Value Of Topological Charge Research Articles

Measuring the topological charge and ellipticity of elliptic vortex

The intensities and phase profiles of the elliptic optics vortex beam both are determined by the topological charge (TC) and ellipticity. This paper presents an efficient and simple method for measuring the TC and ellipticity of elliptic vortex. By observing the diffraction patterns, the TC modulus and ellipticity can be probed with the suitable rectangular aperture, and the TC sign can be detected with the suitable right triangular aperture. The scheme works well even for high-order elliptic vortex with topological charge value as high as ± 18, and ellipticity range from 0.5 to 2 at least. Obviously, the measurement of TC and ellipticity have important research value for promoting the application of elliptical vortex.

Generation of perfect helical Mathieu vortex beams.

We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge (ℓ) but different kr (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

Simple, efficient and reliable characterization of Laguerre-Gaussian beams with non-zero radial indices in diffraction from an amplitude parabolic-line linear grating.

In this work, we report the characterization of a Laguerre-Gaussian (LG) beam with given values of topological charge (TC) and radial index in a simple, efficient, and robust experimental diffraction scheme. The beam diffracts from an amplitude parabolic-line linear grating and the resulting diffraction patterns at zero- and first-order reveals the values of the TC, l, and radial index p of the incident LG beam using a simple analysis. The zero-order diffraction pattern consists of p + 1 concentric intensity rings and the first-order diffraction pattern contains an (l + p + 1) by (p + 1) two-dimensional array of intensity spots. The experimental scheme is robust since it is not sensitive to the relative locations of the impinging beam axis and the grating center, and is efficient since most of the energy of the output beam is in the diffraction order of interest for LG beam characterization. The measurement is also simple since the intensity spots of the array are placed exactly over straight and parallel lines. Both experimental and simulation results are presented and are consistent with each other.

Experimental realization of scalar and vector perfect Laguerre–Gaussian beams

The generation of a perfect optical vortex (POV) has been an important area of research since the concept was introduced by Ostrovsky et al. [Opt. Lett. 38, 534 (2013)]. In this Letter, we provide the details of the experimental demonstration of a POV using perfect Laguerre–Gaussian beams via a phase-only spatial light modulator. The perfect beam properties, including radius, beam width, and ring thickness, are investigated in detail. We verify the vortex nature of the proposed perfect Laguerre–Gaussian beams including their topological charge value and sign. Finally, in addition to the scalar beams, we propose the vector perfect Laguerre–Gaussian beams both theoretically and experimentally and evaluate their perfect characteristics. The derived results clearly illustrate the perfect characteristics of such beams independent of the polarization state. The findings reported here can find significant applications in various fields including optical tweezers, optical imaging, and high capacity optical communications.

Laguerre-Gaussian optical sum-sideband generation via orbital angular momentum exchange

Laguerre-Gaussian optical sum-sideband generation via orbital angular momentum exchange has been studied analytically beyond the linearized approach. We obtain the analytical expression for the amplitudes of these signals within the semiclassical approximation. The pump power dependence of Laguerre-Gaussian sum-sideband generation is discussed, and we find that Laguerre-Gaussian sum-sideband generation can be remarkable even at low power through the satisfaction of matching conditions. The matching conditions for Laguerre-Gaussian sum-sideband generation in an optorotational system are discussed and summarized in detail, and the physical interpretation of matching conditions is discussed. The role of the topological charge value $l$ on the sum-sideband generation is studied, which exhibits a saturation effect for the peak value of the normalized amplitude and consequently limits further improvement of the Laguerre-Gaussian sum-sideband generation. Our results may find applications in Laguerre-Gaussian optical frequency comb and communications and provide a potential method for the determination of the orbital angular momentum of light fields with high topological charges.

