Gaussian Vortex Research Articles

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

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

Propagation characteristics study of radially polarized Gaussian vortex beam in ocean turbulence

Based on the extended Huygens–Fresnel principle, a semi analytical expression of the radially polarized Gaussian vortex (RPGV) beam in ocean turbulence has been deduced. The influence of topological charge, propagation distance, laser wavelength, rate of dissipation of the mean-squared temperature χT, ratio of temperature or salinity contributions to the turbulence ω, rate of dissipation of kinetic energy per unit mass of fluid ε on the propagation characteristics are discussed in detail. The results show that the beams with higher topological charges can mitigate ocean turbulence effect. The scintillation index increases with the increase of propagation distance and laser wavelength and the decrease of topological charge. When χT is less than1×10−9K2/s, scintillation index increases with an increase of χT. When χT is larger than 1×10−9K2/s, saturation phenomenon of the scintillation index will appear. When propagation distance is less than 40 m, scintillation index increases with an increase of ω. However, when propagation distance is larger than 40 m, scintillation index increases with the decrease of ω. The propagation distance is very sensitive to the degree of polarization (DOP). The degree of polarization becomes worse with the increase of propagation distance, χT and ω and the decrease of topological charge and ε.

INFLUENCE OF ANISOTROPIC TURBULENT PLASMA ON THE PARTIALLY COHERENT FOUR-PETAL GAUSSIAN VORTEX BEAMS

Based on the extended Huygens-Fresnel principle, the analytical expressions for partially coherent four-petal Gaussian (FPG) vortex beams propagating in turbulent plasma are obtained, the influence of the turbulent plasma parameters on beam profile and coherence of the beams is discussed in detail using numerical examples. It is found that a four-petal Gaussian-shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent plasma. Meanwhile, turbulent plasma parameters will also influence the coherence characterizations of the beams.

Chirped Lommel Gaussian vortex beams in strongly nonlocal nonlinear fractional Schrödinger equations

Chirped Lommel Gaussian vortex beams (LGVBs) propagating in strongly nonlocal nonlinear fractional Schrödinger equation (NFSE) are numerically studied for the first time. We verify that the chirped LGVBs perform autofocusing effects periodically. The propagation trajectory, the focal position and the focal intensity of the chirped LGVBs are deeply influenced by the appropriate selection of the parameters of the initial beams as well as the Lévy index of fractional diffraction effect in the strongly nonlocal NFSE. Moreover, the Poynting vector and the angular momentum of the beams are also researched. The findings demonstrate many interesting properties related to the chirped LGVBs propagating in the strongly nonlocal nonlinear fractional NFSE, which can broaden the research field of the chirped LGVBs.

Particle Scattering Induced Orbital Angular Momentum Spectrum Change of Vector Bessel–Gaussian Vortex Beam

In this paper, we obtain the intensity and phase distributions of the scattering and external fields of a vector Bessel–Gaussian vortex beam in the far-field region after being scattered by a particle. In our analysis, we use the Generalized Lorenz–Mie theory (GLMT) and the angular spectrum decomposition method (ASDM). The orbital angular momentum (OAM) spectra of the fields are analyzed by using the spiral spectrum expansion method, which is a frequently used tool for studying the propagation of vortex beams in turbulent atmospheres. Both scattered and external fields show a significant difference in spiral spectra for particles with different characteristic parameters, such as the size and complex refractive index. We also examine sampling the phase along with a circle and show that it is unable to fully express the information of the fields. This study can provide a theoretical basis for the inversion of characteristic parameters of the Bessel–Gaussian vortex beam and spherical particle by OAM spectra with applications in remote sensing engineering.

Flow mechanism of Gaussian light-induced vortex motion inside a nanofluid droplet

PurposeThe purpose of this study is to use a weak light source with spatial distribution to realize light-driven fluid by adding high-absorbing nanoparticles to the droplets, thereby replacing a highly focused strong linear light source acting on pure droplets.Design/methodology/approachFirst, Fe3O4 nanoparticles with high light response characteristics were added to the droplets to prepare nanofluid droplets, and through the Gaussian light-driven flow experiment, the Marangoni effect inside a nanofluid droplet was studied, which can produce the surface tension gradient on the air/liquid interface and induce the vortex motion inside a droplet. Then, the numerical simulation method of multiphysics field coupling was used to study the effects of droplet height and Gaussian light distribution on the flow characteristics inside a droplet.FindingsNanoparticles can significantly enhance the light absorption, so that the Gaussian light is enough to drive the flow, and the formation of vortex can be regulated by light distribution. The multiphysics field coupling model can accurately describe this problem.Originality/valueThis study is helpful to understand the flow behavior and heat transfer phenomenon in optical microfluidic systems, and provides a feasible way to construct the rapid flow inside a tiny droplet by light.

