortex pulse

Based on Collins diffraction integral formula, the propagation equation of ultra-short Gaussian vortex pulse beam has been derived. Using the equation, the intensity distribution variations of vortex pulse in the propagation process are calculated. Specially, the spatiotemporal coupling characteristics of ultra-short vortex beams are discussed in detail. The results show that some key parameters, such as transverse distance, transmission distance, pulse width and topological charge number will influence the spatiotemporal coupling characteristics significantly. With the increasing of transverse distance, the waveforms of the pulses distort obviously. And when transmission distance is far than 50 mm, the distribution curve of transverse intensity gradually changes into a Gaussian type. In addition, initial pulse width will affect the distribution of light field, however, when initial pulse width is larger than 3 fs, the spatiotemporal coupling effect will be insignificant. Topological charge number does not affect the time delay characteristics, since with the increasing of topological charge number, the waveform of the pulse distorts gradually but the time delay does not occur.

Probability density performance of Laguerre-Gaussian beams propagating in non-Kolmogorov atmospheric turbulence

Based on the geometrical optics approximation, the analytical expressions of the mode probability density (MPD) and crosstalk probability density (CPD) for a Laguerre-Gaussian (LG) beam propagating through atmospheric turbulence along a horizontal path are derived. Through analytical derivation and numerical simulation, the propagation properties of a single LG beam have been studied in detail. The results of LG beams affected by atmospheric turbulence show that the MPD increases with the smaller topological charge number, lower radial mode number, appropriate waist radius, shorter propagation distance, weaker refractive index structure parameter, and the value much closer to three of non-Kolmogorov turbulence parameter. This investigation is expected to provide useful guidance for study of vortex beams propagating in free-space optical communication.

Characterization method of unusual second-order-harmonic generation based on vortex transformation

When a few-cycle laser beam nonresonantly propagates through an inversion-symmetric medium, beyond the usual odd-order harmonics in the transmission spectra, a well-defined spectral peak at twice the incident laser central frequency is disclosed [T. Tritschler et al., Phys. Rev. Lett. 90, 217404 (2003)]. Beyond the characterization method via the rf measurement of its carrier-envelope phase dependence, here a more direct mode of characterization is proposed by means of vortex transformation where a few-cycle vortex laser is adopted instead: One can easily clarify its origin as an usual third-order harmonic that appears to be a second-order harmonic, based on the criteria that the topological charge number of harmonics is directly proportional to its harmonic order.

Near-field characteristics of highly non-paraxial subwavelength optical fields with hybrid states of polarization**Project supported by the Zhejiang Provincial Natural Science Foundation, China (Grant Nos. LZ17A040001 and LY16A040014), the National Natural Science Foundation of China (Grant Nos. 11574271 and 11574272), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the Science Research Foundation of Zhejiang Sci-Tech

The vectorial structure of an optical field with hybrid states of polarization (SoP) in the near-field is studied by using the angular spectrum method of an electromagnetic beam. Physical images of the longitudinal components of evanescent waves are illustrated and compared with those of the transverse components from the vectorial structure. Our results indicate that the relative weight integrated over the transverse plane of the evanescent wave depends strongly on the number of the polarization topological charges. The shapes of the intensity profiles of the longitudinal components are different from those of the transverse components, and it can be manipulated by changing the initial SoP of the field cross-section. The longitudinal component of evanescent wave dominates the near-field region. In addition, it also leads to three-dimensional shape variations of the optical field and the optical spin angular momentum flux density distributions.

Effect of pump depletion and cross-focusing on twisted terahertz radiation generation

In this paper, the pump depletion and cross-focusing effects on the generation of twisted terahertz radiation are investigated. Based on the beating of two Laguerre-Gaussian lasers in a radial plasma channel, a twisted terahertz radiation can be produced. In the presence of pump depletion, the lasers power is consumed. So, the ponderomotive force nonlinearity decreases and the output terahertz field approaches to a saturation value. Under competition between the diffraction and nonlinearity effects, the amplitude of laser beam width oscillation grows. When the incident laser beams have non-similar topological charge numbers, the normalized generated terahertz amplitude is low and the pump depletion effect on the laser beam width evolution is ignorable.

