Adaptive correction of vortex laser beam in a closed-loop system with phase only liquid crystal spatial light modulator

We propose and demonstrate the wave front correction of a vortex laser beam by using dual phase only liquid crystal spatial light modulators (LC-SLMs) and a stochastic parallel gradient descent (SPGD) algorithm. One phase only LC-SLM is used to generate vortex laser beam by loading spiral phase screen onto the wave front of input quasi-Gaussian beam. The other phase only LC-SLM under SPGD controller based on the subzone control method adaptively compensates the wave front of vortex laser beam. Numerical simulation and experimental results show that after correction, vortex doughnut like beam is focused into a beam with airy disk pattern distribution in the far field. The adaptive corrections of vortex laser beam with different optical topological charges are studied. The results show that the optical topological charge has little influence on adaptive correction. The powers in the main lobe of far field intensity distributions of vortex laser beams with different optical topological charges are all greatly improved by adaptive correction. The technique proposed in this paper can be used in optical communication, relay mirror and atmospheric turbulence correction.     

Optical vortex detector as a basis for a data transfer system: Operational principle,model, and simulation of the influence of turbulence and noise

The principle of determining the topological charge of an optical vortex is suggested based on measuring the light field intensity and designing the corresponding detector. A mathematical model of the performance of the detector of topological vortex charge is presented. Results of numerical experiments imitating the vortex recognition in the presence of turbulence or (amplitude or phase) noise in registered radiation as well as of the displacement of the optical beam source and detector axes are presented. Principles are formulated of designing the position finder for an optical vortex (that is, the detector of vortex coordinates) that allows us to consider its realization in the form of mathematical and numerical model. Conditions of reliable operation of the vortex detector and singular optical communication line constructed on its basis are estimated. Dependencies of the probability of error in data transfer on the turbulence intensity, photodetector noise amplitude, and displacement of the optical axes are investigated for different coding algorithms (absolute and differential with fixed or adaptive threshold). The data of modeling confirm the results of analytical calculations.     

Aspheric surface reconstruction for scanning interference

A simplified reconstructing method for the aspheric surface testing based on scanning interference technology is presented. The aspheric normal intersects the optical axis at different points with different angles, which is called normal congruence; a normal congruence can identify an aspheric surface. In this method, the test aspheric surface is shifted along the optical axis to scan the tested aspheric surface; meanwhile a series of interferograms and phase maps are obtained. The angles between the normal lines and the aspheric axis are obtained using the positions of zero-phase points, according to the image-forming principle of the camera. Here, Zernike polynomials are applied to analyze the phase maps and extract the zero-phase points. Finally, the absolute coordinates of the test surface is rebuilt through iterative integration. Because both the system deformation and amplification do not affect the reconstruction result, this method can avoid complicated stitching algorithm in the subaperture stitching interferometric method. Experimental results show that the method has high accuracy and reliability.     

Thermal crisis of a vortex source in a real gas flowing into vacuum with heat supply under constant pressure

Thermal crisis of a vortex source at energy input under constant pressure is investigated. The energy release intensities per unit mass and per unit volume are analyzed for the case of the vortex source flow into vacuum (regime I). Analytical solutions for gasdynamic parameters and an algorithm for constructing the heat release intensity function for different variants of vortex sources are studied. Limitations on the extension of a constant-pressure interval are determined, and the dependences of the energy input area critical coordinates, critical temperature, and energy input parameters on the mass flow, gas circulation, and initial coordinate of the energy input area are obtained. A small correction to the gas specific heat with rising temperature and a significant correction to the specific heat at a stagnation temperature of 1000 K are considered.     

Gerchberg–Saxton algorithm based phase correction in optical wireless communication

Optical wireless communication (OWC) enables to establish the backhaul in the fifth generation (5G) wireless communication networks. The air turbulence, however, could distort the phases of optical signals, thus limit transmission capacity. In this paper, we study the correction of phase distortions by using the Gerchberg–Saxton (GS) algorithm. The air turbulence-induced phase is generated by the Monte-Carlo phase screen method, which characterizes the realistic air turbulence effect on the optical signals. The numerical results reveal that the GS algorithm is able to retrieve the phase information with fast convergence by adopting a proper initial condition. Also, the GS algorithm based phase correction in OWC is confirmed.     

