Measuring the topological charge of vortex beams by using an annular ellipse aperture

We theoretically and experimentally investigate the Fraunhofer diffraction pattern of a vortex beam passing through an annular ellipse aperture. It is found that the pattern of the far-field diffraction intensity distribution exhibits some dark spots, which become clearer with increasing the value of the ellipticity factor of the annular ellipse aperture. The diffraction phenomenon is more obvious with increasing the value of the ratio of the inner long axis (or short axis) to the outer side of the annular ellipse aperture. The number of the dark spots in the Fraunhofer diffraction intensity distribution is just equal to the topological charge value of the measured optical vortex, and the centre of each dark spot is just a phase-singularity point. Based on this property, we can measure the topological charge of an optical vortex beam.     

Detecting the topological charge of vortex beams using an annular triangle aperture

The Fraunhofer diffraction pattern of a vortex beam by an annular triangle aperture is analyzed theoretically and experimentally. It is found that the pattern of the far-field diffraction intensity distribution exhibits a triangular lattice array, which becomes much clearer with the increase of the ratio of the inner to the outer side of the annular triangle aperture. The number of spot points of any external side of the triangular lattice array minus one is just equal to the topological charge value of the measured optical vortex. For the vortex beam with negative topological charge, the triangular diffraction pattern after the annular triangle aperture will be rotated by 180° in relation to the case of the positive topological charge. Based on the above properties, we propose a simple and feasible method to determine the magnitude and sign of the topological charge of an optical vortex beam.     

Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma

In this paper, diffraction pattern of a vortex carrying beam with a Gaussian background has been studied by using Fresnel-Kirchhoff diffraction integral, in the presence of third-order coma. Results of intensity distribution and encircled energy at the Gaussian plane have been presented for two values of the topological charge. Positional shift and splitting of the dark core have been investigated in detail. It is noticed that the diffraction pattern of a beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We have also verified our results by using the optical transfer function approach. Propagation of an apertured Gaussian background vortex beam through a π-phase shifter has also been studied for two values of the topological charge.     

Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm

The diffraction of an optical vortex through an iris diaphragm which is a close approximation to a circular aperture has been investigated. The results are compared with those obtained from the diffraction of a Gaussian beam through the same aperture. In our findings the diffraction of an optical vortex and a Gaussian beam produce ball bearing sort of structure of darkness and brightness. The singularity of the vortex beam is found to be consistent even after the diffraction through the aperture. The presence of singularity at the centre of diffraction pattern of an optical vortex has been confirmed by interferometry. There is a good agreement between the experimental and numerical results. We propose that these results may find various applications in optical trapping experiments.     

Measuring the topological charge of optical vortices with an axicon

We analyzed the spatial spectrum of the diffraction intensity pattern of an ideal Bessel beam and found an implicit rule that the number of the bright rings in the spatial spectrum is equal to the topological charge of the Bessel beam. The radius of the bright and dark rings has some relation with the topological charge and can be determined accurately. It provides us with a new way for measuring the topological charge of an optical vortex through its diffraction intensity pattern after an axicon. The results of simulation coincide with the theory.     

A crossed focused vortex beam with application to cold molecules

We report the generation of a crossed, focused, optical vortex beam by using a pair of hybrid holograms, which combine the vortex phase and lens phase onto a spatial light modulator. We study the intensity distributions of the vortex beam in free propagation space, and the relationship of its dark spot size with the incident Gaussian beam's waist, the lens's focal length, and its orbital angular momentum. Our results show that the crossed, focused, vortex beam's dark spot size can be as small as 16.3μm and adjustable by the quantum number of the orbital angular momentum, and can be used to increase the density of trapped molecules. Furthermore, we calculate the optical potential of the blue-detuned, crossed vortex beam for MgF molecules. It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling, as the intensity gradient of such vortex beam is extremely high near the focal point.     

4Pi focusing of spatially modulated radially polarized vortex beams

We propose a method for generating focal beams with special intensity distributions using radially polarized vortex beams in a 4Pi configuration. A spherical dark-hollow beam and hollow beam array can be obtained by vortex beams with topological charge of m=1. A dark channel can be generated using vortex beams with topological charge of m=2. The length of the well-defined hollow beam array and the dark channel is about 30λ. These interesting beams are useful in optical trapping and manipulation.     

超衍射极限相干反斯托克斯拉曼散射显微成像技术中空心光束的形成

空心光束的质量是超衍射极限相干反斯托克斯拉曼散射显微成像技术中决定成像质量的一个至关重要的因素. 本文基于菲涅耳衍射理论,分析了螺旋相位片法产生空心光束的物理机理,并且模拟了不同的入射条件对产生的空心光束的影响. 模拟结果表明:波长与相位片中心波长匹配且光强呈圆对称分布的高斯光垂直入射到相位片上,当高斯光束中心与相位片中心完全对准时,可获得较理想的空心光束;入射光光强分布的圆对称性以及入射光中心与相位片中心的对准程度都会影响产生的空心光束的强度分布;同时,高斯光束小角度倾斜入射时,空心光的强度分布仍呈圆对称,却在观察面发生一定的位移;此外,入射光中心波长偏离相位片中心波长不大时,对产生的空心光束的强度分布几乎没有影响. 上述分析结果对用于超衍射相干反斯托克斯拉曼散射显微成像技术中理想空心光束的获取具有重要的指导意义. 关键词： 空心光束 超衍射极限 相干反斯托克斯拉曼散射 螺旋相位片     

Plasmonic tomography of optical vortices

We present a method for analyzing the wavefront of optical vortices that does not involve interferometry but rather uses surface plasmon polaritons (SPPs). We employ a subwavelength slit in a gold film to cut slices from an optical vortex beam and measure the diffraction of the generated SPPs by scattering them off a second slit. By moving the slits across the vortex beam, we create a tomogram, from which we can determine the vortex charge of the incident beam at a glance. We present results for vortex beams of integer- and half-integer-vortex charge.     

