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.     

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     

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.     

Partially coherent vortex beams propagation in a turbulent atmosphere

Based on the Rytov approximation and the cross-spectral density approximation for the mutual coherence function of the partially coherent field, the propagation properties of the partially coherent beams with optical vortices in turbulent atmosphere are discussed. The average intensity and the mutual coherence function of the partially coherent vortex beams propagation in weak turbulent atmosphere are obtained.It is shown that the vortex structure of the average cross-spectral density of partially coherent beams has the same helicoidally shape as that of the phase of the fully coherent Laguerre-Gauss beams in free space and the relative intensity of the beam is degraded by optical vortex.     

Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.     

高阶涡旋光束生成技术研究

应用液晶空间光调制器加载螺旋相位片的方法可以高效地生成涡旋光束,但由于液晶空间光调制器分辨率有限,在加载高阶螺旋相位片时其中心会出现相位失真,造成涡旋光束质量不高。通过在螺线相位片中心区域引入闪耀光栅的方法,得到了光束质量较高的高阶单模涡旋光束和多模涡旋光束,为生成高阶涡旋光束提供了一种很好的方法。     

Phase sensitive parametric amplification of optical vortex beams

Optical vortex beams with different topological charges are amplified in a travelling wave phase sensitive parametric interaction. Amplified beams observed either in the near field or in the far field domains exhibit patterns that depend on the relative phase between the pump and the vortex beams. Experimental results are compatible with the conservation of orbital angular momentum of the input beam whatever phase matching conditions.     

Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex

The focusing properties of the hyperbolic-cosine-Gaussian beam, which contains an optical vortex induced by a non-spiral phase plate, are investigated numerically. The phase plate alters phase distribution linearly in a half-section part of the hyperbolic-cosine-Gaussian beam, which results in one non-spiral optical vortex. Results show that the phase variation rate of the non-spiral phase plate influences focal intensity distribution considerably, and some novel focal patterns, such as line focal spot, “H”-shape focal spot, and intensity peaks array, may occur. Focal shift, focal split, and focal switch appear in focal evolution with increasing phase variation rate. The focal evolution differs for different parameters in cosh parts of the hyperbolic-cosine-Gaussian beam. For big parameters in cosh parts, the value of local intensity peaks is comparable to that of maximum intensity peaks.     

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.     

Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.     

Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam

Diffraction of uniformly polarized laser beams with vortex phase singularity is theoretically analyzed using the plane wave expansion. It is shown that for a high numerical aperture, an intense longitudinal electric field component is formed on the optical axis in this case. It is numerically demonstrated that an analogous effect is ensured for diffraction of a conventional Gaussian beam from asymmetric binary axicons. The field intensity on the optical axis can be varied either by rotating the optical element or by changing the direction of polarization of radiation.     

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.     

Generation of optical vortices with tunable intensity modulation

We analyze vortex properties of the optical beams generated by a spiral phase plate (SPP) which cannot modulate the phase of the incident beam range from 0 to 2π nicely, and find that the vortices have intensity modulation (IM) with central bright speckle. We construct an improved SPP to produce high quality optical vortices with definite IM. Theoretical analysis and real experiments show that this improved SPP can be used to produce optical vortices with configurable intensity modulation degree and without central bright spot.     

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。     

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.     

Propagation of Gaussian background vortex beams diffracted at a half-plane screen

Taking the Gaussian background vortex beam with topological charge +2 as a typical example, a closed-form expression for vortex Gaussian beams passing through a half-plane screen is derived and used to study the propagation dynamics of on-axis and off-axis vortex diffracted beams, and to compare with the case of the free-space propagation. It is shown that there may exist many phase singularities or no phase singularity of vortex diffracted Gaussian beams in the diffraction field. Number and position of phase singularities are dependent on the vortex position at the source plane and propagation distance. The creation, motion and annihilation of phase singularities in the diffraction field may appear by varying the vortex position and propagation distance.     

光在Metasurface中的自旋-轨道相互作用

探讨了光在Metasurface中的自旋-轨道相互作用, 理论分析了Metasurface 对圆偏振和线偏振光的转换. 结果表明: 光与具有空间非均匀性和各向异性性的Metasurface的相互作用导致了自旋-轨道角动量的耦合. 采用Metasurface与螺旋相位片组合在一起进行了验证实验, 所得实验结果与理论分析完全一致. 这些结论有助于我们更加深入理解Metasurface 对光的操控.     

数字全息术测定涡旋光束拓扑电荷数

提出了一种基于数字全息技术测定涡旋光束拓扑电荷数的方法.该方法通过数字全息技术获取涡旋光束和参考光的全息图并重构出涡旋光束的波前相位,判定相位围绕相位奇点的周期性分布来测定涡旋光束的拓扑电荷数.在拓扑电荷数取值分别为整数和分数的情况下,通过对数值模拟和实验结果的比较,表明该方法能够较准确地测定出拓扑电荷数.