用四台阶相位板产生涡旋光束

涡旋光束的产生与应用是当前光学领域的研究热点. 利用傅里叶级数展开法分析了四台阶相位板的相位结构, 发现四台阶相位板可看作是由一系列不同拓扑荷数的螺旋相位板所组成, 用线偏振光直接照射相位板时, 将产生多级衍射光波, 各级衍射光均为不同拓扑荷数的涡旋光波, 由于多级衍射光波间的干涉导致光强分布偏离轴对称分布, 因而与涡旋光波有一定差距. 在此基础上, 提出了用四台阶相位板产生涡旋光束的新方案, 借助于Mach-Zehnder 干涉仪光路, 两块四台阶相位板产生的衍射光干涉叠加, 通过调节干涉仪光路的相位差, 使一部分衍射级干涉相消, 另一部分衍射级干涉相长, 相互加强, 从而把线偏振光转换为涡旋光束. 数值模拟计算了几种周期数不同的四台阶相位板衍射光强和角动量分布, 并与螺旋相位板进行比较, 证明用简单的四台阶相位板不仅能够获得与用螺旋相位板相同的涡旋光束, 而且可以用周期数较小的四台阶相位板产生具有大拓扑荷数的涡旋光束, 降低了制作相位板的难度.     

Front Cover: Chiral nanoemitter array: A launchpad for optical vortices (Laser Photonics Rev. 7(6)/2013)

Optical vortex light has a characteristic rotating phase, usually produced by passing a laser beam through suitable optical elements. The fluorescent emission produced by the electronic decay of excitonic states in amolecular array now offers ameans of directly emitting light with the sought vortex phase and axial singularity. (Picture:M.M. Coles et al. 10.1002/lpor.201300117 , pp. 1087–1092, in this issue)     

The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

In this paper, the new method of determination of the topological charge of vortex points in the interference field obtained by three plane waves interference is presented. Such optical fields are used in the optical vortex interferometer (OVI) and the determination of vortex points’ topological charge allows of unique determination of the relative phase between interfering waves (phase unwrapping problem). The new method uses additional plane wave, which produce a characteristic fork-like fringe structure in the neighbourhood of vortex points. By analysing the orientation of these fork-like patterns one can read the sign of the topological charge of the given vortex point. The method is simple and can be used for OVI calibration performed before the measurements.     

基于界面信号的扫频光学相干层析成像系统相位矫正方法

由于扫频光源的采集触发信号和采样时钟信号存在时间上的随机延时,导致扫频光学相干层析成像(SS-OCT)系统干涉信号光谱的整体错移,进而引发OCT空间域信号的相位跳变,阻碍了基于相位信息的功能成像.为了获得稳定的相位,便于开展功能OCT的研究,提出了一种基于界面信号的数字相位矫正方法.对界面附近相邻A-line间同一深度的相位信号进行差分运算,计算得到相位跳变的A-line位置与光谱错移量(以像素为单位),然后在原始干涉信号上对齐光谱,重新傅里叶逆变换,得到矫正后的复信号.该数字矫正算法不会引入额外的相位噪声,可以实现OCT信噪比受限的相位探测.通过对反射镜、荧光板和小鼠脑皮层血流的多普勒成像验证了该方法的可行性.     

基于光学涡旋相移技术的离面位移测量

设计了基于光学涡旋相移技术的离面位移测量实验方案,实现了电子散斑干涉中相移的数字控制.该方法利用输入液晶空间光调制器中的叉形光栅产生涡旋光束,通过涡旋光束绕轴的旋转产生相移;同时,产生的涡旋光束又作为参考光与物光干涉.实验中,在物体发生离面位移前后依次输入四幅叉形光栅,产生相移步长为π/2的涡旋光束,利用CCD获得涡旋光与物光的干涉光场,从而获得离面位移场的包裹相位;再通过解包裹,获得物体离面变形的相位变化.光学涡旋相移法可应用于离面位移测量.     

泽尼克多项式校正全息阵列光镊像差的实验研究

像差会影响光镊对粒子的捕获效果. 全息阵列光镊中, 像差不仅来自光学元件, 由特定算法设计的光阱相位片也会在光路中引入像差. 本文通过液晶空间光调制器加载泽尼克多项式相位图, 对全息阵列光镊中由光栅透镜组型算法引起的像差进行校正. 结果显示: 利用三阶泽尼克多项式可有效消除光路中由光栅透镜组型算法引 起的慧差, 使得捕获2 μm聚苯乙烯小球的阵列光阱刚度提高了约40%; 对比不同项的像差校正结果发现, 全息阵列光镊中由算法引起的慧差 与光学元件引起的像差一样, 也会对阵列光阱的捕获效果产生较大影响; 同时根据一阶像差校正结果可得光栅透镜 组型算法对于一阶泽尼克像差具有鲁棒性. 实验结果表明, 对全息阵列光镊中由 算法引起的像差进行校正, 对于提高光阱的捕获效果和深化对算法特性的认识都具有重要意义.     