Mutual coherence function based topological charge detection in a Gaussian vortex beam optical communication system

We investigate a topological charge (TC) detection schema for an optical communication system employing Gaussian vortex beam (GVB). In this scenario, the transmitter maps the electrical message symbols to the TCs of GVBs. Thus obtained optical signal propagates in turbulent atmosphere arriving at the receiver, where a detection process is implemented to determine the TC of GVB by correlating the imaginary part of the mutual coherence function (MCF) of the incoming beam against the stored profiles. The feasibility of such a schema is firstly established by examining and comparing the analytical formulation of MCF and that of random phase screen setup. The latter is then used to explore the success rate and boundaries of this particular detection schema. Our results show that the proposed detection schema can operate with a error rate of 5% at a link length of 5.5 km and atmospheric turbulence structure constant of 10−14.

Generation and propagation dynamics of a controllable hollow Airy–Gaussian vortex beam

Generation and propagation dynamics of a controllable hollow Airy–Gaussian vortex beam

Electron Symmetric Pearcey Gaussian Vortex Beams

AbstractIn this manuscript, a new, to the best of the authors' knowledge, class of electron symmetric Pearcey Gaussian vortex beams (ESPGVBs) is introduced for the first time. And the propagation of ESPGVBs is investigated analytically and numerically in free space and in a constant magnetic field. In both two mediums, ESPGVBs possess auto‐focusing and self‐healing properties. It is worth noting that the auto‐focusing ability of ESPGVBs is high‐tunable. The focal length and the probability‐density of ESPGVBs can be flexibly adjusted by altering the distribution factors, the topological charge, and the magnetic flux density. At the auto‐focusing plane, ESPGVBs greatly self‐heal though the maximum of the probability‐density is severely declined. Compared with electron symmetric Pearcey Gaussian beams, ESPGVBs embedded with the vortex behave with a stronger self‐healing property in the whole process of the propagation.

Anomalous beam spreading of Airy vortex beam arrays propagating in a moderate turbulent atmosphere

The effects of transverse displacement parameter d and topological charge (TC) m on the beam spreading (BS) of Airy vortex beam array (AVBA) and Airy Gaussian vortex beam array (AGVBA) propagating in a moderate turbulent atmosphere are analysed and studied numerically. Due to the Gaussian function truncation and optical vortex modulation, the behaviours of the BSs of AVBA and AGVBA in turbulent atmosphere are anomalous. Compared with the AVBA, the BS of lower order AGVBA is less affected by atmospheric turbulence when d is small but more affected when d is large. With the increase of m, the BSs of two vortex beam arrays decrease nonlinearly and AVBA is broadened more seriously by atmospheric turbulence than that of AGVBA as d is set to be zero. Compared with AGVBA, the BS of AVBA with lower TC is less affected by atmospheric turbulence but more seriously affected with higher TC.

Orbital angular momentum spectrum of pin-like optical vortex beams in turbulent atmosphere.

The analytical formula of the probability density of a single orbital angular momentum (OAM) mode for pin-like optical vortex beams (POVBs) in turbulent atmosphere is derived. Its OAM spectrum in the receiving plane is obtained by the numerical calculation. For comparison, the OAM spectrum of commonly Gaussian vortex beams is showed, too. Those results show that POVBs show good performance on resisting the cross talk of the OAM mode induced by the turbulence in some cases, such as smaller radius of the receiving aperture, longer propagation distance, and stronger turbulence. Our finding has application in free-space optical communication based on the OAM mode.

Optical trapping of Rayleigh particles based on four-petal Gaussian vortex beams.

The intensity distribution of four-petal Gaussian vortex (FPGV) beams through a focused optical system and the radiation force acting on a Rayleigh dielectric sphere is obtained based on the extended Huygens-Fresnel principle and the Rayleigh scattering theory. We mainly study the trapping of high and low refractive index Rayleigh particles by FPGV beams and the effect of the topological charge m on the radiation force. The results show that the specific distribution of the incident beam can be controlled by a reasonable choice of topological charge m. The multiple locations in a beam of light where particles of different refractive indices can be captured will be found. On the other hand, when m changes, the number of particles captured and the locations where they can be captured change accordingly. Therefore, the flexibility to simultaneously capture multiple Rayleigh particles with different refractive indices with a single beam at different locations in the focal plane can be achieved using the FPGV beam.

