A detailed study of Mathieu-Gauss beams propagation through an apertured ABCD optical system

Using Collins formula and the expansion of Mathieu beams in terms of Bessel beams we derive the exact propagation equations of Mathieu-Gauss beams through an apertured paraxial ABCD optical system. A comparison between the exact propagation equations and the approximated ones, which are derived by expanding the circ function into a finite sum of Gaussian functions, is presented. The propagation characteristics of zeroth-order Mathieu-Gauss beams in (y-z) and (x-z) planes are analyzed with detailed numerical calculations. It is found that the profile of the propagated Mathieu-Gauss beam is similar to that of Bessel-Gauss beam. Furthermore, the focalization of the Mathieu-Gauss beams through a thin lens is illustrated and analyzed with numerical results.     

Vector Helmholtz-Gauss and vector Laplace-Gauss beams

We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.     

Flat-topped Mathieu-Gauss beam and its transformation by paraxial optical systems

In order to avoid the severe axial intensity oscillations which appear when an ideal Mathieu beam is truncated, we propose to modulate it by a flattened multi-Gaussian envelope. The obtained beam, which is referred as flattened Mathieu-Gauss (FTMG) beam, can be expanded into a finite series of Mathieu-Gauss beams with various waists. The propagation study of this beam reveals that the axial intensity is unchanged within a certain propagation distance as for super-Gaussian-Bessel beams or Gori’s flattened Bessel beams. By using Collins formula, we derive closed-form expressions of FTMG beam propagating through a paraxial axisymmetric ABCD optical system. Some numerical calculations and discussions are also given.     

Focal shift and focal switch of flat-topped Mathieu-Gaussian beams passing through an apertured lens system

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression predominating the distribution of axial intensity for the flat-topped Mathieu-Gauss (FTMG) beams passing through a system with the aperture and lens separated has been derived. The focal shift and the focal switch effect of FTMG beams passing through the system is studied in detail. Numerical calculations have shown that the position of real focal plane is not coincident with the geometrical focus but is somewhat shifted toward the lens. The focal shift and focal switch of FTMG beams take place when the relative separation s/f = 1 by a suitable choice of beam parameter and truncation parameter, for example, the beam parameter is smaller than its corresponding critical value or the truncation parameter is between its two corresponding critical values.     

柱矢量光束在透射时的自旋霍尔效应

有限光束矢量特性可以由全局化的特征单位矢量和广义琼斯矢量完整地描述,特征单位矢量平行于传播轴的光束为柱矢量光束。通过这种表示理论描述了在近轴近似条件下柱矢量光束的透射情况。在透射过程中光束的特征单位矢量发生了变化,透射光束的特征单位矢量既不平行于传播轴,也不垂直于传播轴。特征单位矢量的变化导致光束产生了一个与入射面垂直的横向位移,同时这个横向位移和光束的偏振椭圆率有关,不同圆偏振态(左旋和右旋)的透射光束所产生的横向位移的方向相反。这一结果和近年来在实验中检测到的均匀偏振光束的自旋霍尔效应类似,表明柱矢量光束在透射过程后也会产生光的自旋霍尔效应。     

Circular beams

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams; Bessel-Gauss beams; hypergeometric beams; hypergeometric-Gaussian beams; fractional-order elegant Laguerre-Gauss beams; quadratic Bessel-Gauss beams; and optical vortex beams.     

Propagation of cylindrical vector beams in a turbulent atmosphere

<正>Based on the extended Huygens-Presnel principle,the propagation of cylindrical vector beams in a turbulent atmosphere is investigated.The intensity distribution and the polarization degree of beams on propagation are studied. It is found that the beam profile has a Gaussian shape under the influence of the atmospheric turbulence,and the polarization distribution shows a dip in the cross section as the beam propagates in the turbulent atmosphere.It is also found that the beam profile and the polarization distribution are closely related to beam parameter and atmospheric turbulence.     