Theoretical and experimental studies of the boundaries between two immiscible liquids in a vortex flow with a free surface

This paper discusses an analytical representation of phase boundaries in a composite vortex that result from the circular motion of a given volume of water with a given volume of a light immiscible admixture (oil) on its surface in a cylindrical container. The vortex structure consists of a vortex cavity in the center of a container and an oil body inside the vortex. Under the assumption of axial symmetry, analytical expressions were first derived describing the shape of the phase boundaries. A series of experiments was carried out and numerical calculations were compared with the experimental data. The calculated and measured phase boundary shapes were found to be satisfactorily consistent with each other. Requirements were determined regarding the experimental study of the shape of an oil body in a composite vortex and its stability depending on the governing parameters.     

平板式螺旋相位板的设计与应用

传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件,由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数.本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板.通过理论分析与数值模拟,发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束,而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节.为了实际应用的需要,可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束.这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.     

三环位相型光瞳滤波器的横向超分辨与轴向焦深扩展

用矢量衍射方法分析了线偏振光入射到带有三环位相型光瞳滤波器的高数值孔径物镜时,焦点的轴向和横向光强分布.数值模拟结果表明,高数值孔径物镜聚焦时需同时考虑光强的轴向和横向分布.通过加入三环位相光瞳滤波器,在实现横向超分辨的同时实现了光学系统轴向焦深扩展和轴向光强分布平坦化,并且位相调制深度变化时,会出现轴向焦移现象.对三环位相光瞳滤波器结构进行了优化,得出了优化结果. 关键词： 光学超分辨 扩展焦深 位相型光瞳滤波器 矢量衍射方法     

Spatial correlation singularity of a vortex field

Experimental and numerical techniques allowed us to predict and verify the existence of a robust phase singularity in the spatial coherence function when a vortex is present. Though observed in the optical domain, this phenomenon may occur in any partially coherent vortex wave.     

Velocity field measurements of swirl flow around a forward-swept axial fan using a phase-averaged PTV

The flow characteristics around a rotating axial fan were experimentally investigated using a phase-averaged PTV velocity field measurement technique. The axial fan has 5 forward-swept blades with a radius of 25 mm. Measurements were carried out at 4 axial planes and 4 radial planes perpendicular to the axis of rotation. For the axial plane measurements, one fan blade was divided into 4 different phases in order to analyze the flow structure according to blade phase. For each case, 500 instantaneous velocity fields were measured and ensemble averaged to obtain phase-averaged velocity vector fields and vorticity contours. In addition, measurements were carried out at two planes around the blade surface. Phase averaged velocity fields show periodic variations with respect to the blade phase. The periodic shedding of the tip vortex at the blade tip is also observed. The phase averaged velocity fields measured in the radial planes show periodic variations according to the fan phase and the distance from the fan. These experimental results can be used to validate numerical calculations and to understand the flow characteristics of forward-swept axial fans.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

双头部燃烧室两相燃烧流场数值研究

本文在贴体坐标系下对双头部火焰简内三维两相紊流燃烧过程进行数值模拟,采用代数雷诺应力模型模拟紊流粘性、EBU-二阶矩模型模拟燃烧反应速率、六通量辐射模型考虑热辐射对燃烧流场及火焰筒壁温的影响.分别运用颗粒轨道模型与颗粒随机轨道模型研究燃烧室内气液两相流动与燃烧过程,将所得出口温度分布与实验结果进行比较,均较为相符.     

Quantized vortex stability and interaction in the nonlinear wave equation

The stability and interaction of quantized vortices in the nonlinear wave equation (NLWE) are investigated both numerically and analytically. A review of the reduced dynamic law governing the motion of vortex centers in the NLWE is provided. The second order nonlinear ordinary differential equations for the reduced dynamic law are solved analytically for some special initial data. Using 2D polar coordinates, the transversely highly oscillating far field conditions can be efficiently resolved in the phase space, thus giving rise to an efficient and accurate numerical method for the NLWE with non-zero far field conditions. By applying this numerical method to the NLWE, we study the stability of quantized vortices and find numerically that the quantized vortices with winding number m=±1 are dynamically stable, and resp. |m|>1 are dynamically unstable, in the dynamics of NLWE. We then compare numerically quantized vortex interaction patterns of the NLWE with those from the reduced dynamic law qualitatively and quantitatively. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex stability and interactions in the NLWE. Finally, the vortex motion under an inhomogeneous potential in the NLWE is also studied.