Monolithic‐Integrated Multiplexed Devices Based on Metasurface‐Driven Guided Waves

AbstractThe appearance of metasurfaces has solved the difficult problems of bulkiness, the complexity of traditional optics, and arbitrary optical response controlling. However, most free‐space metasurfaces and existing integrated metadevices do not meet the criteria of full on‐chip integration toward low loss and high information transmission capacity. Here, by decorating silicon‐on‐insulator waveguides with metasurfaces, one can realize the arbitrary phase and intensity manipulation of guided waves. Four‐channel multiplexer is demonstrated with inherent advantages of low loss and independent transmission of electromagnetic waves in x and y directions. As proof‐of‐concept demonstrations, monolithic‐integrated multiplexed orbital angular momentum (OAM) and holographic generators are developed at 1550 nm to realize high information transmission capacity, low loss, and low crosstalk. Specifically, when the electromagnetic wave is incident from x, −x, y, and −y directions, four kinds of OAM mode with different topological charge values (−1, +1, +2, and −2), and four different holographic images of the letter “U,” “C,” “A,” and “S” can be obtained with the four‐channel multiplexed OAM generator and holographic display device, respectively. The design methods proposed here are expected to open a new perspective for future versatile utilization of driven guided waves to achieve numerous functionalities.

Bidirectional multi-mode microwave vortex beam generation enabled by spoof surface plasmon polaritons

The microwave spectrum has become more and more crowded, motivating the investigation of new techniques to increase the communication capacity. Vortex beams carrying orbital angular momentum (OAM) have the capability for providing an extra degree of freedom to increase the channel and capacity of the wireless communication system. In this Letter, we demonstrate an effective route to achieving efficient bidirectional multi-mode microwave circularly polarized vortex beam generation enabled by spoof surface plasmon polariton (spoof SPPs, SSPPs). According to the dispersion relation of the SSPP waveguide and the radiation principle for a leaky-wave antenna, multi-OAM-mode vortex beams with different topological charges can be generated by changing the operating frequency without changing the structure. Interestingly, the emitter simultaneously radiates the right-hand circularly polarized and the left-hand circularly polarized vortex beams with opposite topological charge values upward and downward, respectively. Simulation and experimental results show that this planar SSPP vortex emitter has the advantages of single-fed, bidirectional, multi-mode, and integration compatibility.

Measuring orbital angular momentum of vortex beams in optomechanics

Measuring the orbital angular momentum (OAM) of vortex beams, including the magnitude and the sign, has great application prospects due to its theoretically unbounded and orthogonal modes. Here, the sign-distinguishable OAM measurement in optomechanics is proposed, which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre-Gaussian (LG) rotational-cavity system. Compared with the traditional single LG rotational cavity, an asymmetric optomechanically induced transparency window can occur in our system. Meanwhile, the position of the resonance valley has a strong correlation with the magnitude and sign of OAM. This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM, which causes the spectral shift to be directional for different signs of OAM. Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics, and works well for high-order vortex beams with topological charge value ±45, which is a significant improvement for measuring OAM based on the cavity optomechanical system.

Vortex soliton solutions of a (3 + 1)-dimensional Gross–Pitaevskii equation with partially nonlocal distributed coefficients under a linear potential

A (3 + 1)-dimensional Gross–Pitaevskii equation with partially nonlocal distributed coefficients under a linear potential is followed with interest. The mapping procedure from the distributed-coefficient to the constant-coefficient equations is provided. Via the procedure with solution of constant-coefficient NLSE from the variational principle, an approximate vortex soliton solution is reported. With the increase of value for topological charge m, torus-shaped vortex soliton turns into ring vortex soliton, and central region of ring gradually enlarges. The layer of vortex solitons and their phase along the z-direction is related to the number of $$q+1$$ with the Hermite parameter q. The branch number of spiral phase structures for vortex solitons is related to the value of topological charge m. The stability test from the direct numerical simulation indicates that vortex solitons with $$m=1,2,3,\, q=0$$ are stable, otherwise, vortex solitons with other values of m, q are unstable.