Detection optical vortex topological charges with monocyclic multistage intensity distribution

Generation and application of the vortex beams are part of the hot topics in the optical field. In connection with the limited detection range of topological charge, we introduce a novel monocyclic multistage intensity distribution, which is generated by the coaxial superposition of two vortex beams with different topological charge numbers which have the same radius of ring in the focal plane of fraunhofer diffraction. This novel intensity distribution which is achieved by computer generated hologram is a new application of sidelobe-modulated optical vortices. The detection range of topological charge is expanded to 128 by two detection constants consisting of segments and radius in the monocyclic multistage intensity distribution method. We study the generation and distribution characteristics of monocyclic multistage intensity distribution in the focal plane of fraunhofer diffraction theoretically and experimentally to generate the qualified monocyclic multistage intensity distribution using a spatial light modulator. Excellent agreement between theoretical and experimental results is observed. The study indicates that two orbital angular momenta of vortex beams can be accurately determined by the segments and radius determined in the monocyclic multistage intensity distribution method. The method is immune to harassments from alignment and phase matching between the beams and optical elements, and has a large detection range, which is enlarged one order of magnitude compared with the previous way of detecting topological charges with sidelobe-modulated optical vortices. Our method provides a more large detection range of topological charge, which enables the vortex beams as the information carriers to carry more data in communication. Therefore, this method possesses research potential and applicability in future free-space optical communication.

Three-sublattice skyrmion crystal in the antiferromagnetic triangular lattice

The frustrated classical antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions on the triangular lattice is studied under a magnetic field by means of semiclassical calculations and large-scale Monte Carlo simulations. We show that even a small DM interaction induces the formation of an Antiferromagnetic Skyrmion crystal (AF-SkX) state. Unlike what is observed in ferromagnetic materials, we show that the AF-SkX state consists of three interpenetrating Skyrmion crystals (one by sublattice), and most importantly, the AF-SkX state seems to survive in the limit of zero temperature. To characterize the phase diagram we compute the average of the topological order parameter which can be associated to the number of topological charges or Skyrmions. As the magnetic field increases this parameter presents a clear jump, indicating a discontinuous transition from a spiral phase into the AF-SkX phase, where multiple Bragg peaks coexist in the spin structure factor. For higher fields, a second (probably continuous) transition occurs into a featureless paramagnetic phase.

Propagation of sharply autofocused ring Airy Gaussian vortex beams.

Controlling the focal length and the intensity of the optical focus in the media is an important task. Here we investigate the propagation properties of the sharply autofocused ring Airy Gaussian vortex beams numerically and some numerical experiments are performed. We introduce the distribution factor b into the initial beams, and discuss the influences for the beams. With controlling the factor b, the beams that tend to a ring Airy vortex beam with the smaller value, or a hollow Gaussian vortex beam with the larger one. By a choice of initial launch condition, we find that the number of topological charge of the incident beams, as well as its size, greatly affect the focal intensity and the focal length of the autofocused ring Airy Gaussian vortex beams. Furthermore, we show that the off-axis autofocused ring Airy Gaussian beams with vortex pairs can be implemented.

Characterizing the polarization and cross-polarization of electromagnetic vortex pulses in the space-time and space-frequency domain.

The dynamics of the degree of polarization and the degree of cross-polarization for electromagnetic pulsed vortex beams in dispersive media are explored both in the space-time and space-frequency domains. It is shown that the impacts, arising from the second-order dispersion coefficient and the temporal coherence length, on the variations of the temporal degree of polarization are distinctly different from those on the spectral degree of polarization. Besides, we also suggest a method to access the measurement of the orbital angular momentum of pulsed vortex beams through the mapping relationship between the distribution of the temporal degree of cross-polarization and the number of topological charge.