Approach to select optimal cross-correlation parameters for light field particle image velocimetry

The light field particle image velocimetry (LF-PIV) has shown great potential for three-dimensional (3D) flow measurement in space-constrained applications. Usually, the parameters of the cross correlation calculation in the LF-PIV are chosen based on empirical analysis or introduced from conventional planar PIV, which lowers the accuracy of 3D velocity field measurement. This study presents an approach to selecting optimal parameters of the cross correlation calculation and thereby offers systematic guidelines for experiments. The selection criterion of the interrogation volume size is studied based on the analysis of the valid detection probability of the correlation peak. The optimal seeding concentration and the size of tracer particles are then explored through synthetic Gaussian vortex field reconstruction. The optimized parameters are employed in a cylinder wake flow measurement in a confined channel. A comparative study is conducted between the LF-PIV and a planar PIV system. Results indicate that the LF-PIV along with the optimized parameters can measure the 3D flow velocity of the cylinder wakes accurately. It has been observed that the mean and max errors of velocity decrease by 32.6% and 18.8%, respectively, compared to the related LF-PIV techniques without consideration of optimal parameters. Therefore, it is suggested that the optimized cross correlation parameters in the LF-PIV can improve the accuracy of 3D flow measurement.

The multi-consecutive optical bottles generated from the chirped elliptical Pearcey Gaussian vortex beams

The evolution of the chirped elliptical Pearcey Gaussian vortex (CEPGV) beams in free space is numerically investigated. The optical bottle and multi-consecutive optical bottles can be directly generated from an elliptical Pearcey Gaussian beam with central vortices and the second-order chirp. In particular, the focusing intensity of CEPGV beams will increase when the elliptical structure deflects larger or the ratio of the long axis to the short axis of the ellipse is larger. Furthermore, we can obtain multi-consecutive optical bottles by manipulating elliptical structure parameters and second-order chirp factors. In the meantime, the transverse intensity distributions at foci of CEPGV beams appear like a slit in a fixed direction. Our results show that the focusing intensity, the focal length and the transverse intensity distribution of CEPGV beams during the propagation can be controlled.

Geometric Progression of Optical Vortices

We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. However, it always remains integer when the light field propagates in free space. In the general case, the geometric progression of optical vortices (GPOV) has three integer parameters and one real parameter, values which define its TC. The GPOV does not conserve its intensity structure during propagation in free space. However, the beam can have the intensity lobes whose number is equal to one of the family parameters. If the real GPOV parameter is equal to one, then all angular harmonics in the superposition are of the same energy. In this case, the TC of the superposition is equal to the order of the average angular harmonic in the progression. Thus, if the first angular harmonic in the progression has the TC of k and the last harmonic has the TC of n, then the TC of the entire superposition in the initial plane is equal to (n + k)/2, but the TC is equal to n during propagation. The experimental results on generating of the GPOVs by a spatial light modulator are in a good agreement with the simulation results.

A meshless method to compute pressure fields from image velocimetry

We propose a meshless method to compute pressure fields from image velocimetry data, regardless of whether this is available on a regular grid as in cross-correlation based velocimetry or on scattered points as in tracking velocimetry. The proposed approach is based on radial basis functions (RBFs) regression and relies on the solution of two constrained least square problems. The first one is the regression of the measurements to create an analytic representation of the velocity field. This regression can be constrained to impose boundary conditions (e.g. no-slip velocity on a wall or inlet conditions) or differential constraints (e.g. the solenoidal condition for an incompressible flow). The second one is the meshless integration of the pressure Poisson equation, achieved by seeking a solution in the form of a RBF expansion and using constraints to impose boundary conditions. We first illustrate the derivation of the two least square problems and the numerical techniques implemented for their solution. Then, we showcase the method with three numerical test cases of growing complexity. These are a 2D Gaussian Vortex, a 2D flow past a cylinder from CFD and a 3D Stokes flow past a sphere. For each case, we consider randomly sampled vector fields simulating particle tracking measurements and analyze the sensitivity to noise and seeding density.

Rectangular Beam Pumped Raman Microchip Laser for Generating Multiwavelength High‐Order Hermite–Gaussian Lasers and Vortex Lasers

AbstractHigh‐order Hermite–Gaussian (HG) lasers oscillating at multiple wavelengths are extensively needed for generating vortex lasers carrying orbital angular momentum (OAM), which have wide applications on optical communication, high capacity storage, and high resolution imaging. Off‐axis pumping or off‐axis resonator has been used to generate high‐order HG0,n lasers, however, low optical efficiency limits practical applications of these lasers. Here, direct generation of multiple wavelength high‐order HG0,n lasers in a rectangular beam pumped Raman microchip laser constructed with Yb3+:Y3Al5O12 (Yb:YAG) and yttrium vanadate (YVO4) crystals is demonstrated. The order n of HG0,n mode lasers can be tuned from 1 to 9. HG0,n (n > 3) mode Raman lasers oscillate at multiple wavelengths and shift to longer wavelength with n. The output power is 137 mW for multiwavelength HG0,9 mode Raman laser when the input pump power is 2.7 W. The optical conversion efficiency is as high as 5.1%. Excellent beam quality with My2 close to theoretical values (My2 = 2n+1) for high‐order HG0,n lasers has been achieved. Topological charge tunable Laguerre–Gaussian (LG) vortex lasers with high beam quality are generated from HG0,n mode lasers with an astigmatic mode converter. This work demonstrates that rectangular beam pumping is an effective method for developing efficient multiwavelength high‐order HG0,n mode Raman lasers.

