Analytical vectorial structure of an apertured hollow Gaussian beam in the far field

Based on the vector angular-spectrum and the complex Gaussian expansion of the aperture function, the structure of an apertured hollow Gaussian beam in the far field is given in a integral form. In virtue of the method of stationary phase approximation, the analytical vectorial structures are derived. Starting from the analytical expressions, the propagation properties of apertured hollow Gaussian beams with different order in the far field are illustrated graphically. In addition, the influence of the truncation parameter on far field distribution is studied detailedly. This research can shed light on the further understanding of the vectorial property of an apertured hollow Gaussian beam.     

Analytical vectorial structure of the anomalous hollow beam in the far field

On the basis of the vector angular spectrum representation of the Maxwell equations and the method of stationary phase, the analytical vectorial structure of an anomalous hollow beam in free space is presented. The energy flux distributions of the anomalous hollow beam, its TE and TM terms in the far field are investigated. The analytical results are analyzed with numerical examples.     

Elegant Laguerre-Gaussian beam in a turbulent atmosphere

Paraxial propagation of an elegant Laguerre-Gaussian beam (ELGB) in a turbulent atmosphere is investigated in detail. Analytical formulae for the average intensity and effective beam size of an ELGB in a turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The average intensity and spreading properties of an ELGB in a turbulent atmosphere are studied numerically and compared with those of a standard Laguerre-Gaussian beam (SLGB). Our results indicate that the propagation properties of an ELGB in a turbulent atmosphere are much different from its properties in free space, and are closely related to its beam parameters and the structure constant of the atmospheric turbulence. The ELGB with higher mode orders is less affected by the turbulence. The SLGB spreads more rapidly than the ELGB in a turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications. ©2010 Elsevier Science B.V. All rights reserved.     

非傍轴矢量拉盖尔-高斯光束的二阶矩表示

基于Porras提出的光传输的非傍轴矢量矩理论，推导出初始圆偏振的非傍轴矢量拉盖尔-高斯(LG)光束的特征参数，包括束宽、远场发散角和M²因子等的公式，并表示为级数求和形式.非傍轴矢量高斯光束公式作为特例给出.研究表明，基于二阶矩定义的束宽按双曲线规律传输，当w₀/λ→0(w₀为束宽，λ为波长)时，远场发散角θ趋于90°，大于非傍轴标量理论预示的值63.435°.非傍轴矢量LG光束的M²因子不仅与模指数p有关，而且还与w₀/λ有关.最后，对非傍轴矢量LG光束和非傍轴标量LG光束的传输作了比较，结果表明在w₀/λ较小时，矢量效应对远场发散角的影响十分显著.对θ→90°引起的问题和非傍轴矢量矩理论的适用范围，以及解决问题的可能途径作了分析和讨论. 关键词： 非傍轴矢量拉盖尔-高斯光束 圆偏振 非傍轴矢量矩理论 光束参数     

拉盖尔-高斯光束的近场矢量结构特征

直接以麦克斯韦方程组的解表征拉盖尔-高斯光束。基于麦克斯韦方程组解的矢量角谱表述和电磁光束的矢量结构理论,利用一些数学技巧导出了拉盖尔-高斯光束的TE项和TM项在近场的解析表达式。利用所导出的公式,在近场描绘了拉盖尔-高斯光束的TE项、TM项及整个光束的光强分布。并对角度依赖分别为余弦和正弦关系的拉盖尔-高斯光束的矢量结构进行了比较,结果显示两者整个光束的光斑完全相似,唯一的区别是子瓣的空间方位不同且两者的内部矢量结构完全不相同。     

拉盖尔-高斯光束的近场矢量结构特征

直接以麦克斯韦方程组的解表征拉盖尔-高斯光束。基于麦克斯韦方程组解的矢量角谱表述和电磁光束的矢量结构理论,利用一些数学技巧导出了拉盖尔-高斯光束的TE项和TM项在近场的解析表达式。利用所导出的公式,在近场描绘了拉盖尔-高斯光束的TE项、TM项及整个光束的光强分布。并对角度依赖分别为余弦和正弦关系的拉盖尔-高斯光束的矢量结构进行了比较,结果显示两者整个光束的光斑完全相似,唯一的区别是子瓣的空间方位不同且两者的内部矢量结构完全不相同。     

均匀椭球粒子对拉盖尔-高斯光束的散射特性研究

基于广义Mie理论, 研究了椭球粒子对在轴入射的拉盖尔-高斯光束的散射特性. 通过局域近似法求解椭球坐标系中的波束因子, 计算得到了波束因子之间满足的普遍关系. 对散射强度随椭球粒子不同尺寸参数和扁圆程度的变化特性进行了数值计算, 并针对不同拓扑荷时的散射强度进行了对比分析. 结果表明: 当椭球粒子尺寸在与入射光波长可比拟的范围内变化时, 散射强度随尺寸参数的增大而增大, 随椭球长短轴之比和拓扑荷的增大而减小. 本文的理论研究能够为拉盖尔-高斯光束在粒径测量、大气激光通信、 大气遥感等领域的应用提供更准确的粒子模型和参考价值. 关键词： 椭球粒子 拉盖尔-高斯光束 波束因子 散射强度     

Vectorial structure of the far-field of an apertured four-petal Gaussian beam

Based on the theorem of vectorial structure and the method of stationary phase, an analytical vectorial structure of the far-field of an apertured four-petal Gaussian beam has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured four-petal Gaussian beam are also presented in the far-field reference plane, respectively. The energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam are graphically demonstrated in the far-field plane. The dependences of the energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam on the f-parameter, the truncation parameter, and the beam order are also examined.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.     

