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.     

双曲余弦高斯涡旋光束的远场特性研究

运用电磁光束的角谱法和稳相法, 推导出双曲余弦高斯(ChG) 涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式, 用以研究了ChG涡旋光束在远场中的位相奇点和能流密度分布特性. 结果表明, 改变ChG 涡旋光束中的离心参数或束腰宽度, 位相奇点的密度、位置会发生变化. 涡旋离轴量的变化会导致能流密度分布的不对称性. 当离心参数增大时, 原点周围黑核会向原点中心移动. 关键词： 双曲余弦高斯涡旋光束 位相奇点 能流密度     

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.     

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.     

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.     

空心高斯涡旋光束的远场特性

基于角谱法和稳相法,推导出了空心高斯涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式,研究了其相位奇点和能流密度分布。结果表明,空心高斯涡旋光束的远场特性主要跟控制参数有关。改变光束中的涡旋离轴量,光涡旋和能流密度黑核会发生移动。圆刃型位错线的半径和能流密度暗环位置跟束腰宽度有关,而能流密度的对称性主要受涡旋离轴量的影响。     

Effect of Coma Aberration on Orbital Angular Momentum Spectrum of Vortex Beams

Spiral spectra of vortex beams with coma aberration are studied. It is shown that the orbital angular momentum （OAM） states of vortex beams with coma aberration are different from those aberration-free vortex beams. Spiral spectra of beams with coma aberration are spreading. It is found that in the presence of coma aberration, the vortex beams contain not only the original OAM component but also other components. A larger coma aberration coefficient and/or a larger beam waist will lead to a wider spreading of the spiral spectrum. The results may have potential applications in information encoding and transmittance.     

高阶贝塞尔-高斯脉冲光束相位奇点的演化

 推导出被光阑衍射高阶贝塞尔-高斯脉冲光束的场和光强分布的解析公式,对其相位奇点的演化特性做了计算和分析。结果表明,高阶贝塞尔-高斯脉冲光束经光阑衍射后,中心光涡旋始终存在,拓扑电荷守恒。随脉冲频率和脉冲宽度增加,等相位线均沿逆时针方向旋转,涡旋核随脉冲频率增加而减小,而脉冲宽度对涡旋核大小几乎无影响。等相位线随截断参数和传输距离的增加分别沿逆时针和顺时针方向旋转,涡旋核大小随截断参数增加而变化,随传输距离和光束阶数的增加而增大。     

高阶贝塞尔-高斯脉冲光束相位奇点的演化

推导出被光阑衍射高阶贝塞尔-高斯脉冲光束的场和光强分布的解析公式,对其相位奇点的演化特性做了计算和分析。结果表明,高阶贝塞尔-高斯脉冲光束经光阑衍射后,中心光涡旋始终存在,拓扑电荷守恒。随脉冲频率和脉冲宽度增加,等相位线均沿逆时针方向旋转,涡旋核随脉冲频率增加而减小,而脉冲宽度对涡旋核大小几乎无影响。等相位线随截断参数和传输距离的增加分别沿逆时针和顺时针方向旋转,涡旋核大小随截断参数增加而变化,随传输距离和光束阶数的增加而增大。     

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.     

Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness

Vortex-wave beams are beams that carry angular momentum. Their specific feature is a ring-like transverse distribution of wave intensity with zero intensity at the axis. A method for generating an ultrasonic vortex beam by combining a single-element transducer and a phase plate with a nonuniform thickness is proposed. The method is examined theoretically and tested experimentally. In the theoretical analysis, the acoustic field was calculated using the Rayleigh integral. Experiments were performed in water with a focusing piezoceramic source with a frequency of the order of 1 MHz; the radiation from it was transmitted through a 12-sector organic-glass phase plate. The beam vorticity was established by setting the correct thickness of sectors. The results of scanning the field with a miniature hydrophone confirmed that the amplitude and phase distributions of the generated wave field were in fact consistent with a vortex beam. The capacity of the obtained beam to induce the rotation of scatterers positioned in the focal region was demonstrated.     

基于双开口谐振环超表面的宽带太赫兹涡旋光束产生

提出了一种基于双开口谐振环单元结构超表面的太赫兹宽带涡旋光束产生器.该结构由金属-电介质两层构成,位于顶层的是基于双开口谐振环单元结构的超表面,底层为介质层.对单元结构阵列进行数值仿真,圆偏振的入射光可以被转换成相应的交叉偏振透射光,通过旋转表层金属谐振环,可以控制交叉偏振透射光具有相同的振幅和不同的相位.这些单元结构按照特定的规律排列,可以形成用以产生不同拓扑荷数的涡旋光束的涡旋相位板.以拓扑荷数1和2为例,设计了两种涡旋相位板,数值分析了圆偏振波垂直入射到该涡旋相位板生成交叉圆偏振涡旋光束的特性.结果表明,在1.39—1.91 THz的频率范围内产生了比较理想的不同拓扑荷数的涡旋光束,且透过率高于20%,最高可达到24%,接近单层透射式超表面的理论极限值.     

Optimal phase steps of multi-level spiral phase plates

We analyze vortex properties of the optical beams generated by a multi-level spiral phase plate (MLSPP) and find that this kind of beams consists of vortex components with topological charges of L − kM, where k is zero or any integer, M is the level number and L is the intrinsic topological charge of the MLSPP. We proved that the orbital angular momentum of the beams generated by a MLSPP reaches its maximum only if the phase steps (or the ratio of M to L) satisfies some special conditions.     

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.     

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。     

4pi聚焦系统中振幅和相位调制的径向偏振涡旋光束聚焦特性的研究

基于Richards-Wolf矢量衍射积分公式, 研究了径向偏振涡旋光束在振幅和相位调制下的4pi聚焦特性.振幅调制是通过振幅滤波实现, 即改变入射光束起始积分值达到调节,相位调制是通过添加相位延迟角δ 的液晶相位延迟器来改变入射光束的偏振态.模拟结果显示,随着振幅的减小, 4pi聚焦系统焦点附近的光轴上呈现出多光球结构; 而相位调制对焦点附近的光强分布产生拉伸作用, 即调节入射光束的拓扑核m和相位延迟器的延迟角δ,可以得到特殊的光强分布. 随着相位δ增大, m=0产生的多光球结构慢慢向光链结构转变,最终变成暗通道;而m=1产生的光链结构慢慢变成光球结构; m=2产生的暗通道变成光球和光链叠加的结构, 这种特殊聚焦光束在光学微操纵领域具有潜在的应用价值. 关键词： 物理光学 偏振 光链 4pi聚焦系统     

Topological defects, geometric phases, and the angular momentum of light

Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Orbital angular momentum (OAM) shift within the light beam has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.     

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.     

STED microscopy based on axially symmetric polarized vortex beams

A stimulated emission depletion(STED) microscopy scheme using axially symmetric polarized vortex beams is proposed based on unique focusing properties of such kinds of beams. The concept of axially symmetric polarized vortex beams is first introduced, and the basic principle about the scheme is described. Simulation results for several typical beams are then shown, including radially polarized vortex beams, azimuthally polarized vortex beams, and high-order axially symmetric polarized vortex beams. The results indicate that sharper doughnut spots and thus higher resolutions can be achieved, showing more flexibility than previous schemes based on flexible modulation of both phase and polarization for incident beams.