Mathieu-Gauss beams: A thermal consideration

The generation of Helmholtz-Gauss beam families such as Mathieu-Gauss (MG) and Bessel-Gauss (BG) beams can be dramatically suffered from heat-induced thermal effects. This work is devoted to the generation of MG beams under severe induced thermal loads. The output MG beams of a solid-state laser were assumed to pass through an ABCD system matrix. The simulated results which were achieved by characterization of the transfer matrix of the thermally affected inhomogeneous medium report systematic variations of the intensity profile of MG beams from pump power of 1-5 W. It is shown that for high values of pump power, the thermal effects are so influential and the beam intensity profile is so changed that the identification of MG beams is not easily possible at first hand. The results can facilitate this identification and can be utilized for deeper understanding of thermal effects phenomena.     

轴对称矢量光束聚焦特性研究现状及其应用

轴对称矢量光束是一种空间非均匀偏振光束, 中心光强为零, 经物镜聚焦后能在焦点附近产生空间场分量. 在高变迹系数光学系统成像情况下, 与线偏光、圆偏光相比, 径向偏振光与光瞳滤波技术及图像复原技术结合, 能获得较小焦斑, 提高横向分辨力. 介绍了轴对称矢量光束的特性, 基于电偶极子辐射模型和矢量衍射理论研究了轴对称矢量光束经高数值孔径物镜聚焦后的特性, 系统介绍了基于轴对称矢量光束实现光斑紧聚焦的几种方法, 并简述了轴对称矢量光束在差动共焦超分辨成像领域的研究设想. 关键词： 差动共焦显微技术 紧聚焦 光瞳滤波 轴对称矢量光束     

基于扭曲向列液晶空间光调制器的矢量光生成

基于扭曲向列型液晶空间光调制器的旋光特性, 根据空间光调制器所加电压和加载相位与旋光角度的对应关系, 设计了可以生成多种涡旋矢量光的通用光路. 利用该原理和光路系统, 在实验上生成了多种携带轴对称相位的矢量光以及图案般复杂的矢量光, 观察和检测了它们的偏振特性, 获得了较好的实验结果. 并且模拟了具有涡旋相位的矢量光的紧聚焦场, 分析了它们的紧聚焦特性. 由于这种生成矢量光的方法光路装置简单、操作容易, 产生矢量光的过程中几乎不损失能量, 并且不存在聚焦过程, 因此在如强激光矢量光束与物质相互作用、激光加速等方面具有重要的应用潜力.     

Propagation of self-trapped circular beams in strongly nonlocal nonlinear media

A very general family of self-trapped circular beams (CiBs) in circular cylindrical coordinates is presented in strongly nonlocal nonlinear media. The complex amplitude of the CiBs is depicted by the product of the Whittaker functions and the Gaussian function, and is characterized by two parameters. Special cases of the CiBs and the even and odd mode CiBs are the standard, elegant, and generalized Laguerre-Gaussian beams and the even and odd mode standard, elegant, and generalized Laguerre-Gaussian beams.     

Electromagnetic wave beam propagation through a chiral slab

A general scheme for investigating the electromagnetic wave beam reflection by and transmission through a chiral slab is proposed. The electromagnetic wave beams within different regions are described by appropriate cylindrical vector wave function expansions, and their expansion coefficients are determined by using the boundary conditions and projection method. Under illumination by a fundamental Gaussian beam, a Hermite–Gaussian beam and a doughnut mode beam, numerical results of the normalized field intensity distributions are provided and discussed briefly.     

环状光束通过透镜的聚焦特性研究

给出了环状光束在柱坐标系下的一种描述模型,并利用广义衍射积分理论,推导出环状光束经过近轴ABCD光学系统的传输公式.在此基础上,通过数值模拟方法定量分析了环状光束的聚焦光强分布以及焦面处的桶中功率.研究结果表明,环状光束的聚焦特性与光束阶数以及系统菲涅耳数有关;环状光束在实际焦面和几何焦面上的桶中功率均随着遮拦比的增大而降低,而随着系统菲涅耳数的增大而增大.在实际工作中,通过合理地选取系统菲涅耳数和光束遮拦比可以有效地控制环状光束聚焦后的光束质量.     

Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures

The propagation properties of Bessel beam is a meaningful research. In this paper, based on the expanding the hard-edged circular aperture as a finite sum of complex Gaussian functions and the scalar diffraction theory, an approximate analytical solution for Bessel beam propagating through a fractional Fourier transform system is derived in the cylindrical coordinates. Then, the detailed numerical calculation for Bessel beam is presented. The simulation also shows that the beam parameter and the order of fractional Fourier transform result in the change of field distribution, including location, intensity and width.     