相位片角向衍射产生拉盖尔-高斯光束的实验研究

设计了一种角向分布的相位片,利用离子束刻蚀技术加工成0和π二级的相位片.利用角向衍射理论对相位片的衍射场分析表明,衍射场为拓扑指数相反的两束拉盖尔-高斯光束的叠加场.用直径为4 mm的近平行光照射相位片,获得径向指数为零,拓扑荷相反的叠加拉盖尔-高斯光场.采用较大孔径的光束入射时,仍为拓扑荷相反的两束光的叠加,但径向指数会发生变化. 关键词： 信息光学 拉盖尔-高斯光束 相位片 离子束刻蚀     

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Rayleigh--Sommerfeld integral formula and the complex Gaussian expansion of the hard-edge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.     

Propagation of vectorial apertured cosh-Gaussian beams beyond the paraxial approximation

By using the vectorial Rayleigh-Sommerfeld diffraction integrals, the propagation equation of vectorial nonparaxial cosh-Gaussian (ChG) beams in the presence of an aperture is derived and expressed in a closed form. The on-axis, far-field and paraxial cases are studied as special cases. Analytical results are illustrated with numerical examples.     

Analytical vectorial structure of Laguerre-Gaussian beam in the far field

Based on the vector angular spectrum of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Laguerre-Gaussian beam has been presented in the far field. According to the analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are investigated in the far field, respectively. The formulas obtained are applicable not only to the paraxial case, but also to the nonparaxial case. The physical pictures of Laguerre-Gaussian beams are well illustrated from the vectorial structure, which may provide a new approach to manipulate laser beams.     

Propagation of vectorial Gaussian beams behind a circular aperture

Based on the vectorial Rayleigh diffraction integral and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian functions, an approximate analytical expression for the propagation equation of vectorial Gaussian beams diffracted at a circular aperture is derived and some special cases are discussed. By using the approximate analytical formula and diffraction integral formula, some numerical simulation comparisons are done, and some special cases are discussed. We find that a circular aperture can produce the focusing effect but the beam becomes the shape of ellipse in the Fresnel region. When the Fresnel number is equal to unity, the beam is circular and the focused spot reaches a minimum.     

基于拉盖尔-高斯光束的通信系统在非Kolmogorov湍流中传输的系统容量

涡旋波束在大气湍流中的传输有非常重要的理论研究和实际应用意义. 本文基于利托夫近似和广义惠更斯-菲涅耳原理, 推导出拉盖尔-高斯(LG)光束在非Kolmogorov湍流中斜程传输时的螺旋谱, 并进一步推导出系统的容量. 对基于LG光束的通信系统容量进行了数值计算, 并对指数参数、光束波长、天顶角、湍流内尺度、外尺度、结构常数对系统容量的影响进行了分析比较. 本文的结论能够为LG光束在非Kolmogorov湍流中的通信提供一定的参考价值. 关键词： 拉盖尔-高斯光束 非Kolmogorov湍流 平均容量     

利用振幅光栅生成拉盖尔-高斯光束的实验研究

拉盖尔高斯(Laguerre-Gaussian,LG)光束由于其独特的相位结构和轨道角动量特性在微粒旋转操纵和信息处理等方面得到了越来越多的重视.对利用振幅型叉状衍射光栅产生LG光束进行了理论分析,采用计算全息图的方法制作了振幅型叉状衍射光栅,实验上获得了角量子数为±1的LG光束,并对光束变换过程中影响光束特性的主要因素进行了讨论. 关键词： 信息光学 拉盖尔高斯光束 计算全息光栅 光束轨道角动量     

在大气湍流斜程传输中拉盖高斯光束的轨道角动量的研究

大气湍流引起大气折射率随机变化,导致空间不均匀性.拉盖高斯光束在大气湍流中传输时,空间不均匀性会使光子波函数改变,引起轨道角动量的变化.本文讨论了拉盖尔高斯光束在大气斜程传输时,湍流介质改变光子轨道角动量而形成不同的光子态.计算了螺旋谐波各分量所占光束总能量的权重,分析了拉盖高斯光束的轨道角动量的变化规律.     

Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma

In this paper, diffraction pattern of a vortex carrying beam with a Gaussian background has been studied by using Fresnel-Kirchhoff diffraction integral, in the presence of third-order coma. Results of intensity distribution and encircled energy at the Gaussian plane have been presented for two values of the topological charge. Positional shift and splitting of the dark core have been investigated in detail. It is noticed that the diffraction pattern of a beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We have also verified our results by using the optical transfer function approach. Propagation of an apertured Gaussian background vortex beam through a π-phase shifter has also been studied for two values of the topological charge.