Self-reconstruction of an optical vortex

The results of experiments devoted to the diffraction of a light beam with an axial optical vortex from the edge of an opaque screen are presented. The reconstruction of an optical vortex in the transmitted beam is observed under conditions when the screen cuts off the central part of the incident beam.     

Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

带初相位分布的径向基模激光束列阵在湍流大气中的传输特性研究

利用相干叠加原理和广义Huygens-Fresnel 衍射积分公式,理论上研究了具有确定初始相位排列的激光束列阵通过大气湍流的传播特性.发现在近距离的传输过程中,列阵光束的光强分布会出现螺旋状分布（即光学涡旋）.但由于大气湍流的影响,光束列阵远场涡旋特性随着传输距离的增加逐渐消失,成为无旋涡的实心光束;且当大气湍流变弱时,旋涡特性的有效传输距离逐渐变长. 关键词： 大气湍流 涡旋     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

Tight focusing properties of radially polarized Lorentz–Gaussian beam

Focusing properties of radially polarized Lorentz–Gauss beam with one on-axis optical vortex was investigated by vector diffraction theory. Results show that intensity distribution in the focal region can be altered considerably by charge number of the optical vortex and the beam parameters. Many novel focal patterns may occur, Such as Peak-centered, donut focal shapes which is potentially useful in optical tweezers, material processing and laser printing.     

圆柱型光纤螺线圈轨道角动量模式

传统的沿z轴光纤传输光线的轨道角动量(orbital angular momentum,OAM)光束的制备方法共同之处都是从内部结构着想,光束的主光线基本上不变,只是波面在变.但要获得携带高mh的光有一定的难度.针对上述问题,本文建立以波面不变,光束主光线变化为基础的理论框架,利用微分几何理论验证不沿z轴圆柱型光纤螺线圈传输的光线可以携带高mh OAM的理论设想.研究发现:利用流动坐标(α,β,γ)计算光线在绕圆柱体的光纤中传输时光纤截面的衍射分布图呈现涡旋特征,有高阶OAM模式.当θ=θ0时,圆柱形轨道光纤过渡到直线轨道光纤.计算光线沿直线传输时光纤截面的衍射分布图是Airy斑,即圆孔衍射斑,无高阶OAM模式.     

Structure of a tightly focused vortex beam in the presence of primary coma

Structure of a tightly focused circularly polarized vortex beam in the presence of primary coma has been studied by using Debye-Wolf diffraction integral. The role of topological charge and handedness of the polarization on the focused structure has been discussed. Results have been presented for the total intensity and squares of the polarization components for left-, and right circularly polarized vortex beams. Impact of coma, on the dark core of an azimuthally polarized non-vortex beam is also investigated and compared with the dark core of a circularly polarized vortex beam. The presence of comatic aberration in the focusing system results in a positional shift of the high intensity lobes, and reduction of the intensity on one side of the center. Effect of coma on the focused structure has also been discussed in the context of STED microscopy.     

Formation of a quadrupole vortex and a second-order optical vortex in caustics upon focusing of light by a two-component crystal-optics element

A wave field of a structurally stable diffraction caustic that is formed upon focusing of a collimated laser beam with the help of a two-component crystal-optics element consisting of uniaxial crystals is characterized by a crystal-like cellular structure. Near the cusp of this caustic (diffraction catastrophe), a well-pronounced localized quadrupole optical vortex is observed that consists of four isolated vortices with pairwise opposite topological charges of −1, +1, +1, and −1. The creation and annihilation points of this combined quadrupole vortex are determined. Upon reversal of the direction of propagation of the laser beam through the crystal-optics element, the caustic in the focal region has already become a binary combination and inhomogeneously polarized, and a second-order optical vortex is observed near the cusp of this caustic.     

Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex

Intensity distribution in focal region plays an important role in many optical systems. In this paper, the focal patterns of higher order hyperbolic-cosine-Gaussian (HOCG) beam in focal plane were investigated. The HOCG beam contains one spiral optical vortex on its optical axis. Results show that the focal pattern can be altered considerably by beam order of the incident HOCG beam, and some novel focal patterns may occur, including foursquare focal pattern, cross-shaped dark focal focus, foursquare intensity peaks chain, and multiple intensity peaks array. Focal pattern evolution principle on increasing beam order also differs remarkably under condition of different topological charge of the optical vortex and displacement parameter associated with the cosh parts. And like topological charge and displacement parameter, the beam order and numerical aperture may affect focal pattern.     

Three-dimensional vortex solitons in self-defocusing media

We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schr?dinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.     

Generalized expression for optical source fields

A generalized optical beam expression is developed that presents the majority of the existing optical source fields such as Bessel, Laguerre–Gaussian, dark hollow, bottle, super Gaussian, Lorentz, super-Lorentz, flat-topped, Hermite–sinusoidal-Gaussian, sinusoidal-Gaussian, annular, Gauss–Legendre, vortex, also their higher order modes with their truncated, elegant and elliptical versions. Source intensity profiles derived from the generalized optical source beam fields are checked to match the intensity profiles of many individual known beam types. Source intensities for several interesting beam combinations are presented. Our generalized optical source beam field expression can be used to examine both the source characteristics and the propagation properties of many different optical beams in a single formulation.