Measuring the orbital angular momentum states of vortex beams with defocusing intensity

Optical vortex beams (VB) have been extensively applied in many fields for their unique features. In this paper, we explore the defocusing intensity of VB modulated by axial symmetry polarization. Combining appropriate polarization order of the modulator, we show that defocusing can result in a spiral structure of intensity distribution, of which the number of spiral arms is determined by the polarization order of the modulator, and the rotation direction of spiral arms depends on the topological charge (TC) of incident beams. The helical structure of defocusing intensity holds a small solid spot when the TC value of VB matches the polarization order number. Therefore, the magnitude of the tested TC can be inferred from the small solid spot distribution, and the sign of the TC can be determined by the rotation direction of the helical intensity. The peculiar phenomena exploited in this paper stimulate the new applications of VB in many fields.

Measuring the topological charge of terahertz vortex beams with a focal hyperbolic lens.

An efficient method is proposed to measure the topological charge (TC) of terahertz (THz) vortex beams with a focal hyperbolic (FH) lens at 0.1 THz. The FH lens is designed and fabricated by 3D printing. The diffraction fringes acquired in the focal plane of the FH lens can judge the number and sign of the TC. Furthermore, after the horizontal or vertical measurement curve is recorded by rotating the FH lens to a suitable angle, the TC value can then be simply and effectively identified. The TC value of the experiment measurement reaches 5. The experiment results are in excellent accord with the simulation.

Description of a multifocal arrangement of asymmetric Kummer-beam optical vortices

In this work, we derived an analytic expression for the optical field generated by an off-axis Gaussian beam diffracted by a Discretized Vortex-Producing Lens. With this system, a multifocal arrangement of asymmetric optical vortices is obtained whose topological charge values change with the position along the optical axis. This scheme allows both, obtaining a principal asymmetric vortex corresponding with the topological charge value of the phase mask, and other asymmetric vortices with charges different from the phase mask charge. With the analytical expression, the effects induced by the discretization and misalignment on the irradiance and phase of each vortex can be simultaneously studied. A signal-to-noise ratio expression is derived to verify if the noise of the multifocal system might affect the optical vortices of interest in a significant way: We found that noise is not a problem. In conclusion, a Discretized Vortex-Producing Lens can be used as a continuous Spiral Phase Plate. Finally, we explored the feasibility that the vortex phase could be employed as a displacement estimator.

Electric field-driven reconfigurable multistable topological defect patterns.

Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between pre-determined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilised by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed Atomic Force Measurement scribing method, where NLC configurations are monitored via polarised optical microscopy. We show numerically and experimentally that an "alphabet" of up to 18 unique line defect configurations can be stabilised in a 4x4 lattice of alternating s=±1 surface defects, which can be "rewired" multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely-spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned.

Topological Charge Detection Using Generalized Contour-Sum Method from Distorted Donut-Shaped Optical Vortex Beams: Experimental Comparison of Closed Path Determination Methods

A generalized contour-sum method has been proposed to measure the topological charge (TC) of an optical vortex (OV) beam using a Shack–Hartmann wavefront sensor (SH-WFS). Moreover, a recent study extended it to be workable for measuring an aberrated OV beam. However, when the OV beam suffers from severe distortion, the closed path for circulation calculation becomes crucial. In this paper, we evaluate the performance of five closed path determination methods, including watershed transformation, maximum average-intensity circle extraction, a combination of watershed transformation and maximum average-intensity circle extraction, and perfectly round circles assignation. In the experiments, we used a phase-only spatial light modulator to generate OV beams and aberrations, while an SH-WFS was used to measure the intensity profile and phase slopes. The results show that when determining the TC values of distorted donut-shaped OV beams, the watershed-transformed maximum average-intensity circle method performed the best, and the maximum average-intensity circle method and the watershed transformation method came second and third, while the worst was the perfect circles assignation method. The discussions that explain our experimental results are also given.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Variations of topological charge of vortex beam based on a diffraction plate with spiral transmission structures

The phenomenon of vortex beams passing through a diffraction plate with rotationally symmetric superposition of spiral pinholes array is investigated. The variations of the topological charges of vortex beams are theoretically analyzed, numerically simulated and experimentally observed. It proves that the obtained topological charge value (l) is a combination of that of incident beam (l0) and the number of the spiral structures (m). The relationship is l = Mm-l0, where M is an integer. With this study, we proved that spiral transmission structures can also achieve the variations of the topological charge of a vortex beam. And this method is simple and costless. With the advantages of this method, it might have important applications in optical communications and optical tweezers.

