Transformation of optical-vortex beams by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by the “fork” holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram’s groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed.The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.     

Generation and detection of optical vortices using all fiber-optic system

We demonstrate simultaneous generation, propagation and detection of optical vortices using all fiber-optic system. A fiber-optic Y-coupler was used for generating spherical and doughnut beams, simultaneously. Gaussian (TEM₀₀) beam emitted from CW red He-Ne laser is coupled into the fiber coupler and is converted into vortex beam via second arm of fiber which propagates with azimuthal phase dependence having well defined orbital angular momentum. The phase structure of vortex beam was detected by interfering both the beams using simple fiber-optic interferometer. The present all fiber-optic system might find application for detecting, sensing physical parameters and is simple and cost effective for generating and detecting optical vortices.     

Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams.     

Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams

We propose the generation of novel composite vortex beams by coaxial superposition of Laguerre–Gaussian (LG) beams with common waist position and waist parameter. Computer-generated holography by conjugate-symmetric extension is applied to produce the holograms of several composite vortex beams. Utilizing the holograms, fantastic light modes including optical ring lattice, double dark-ring and double bright-ring composite vortex beams etc. are numerically reconstructed. The generated composite vortex beams show diffraction broadening with some of them showing dynamic rotation around beam centers while propagating. Optical experiments based on a computer-controlled spatial light modulator (SLM) verify the numerical results. These novel composite vortex beams possess more complicated distribution and more controllable parameters for their potential application in comparison to conventional optical ring lattice.     

离轴高斯涡旋光束的深聚焦特性

基于德拜矢量衍射积分理论,对离轴高斯涡旋光束经过大数值孔径透镜后聚焦场的特性进行了研究,获得了离轴高斯涡旋光束深聚焦后复振幅分布函数,在此基础上对离轴高斯涡旋光束深聚焦场的光强和相位分别进行了分析.数值模拟结果表明:离轴距离的改变对高斯涡旋光束在焦平面上的光强分布和相位分布会产生影响,离轴距离的增加会加剧聚焦场光强在y轴方向上分布的差异,而离轴距离的符号决定了光强集中区域的方向.另一方面,与一阶离轴涡旋光束不同,高阶离轴涡旋光束经过深聚焦后会发生暗核分裂现象,出现多个相位奇点,奇点个数等于原始光束对应的拓扑荷数,且分裂后的奇点具有明显的对称性.研究表明,这种暗核分裂现象由大数值孔径透镜深聚焦引起.     

Modal Power Analysis for Two-Mode Fibers Illuminated by an Offset Beam Based on Near Field Pattern Measurement

A novel method for determining mode power distribution in a two-mode fiber illuminated by an offset beam by measuring the near field pattern on the test fiber endface is developed. This method utilizes the different field symmetries of the fundamental and the second order modes. Coupling efficiencies from a quasi Gaussian beam to the fundamental and the second order modes in a two mode fiber were measured by the new technique for various offset launching conditions, and were in good agreement with the theoretical ones.     

Quantum state for the two-variable Hermite polynomial–Gaussian laser modes of the electromagnetic field

In Ref. [7] by using the plane-wave representation of the fundamental Gaussian mode as a seed function, Enderlein and Pampaloni derived higher-order beam modes (Laguerre–Gaussian laser beams) of the electromagnetic field by acting with differential operators on this fundamental solution. In this paper we show that their approach can be improved by directly performing the integration with the aid of the two-variable Hermite polynomials, in so doing these modes can exhibit some new good characters. Their relationship to the eigenmodes of light propagation in the quadratic graded-index (GRIN) medium is pointed out. By introducing the two-mode entangled state representation the quantum states corresponding to these modes are also found which turns out to be the Hermite-polynomial excitation on the two-mode squeezed vacuum state.     

Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.     

Electrically tunable generation of vectorial vortex beams with micro-patterned liquid crystal structures

We develop a new method for smooth and continuous space-variant alignment of the liquid crystal medium in micro-patterned structures, which is based on a radial micro-structured pattern of polymeric ribbons exhibiting out-of-plane orientation with respect to the ITO-coated glass plates. Thanks to the broad range of electrical tunability of the optical retardation for the micro-patterned liquid crystal structures, transformation of the fundamental Gaussian beam into different types of specific beams, including generalized cylindrical vector beams, vortex beams, and vectorial vortex beams, is efficiently demonstrated.     

Vortex and anti-vortex compositions of exact elegant Laguerre–Gaussian vector beams

Reformulation of conventional beam definitions into their bidirectional versions and use of Hertz potentials make beam fields exact vector solutions to Maxwell’s equations. This procedure is applied to higher-order elegant Laguerre–Gaussian beams of transverse magnetic and transverse electric polarization. Their vortex and anti-vortex co-axial compositions of equal and opposite topological charges are given in a closed analytic form. Polarization components of the composed beams are specified by their radial and azimuthal indices. The longitudinal components are common for beam compositions of both types; meanwhile, their transverse components are different and comprise two—nonparaxial and paraxial—separate parts distinguished by a paraxial parameter and its inverse, respectively. The new solutions may appear useful in modeling and tailoring of arbitrary vector beams.     