Generation of vortex beams by the four-step phase plates

The generation and application of the vortex beams are part of the hot topics in the optical field. In this paper, the phase structure of the four-step phase plates, analyzed by Fourier series expansion method, is composed of a series of spiral phase plates. When the phase plate is directly irradiated by linearly polarized light, multi-order diffraction waves with different topological charge numbers are generated. Unlike vortex waves, the intensity distribution of the multi-order diffraction has a deviation from the axial symmetry due to the interference with each other. On this basis, a new scheme is proposed to generate vortex beams by the four-step phase plates. With the help of Mach-Zehnder interferometer, the diffraction waves generated by two pieces of the four-step phase plates overlap each other. By adjusting the phase difference of the Mach-Zehnder interferometer, some orders of diffraction waves generate destructive interference while the others generate constructive interference. Thus the linear polarized light can be converted into vortex beams. The diffraction intensity and angular momentum distributions of the four-step phase plates with different cycle numbers are numerically simulated and compared with the spiral phase plates, we can provethat the vortex beams can be obtained by simple four-step phase plates which are the same as those obtained by spiral phase plates. In addition, the four-step phase plates with a small cycle number can generate vortex beams with a large topological charge number and the fabrication difficulty of the phase plates is reduced.

Evaluating the effectiveness of correlation digital speckle photography method for non-destructive testing of rough surfaces

The work is devoted to the investigation of the process of reflection of laser beams from rough surfaces with different degrees of roughness. Based on the results of numerical experiments the applicability of the method of correlation analysis of speckle-structures for non-destructive inspection of surfaces with different parameters of roughness was evaluated. The optimal ratios between the parameters of the rough surfaces and parameters of the optical system, which provide the best efficiency of the method, were determined. It was established that in case of the increase of the number of topological charges the sensitivity of the optical system to changes of parameters of surface roughness increases.

Experimental study on multiple-ring vortex beams

The generation, propagation and application of vortex beams have been hot research topics in recent years. In this paper we introduce the novel multiple-ring vortex beams, including double-ring vortex beams and triple-ring vortex beams, which are generated by the coaxial superposition of multiple Laguerre-Gaussian vortex beams with different topological charge numbers and different waist parameters, and their intensity distribution is of multiple-ring. We study the generation and distribution characteristics of multiple-ring vortex beams theoretically, obtain the computer generated hologram of multiple-ring vortex beams based on conjugate symmetric extension Fourier computer generated holography, and experimentally generate quality multiple-ring vortex beams using a spatial light modulator. Excellent agreement between theoretical and experimental results is observed. The study indicates that each ring of multiple-ring vortex beams carries different orbital angular momentum, and the spatial distribution is independent. The novel multiple-ring vortex beams provide more controllable parameters and more diverse structure distributions, which enable their applications in the fields of micro-manipulation as optical tweezers or optical spanner. Furthermore, they also have potential applications as available encoding tools in optical communication.

Study on the spatial coherence of vortex Gaussian beams passed atmospheric turbulence

In this paper, the spectral degree of coherence formula was derived by using the generalized Huygens–Fresnel principle and the method of Rytov phase structure function quadratic approximation. The spatial coherence of vortex Gaussian beams passed atmospheric turbulence was studied. It showed that the spatial coherence was mainly affected by the coherence of light source, the number of topological charges and the transmission distance. The distance of transmission was farther, the spatial coherence of beam was better. The number of topological charges were more, the spatial coherence of beam was better. In a certain transmission distance, the coherence of light source was better, the spatial coherence of beam was worse. In addition, there were coherent vortexes which spectral degree of coherence was zero after the partially coherent vortex beams getting through atmospheric turbulence transmission.

Optical vortices induced in nonlinear multilevel atomic vapors

In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing effect. We find that the number of beads and topological charge of the incident beam, as well as its size, greatly affect the formation and evolution of vortices. To determine the number of induced vortices and the corresponding rotation direction, we give common rules associated with the initial conditions coming from various incident beams.

Azimuthal vortex clusters in Bose-Einstein condensates

We describe, analytically and numerically, topologically nontrivial stationary states with azimuthal modulation of density in a repulsive Bose-Einstein condensate (BEC) confined in a harmonic trap. We show that, depending on the number of density peaks and total topological charge, these states can have a sophisticated phase texture associated with a vortex cluster. For a given topological charge, the form of density distribution and the structure of phase singularities are uniquely linked, thus simultaneous phase and density modulation enforces the formation of a vortex cluster both in rotating and in nonrotating BEC clouds.