High-efficiency sorting and measurement of orbital angular momentum modes based on the March–Zehnder interferometer and complex phase gratings

With the recent exponential developments of high-speed optical communications, traditional optical communications systems are showing their limitations. Over the past decade, the orbital angular momentum (OAM) is attracting more and more research attention, due to its orthogonality between two OAM states, which supplies new degrees of freedom and can be used in fiber or free-space optical communication systems for increasing the communication capacity. Here, we propose a novel OAM de/multiplexing method based on the combination of the March–Zehnder interferometer (MZI) implanted pair of dove prisms (DP) (MZI-DP) and a complex phase gratings (CPG), which can be used to sort and detect multiple OAM modes simultaneously. The fundamental Gaussian beam illuminates the spatial light modulator (SLM) to produce the multiplexed Laguerre–Gaussian modes with different topological charges. The MZI-DP system can sort different OAM modes into odd and even values of topological charges. And then, the designed CPGs perform the concrete measurements of different sorted OAM modes. The propagating directions of different modes are arbitrarily steered by two CPGs in two MZI-DP outputting planes. With this designed system, we can simultaneously sort the OAM modes into odd and even values of topological charges, as well as performing the measurement of a large number of OAM modes without any overlapping between adjacent modes. Furthermore, we have simultaneously demultiplexed 50 different OAM modes and controlled their propagation directions successfully, which shows high-recognition rates and superior performances.

Theory of diffraction of vortex beams from 2D orthogonal periodic structures and Talbot self-healing under vortex beam illumination.

This work presents a detailed analytic approach to the diffraction of vortex beams from 2D orthogonal periodic structures. Using the presented formulation, the diffraction of vortex beams from 2D sinusoidal and Ronchi gratings is investigated. For these gratings, the Talbot self-healing effect under vortex beam illumination is examined. In the illumination of a 2D grating with a vortex beam, we refer the Talbot self-healing effect to the filling of the null area of the incident beam under propagation. We show that, for an incident vortex beam having odd value of topological charge, the generated Talbot self-images over the self-healing area are a 2D array of optical vortices, in which each of the individual self-images gets the form of an optical vortex with a topological charge of l=1 regardless of the topological charge of the incident beam. Both the Talbot self-healing effect and generation of the 2D array of optical vortices occur optimally between a definite interval of propagation distance. Using an intuitive approach based on the interference of the diffracted orders of the grating, we determine the self-healing interval. We show that a 2D array of optical vortices can be generated directly in the interference of eight copies of a vortex beam having proper lateral shifts and relative tilts. Easy tuning and energy preservation are two main advantages that the interference-based method has over the above-mentioned diffraction-based method for generating a 2D array of optical vortices. However, setup and implementation of the diffraction-based method are very simple. We believe that both the diffraction-based and interference-based methods for creating vortex beam arrays might find applications in optical tweezers, micromanipulations, and microfluidics.

Generation of a double-ring perfect optical vortex by the Fourier transform of azimuthally polarized Bessel beams.

The perfect optical vortex (POV), the ring size being independent of its topological charge, has found potential applications in optical tweezers and optical communications. In this Letter, we report a new kind of POV, termed as double-ring POV (DR-POV), whose diameters of the two rings are independent of topological charge. We theoretically demonstrate that such a vortex is the Fourier transform of an azimuthally polarized Bessel beam. Experimental results agree well with theoretical prediction. We further investigate the vortex nature of the DR-POV through an interferometric method, showing that the two rings of the vortex have the same topological charge value (magnitude and sign). The specular properties of the DR-POV may find application in optical tweezers, such as trapping and rotating of low-refractive-index particles in the dark region between the two rings.