贝塞尔-高斯涡旋光束相干合成研究

基于相干合成技术,提出了对特定离散空间分布的高斯光束阵列加载离散涡旋相位生成二阶贝塞尔-高斯(Bessel-Gaussian,BG)涡旋光束的方案.利用干涉法、桶中功率和相关系数对合成BG涡旋光束的拓扑荷、光束质量进行了定量评价及参数优化.结果表明:基于相干合成技术能够产生特定的目标BG涡旋光束,阵列子光束紧密排布时合成BG光束的光束质量更高.该方法的提出对于其他涡旋光束的产生或者涡旋光束功率的提高具有一定的参考意义.     

高斯涡旋光束的傍轴度

按单色光束傍轴度的定义,对高斯涡旋光束的傍轴度进行了研究.使用角谱表示法推导出高斯涡旋光束傍轴度的解析公式,用此研究了傍轴度和高斯涡旋光束参数之间的关系.结果表明,随背景高斯光束束腰宽度和光涡旋离轴参数的增加及随光涡旋拓扑电荷的减少,高斯涡旋光束的傍轴度增加.对所得结果用傍轴度与远场发散角间的关系做了物理解释.     

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     

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

A higher-order Poincaré sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincaré sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.     

超高斯涡旋光束在空间中的传输特性

研究了超高斯涡旋光束光强最大值、光斑半径以及环围能量半径等参数随传输距离和拓扑荷数的变化规律,并与高斯涡旋光束做了比较,结果表明:超高斯涡旋光束的光斑半径和环围能量半径随拓扑荷数及传输距离呈近似线性关系;对同一拓扑荷数和传输距离,高斯涡旋光束的能量较超高斯涡旋光束要发散;当拓扑荷数较大时,超高斯涡旋光束的光斑半径比高斯涡旋光束更大。针对光束质量研究了广义光束质量因子随传输距离和拓扑荷数的变化,结果表明传输距离足够远时,拓扑荷数较小的超高斯涡旋光束具有更好的光束质量。     

Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter

We propose a new approach to generating a pair of initial beams for a polarization converter that operates by summing up two opposite-sign circularly polarized beams. The conjugated pairs of vortex beams matched with laser modes are generated using binary diffractive optical elements (DOEs). The same binary element simultaneously serves two functions: a beam shaper and a beam splitter. Two proposed optical arrangements are compared in terms of alignment complexity and energy efficiency. The DOEs in question have been designed and fabricated. Natural experiments that demonstrate the generation of vector higher-order cylindrical beams have been conducted.     

椭圆涡旋光束在海洋湍流中的传输特性

本文采用分步相位屏方法来仿真椭圆涡旋光束在海洋中的实际传输情况,并对椭圆涡旋光束在海洋湍流中的传输光强和闪烁因子进行了仿真。研究发现,椭圆涡旋光束在海洋传输过程中,光斑会发生明显的旋转,同时光斑会产生暗核且暗核个数与光束的拓扑荷数相等。一个拓扑荷数为m的相位奇点会分裂成m个拓扑荷数为1的相位奇点,并且海洋湍流越强,光斑受到的干扰越严重。研究还发现,在较弱的海洋湍流中,随着传输距离的增加,椭圆涡旋光束的闪烁因子会低于高斯光束和涡旋光束的闪烁因子,而且在远距离处拓扑荷数越大闪烁因子降低越明显,同时也发现,传播一段距离后涡旋光束的闪烁因子会低于高斯光束的闪烁因子。在较强湍流中,椭圆涡旋光束的闪烁因子会交叠在一起。对于不同强度的海洋湍流,随着均方温度耗散率的增大,椭圆涡旋光束的轴上点闪烁因子也增大。在同一传输距离处,束腰宽度越小的椭圆涡旋光束闪烁因子越小。     

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.     

Influence of retardation between orthogonal components of circularly polarized light in the vortex phase plate on the structure of diffracted beam

The influence of retardation between orthogonal components of circularly polarized light on diffraction pattern generated by the vortex phase plate with a birefringence medium is considered. It is shown that if the ideal retardation π is broken, the pattern diffracted from the phase plate is described by superposition of two components: the vortex beam with the deep hole and the incident beam which preserves its initial characteristics. The computation results characterizing the influence of retardation on the Gaussian and Airy beams transformation in the vortex phase plate are presented. These results point out that vortex beam characteristics are very sensitive to retardation shift from its ideal value. We analyze and present the characteristics of the vortex phase plate that are required for the true vortex pattern generation.     

Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture

Analytical expression for the propagation of nonparaxial cosh-Gaussian (ChG) beams diffracted by a rectangular aperture is derived based on the vector Rayleigh-Sommerfeld diffraction integrals and expansion of the aperture window function into a finite sum of complex Gaussian functions, and used to study the phase singularities of nonparaxial diffracted ChG vortex beams. The pair creation, annihilation, motion of phase singularities in the diffracted field and the dependence of position and number of phase singularities on the aperture and beam parameters, as well as on the beam nonparaxiality are illustrated by numerical examples.