Influence of optical "dipoles" on the topological charge of a field with a fractional initial charge.

In this work, using the Rayleigh-Sommerfeld integral and Berry formula, a topological charge (TC) of a Gaussian optical vortex with an initial fractional TC in the far field was calculated. It was found that, for diverse fractional parts of the TC, the beam contained different numbers of screw dislocations, which determined the TC of the entire beam. If a fractional part of the TC was small, the beam consisted of the main optical vortex centered on the optical axis, with the TC equal to the nearest integer (say n>0) and two edge dislocations located on the vertical axis (one above and the other below the center). When the fractional part of the initial TC increased, a "dipole" was formed from the upper edge dislocation, consisting of two vortices with TCs equal to +1 and -1. With a further increase in the fractional part, the additional vortex with TC=+1 moved to the center of the beam, and the vortex with TC=-1 moved to the periphery. When the fractional part of the TC increased further, another "dipole" was formed from the lower edge dislocation, in which, on the contrary, the vortex with TC=-1 was displaced to the optical axis (to the center of the beam) and the vortex with TC=+1 moved to the beam periphery. When the fractional part of the TC became equal to 1/2, the lower vortex with a TC=-1, which was earlier displaced to the center of the beam, began to shift to the periphery, and the upper vortex with a TC=+1 moved closer and closer to the center of the beam, eventually merging with the main vortex when the fractional part approached 1. Such dynamics of additional vortices with TCs above +1 and below -1 determined which whole TC the beam would have (n or n+1) for different values of the fractional part from the segment [n,n+1]. Our analysis has shown that, for any value of the fractional part of the initial topological charge, the TC of the beam in the far field will not be determined. Since, with an increase in the radius of the circle in the beam section on which the TC is calculated, more optical "dipoles" will appear, and the TC will be either n or n+1.

Research on the influence of anisotropic ocean on the capacity of vortex Hankel–Bessel beam

Vortex optical communication is a method to improve the spectral efficiency of underwater wireless optical communication. However, facing the complex marine environment, the turbulence effect in the offshore area is a big challenge to vortex optical communication. Oceanic turbulence will influence the transmission performance of the vortex beam. After turbulent transmission, crosstalk will inevitably occur between different topological modes. This paper studies the degree of crosstalk of Hankel–Bessel (HB) vortex light in different oceanic turbulences. By establishing a mathematical model of anisotropic oceanic turbulence, the main focus is on average temperature dissipation rate, turbulent energy dissipation rate, and temperature-salinity balance parameters. The influence of different turbulence parameters on the propagation of HB vortex light is discussed, and the degree of influence of the above parameters on the channel capacity of the orbital angular momentum HB (OAM-HB) optical communication system is studied. Simulation experiments show that anisotropic oceanic turbulence will cause energy migration in different topological models and cause significant decreases in channel capacity. We observed the capacity of HB vortex beams and compared the communication effects of Laguerre–Gaussian and HB vortex beams in anisotropic ocean turbulence. The communication performance of OAM-HB light in anisotropic turbulent is better than that in an isotropic one. The research results of the transmission characteristics of the vortex HB light underwater show that the OAM-HB underwater communication is worthy of further study.

Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"

In this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, which determine the TС of the entire beam. With a small fractional part of the TС, the beam consists of the main optical vortex centered on the optical axis with the TС equal to the nearest integer (let be n), and two edge dislocations located on the vertical axis (above and below the center). With an increase in the fractional part of the initial TC, a "dipole" is formed from the upper edge dislocation, consisting of two vortices with TC+1 and –1. With a further increase in the fractional part, the additional vortex with TC+1 is displaced to the center of the beam, and the vortex with TC–1 is displaced to the periphery. With a further increase in the fractional part of the TC, another "dipole" is formed from the lower edge dislocation, in which, on the contrary, the vortex with TC–1 is displaced to the optical axis (to the center of the beam), and the vortex with TC+1 is displaced to the beam periphery. When the fractional part of the TC becomes equal to 1/2, the "lower" vortex with TC–1, which was displaced to the center of the beam, begins to shift to the periphery, and the "upper" vortex with TC+1 moves closer and closer to the center of the beam and merges with the main vortex when the fractional part approaches 1. Such dynamics of additional vortices with upper TC+1 and lower TC–1 determine the whole TC the beam have (n or n+1) for different values of the fractional part from the segment [n, n+1].