拉盖尔-高斯光束在界面反射和折射的质心偏移特性研究

在圆柱坐标系中研究了傍轴线偏振拉盖尔-高斯光束在两种各向同性介质界面反射和折射后光强质心的偏移. 基于菲涅耳近似和泰勒级数展开,分别得到了部分反射和全反射两种情形下,质心的横向偏移和纵向偏移与光束拓扑荷的解析关系式. 研究表明,部分反射时,反射和折射光束的横向偏移的大小与光束的拓扑荷成正比,方向由拓扑荷的符号决定;而纵向偏移仅仅大小与光束的拓扑荷有关. 全反射时,反射光束质心偏移不受拓扑荷影响. 通过数值模拟验证了解析结果的正确性,并得到了解析公式的适用条件. 拉盖尔-高斯光束的质心偏移特性可应用于测量光 关键词： 拉盖尔-高斯光束 横向偏移 纵向偏移 拓扑荷     

高阶邦加球上柱矢量光束的变换

本文从理论和实验上系统研究了利用半波片实现高阶邦加球上柱矢量光束变换的方法.通过琼斯矩阵的方法理论分析得出变换前后柱矢量光束在高阶邦加球上两个对应点的纬度相反,经度随半波片的光轴方向角的不同而改变.最后,基于空间光调制器搭建了一套柱矢量光束产生及其变换系统,实验结果证明了这种方法的可行性.     

柱矢量光束的角动量性质

介绍了非近轴光束的表示理论,利用该表示理论很好地解决了非近轴光束的角动量问题,发现非近轴光束的总角动量可以严格地分解成自旋和轨道两部分,但是两者都依赖于由偏振椭圆度表征的光束的偏振状态。主要研究了柱矢量光束的角动量问题。给出了动量空间和位形空间中的柱矢量光束表达式和角动量算符表达式。通过分析两个空间中的角动量算符及柱矢量光束表达式,发现在这两种空间中,具有螺旋型相位的柱矢量光束是角动量算符沿着传播方向的分量的本征态,其本征值与偏振椭圆度无关,这为计算这类特殊光束的角动量提供了一种新方法。     

三环非均匀混合偏振同轴矢量光束的聚焦特性

基于Richards-Wolf矢量衍射积分公式,数值分析了同轴三环非均匀混合偏振矢量光束经过高数值孔径透镜的聚焦特性。该矢量光束由同轴三环局域线偏振矢量光束通过一个相位延迟角为δ的液晶相位延迟器产生,光束偏振变为包含线偏振、圆偏振和椭圆偏振的混合态。同轴三环局域线偏振矢量光束的偏振分布是由径向向内偏振的外环光束、径向向外偏振的内环光束和线偏振方向与径向方向夹角为φ2的中环光束构成。数值模拟结果显示该混合偏振矢量光束的聚焦强度分布与参数φ2和相位延迟角δ密切相关,当选取适当的φ2和δ时,在焦平面附近产生沿光轴方向的三维多点光俘获结构——暗光链,这在光学微操纵领域具有潜在的应用价值。     

基于格林函数法的奇型Mathieu-Gaussian光束

根据光束传播的独立性和叠加性原理,引入了一组能够产生第一类(2n+2阶)奇型Mathieu-Gaussian光束的虚光源点.利用虚源点技术和格林函数法,计算得到第一类奇型Mathieu-Gaussian光束的严格解析积分表达式.利用该表达式得到了轴上光场分布的积分解析解.以三阶非旁轴修正为例,得到了第一类奇型Mathieu-Gaussian光束保留到三阶非旁轴修正项的轴上光场分布精确解.     

Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system

The properties of Bessel-Gaussian beams (BGBs) and Bessel beams (BBs) propagating through a fractional Fourier transform (FRT) optical system have been investigated. The analytical transformation formulae for BBs and BGBs propagation through a FRT optical system are derived based on definition of the FRT in the cylindrical coordinate system. By using the derived formula, numerical examples are illustrated.