The refined theory of transversely isotropic piezoelectric rectangular beams

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.     

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。     

特殊关联结构光束的大气传输研究进展

近年来,光场调控逐渐成为光学领域的热点研究课题,光场相干性调控可以引发许多新颖物理效应。其中,通过相干性调控得到的特殊关联结构光束不仅展现出奇特的传输特性,而且可以有效地降低大气湍流引起的光强退化、光束漂移、光强闪烁和退偏振等负面效应。因此,特殊关联结构光束在自由空间光通信领域具有重要的应用前景。本文回顾了特殊关联结构光束的构建基础理论和大气传输研究方法及其发展历程,举例展示近些年典型特殊关联结构光束的大气传输研究成果。     

一种含时贝塞尔光束的理论性质研究

本文从理论角度提出了一种"含时贝塞尔光束"的概念.在非傍轴和非时谐条件下,直接从麦克斯韦方程出发,借鉴半贝塞尔光束的处理方法,同时引入第四维虚数坐标,由此获得了完整的"含时贝塞尔光束"的解析表达式.并从无衍射性质和时空特性两个方面对其进行了探讨和研究,发现该光束具有如下性质:符合贝塞尔光束类型的无衍射特征;在时空双曲线上强度保持不变;光波时空特性的临界条件类似于相对论中的光锥."含时贝塞尔光束"的概念为无衍射自加速光束的研究开拓了新的思路和方向.     

The Transverse Oscillation of Coaxial Multiple Beams Propagating along a Magnetic Field in a Vacuum Tube

A fluid Maxwell theory has been derived to study a system of multibeams propagating parallel to an applied axial magnetic field in an evacuated conducting drift tube. The stability analysis is performed for a rigid-rotor and cold-laminar flow equilibria. It is assumed that the particle beams are tenuous and the guiding field is very strong. As a result, the perturbation theory is derived under the condition that the plasma frequency is much smaller than the cyclotron frequency for each beam particle. A dispersion relation is obtained for a special case of sharp-boundary density profiles. The stability properties of infinitely long beams are illustrated in detail for different geometries and various beam parameters. The results agree with those obtained by Uhm [8] in a special case where a solid electron beam propagates through an annular electron beam. The finite geometry effect of the accelerator is discussed briefly. It might have a substantial influence on the behavior of a real device.     

直流固态继电器电磁脉冲失效模式实验研究

采用电流注入法对某型直流固态继电器输入端与输出端的电磁脉冲损伤机制及失效模式进行了实验研究,结果表明:输入端注入电磁脉冲信号时,输出端会产生误动作,并可造成输入电路中三极管BE节产生短路损伤,导致输入端施加控制信号时输出端无法导通;输出端注入电磁脉冲信号时,可造成输出电路中MOSFET管的栅极和漏极产生短路损伤,导致输出端短路。     

被动方式产生近似无衍射贝塞尔光技术

无衍射光束具有中心光斑小且不随传播距离变化、自再现、产生局域空心光等特点,由于这些特殊的光束特性而在许多领域,如计量学,经典光学,非线性光学和生命科学等领域中得到广泛的应用。无衍射光束的产生与变换是目前的一个研究热点。通过衍射理论、干涉理论和几何光学方法可对无衍射光进行描述。实现无衍射贝塞尔光束的方法可分为主动式和被动式。本文主要综述地介绍了几种被动式产生近似无衍射贝塞尔光束的最新技术,通过分析其优缺点,给出了这些技术的适用范围。     

基于调制光束的空间相干性获得局域空心光束

 通过调制部分相干光的空间相干性,实现了局域空心光束的产生。理论上根据范西泰特-策尼克定理及标量衍射积分,构造出具有一定空间相干性的部分相干光,并研究其聚焦特性。实验上采用理论上要求的光学系统来构造具有特定空间相干性的部分相干光,并采用薄透镜聚焦部分相干光。研究表明,当构造出的部分相干光经透镜聚焦,可得到局域空心光束。研究了光学系统的参数及透镜焦距对产生局域空心光束的影响,结果显示：光阑的拦截比及透镜的焦距越大,获得的空心光束的尺寸就越大。     

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     

Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

A general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading is investigated using Timoshenko and high-order shear deformation theory. It is assumed that the set beams of the system are simply supported and continuously joined by a Winkler elastic layer. The model of beam includes the effects of axial loading, shear deformation and rotary inertia. In the special case of identical beams, explicit expressions for the natural frequencies and the critical buckling load are determined using a trigonometric method. The influences of the compressive axial loading and the number of beams in the system on the natural frequencies and the critical buckling load are discussed. These results are of considerable practical interest and have wide application in engineering practice of frameworks.     

Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere

The polychromatic partially coherent electromagnetic Cosh-Gaussian (EChG) beam is introduced and taken as a typical example of polychromatic partially coherent electromagnetic beams. Based on the unified theory of coherence and polarization, the expressions for the spectrum and the degree of polarization of polychromatic partially coherent EChG beams in the turbulent atmosphere are derived, and the conditions for keeping polarization invariance and for determining the position where the degree of polarization becomes zero along the propagation path are also given. It is shown that the normalized spectrum is close to the normalized source spectrum due to turbulence. The reasonable physical explanation of spectral shift is given. On the other hand, the bandwidth does not affect the degree of polarization, and the degree of polarization tends to the value at the source plane due to turbulence in the long-propagation distance limit. The spectrum and polarization of polychromatic electromagnetic Gaussian Schell-model (EGSM) beams and electromagnetic Gaussian (EG) beams in turbulence are treated as special cases of polychromatic partially coherent EChG beams.     

柱坐标系中截断光束的广义M2因子

推导出截断圆对称光束二阶矩的传输方程，它们与无截断光束的二阶矩满足相似的传输定律.因此，基于广义截断二阶矩方法，将直角坐标系中截断二维光束的二阶矩特征参数推广到柱坐标系中的截断圆对称光束，类似方法定义的广义M²因子（M²_G因子）是一个传输不变量.对理论的自洽性作了物理解释.推导出柱坐标系中截断超高斯光束的二阶矩参数和M²_G因子.对一些有意义的特殊情况作了讨论，并以数值计算例作了说明. 关键词： 光束描述 截断光束 圆对称性 广义截断二阶矩(GTSM) 2因子（M²_G因子）')" href="#">广义M²因子（M²_G因子）     

Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems. IV. Plane waves

This paper is the fourth of a series devoted to the transformation of beam shape coefficients through rotations of coordinate systems. These coefficients are required to express electromagnetic fields of laser beams in expanded forms, for instance for use in some generalized Lorenz-Mie theories. The main result of Part I has been the theorem of transformation of beam shape coefficients under rotations. Part II dealt with the special case of on-axis axisymmetric beams. Part III dealt with other special cases, namely when the Euler angles specifying the rotation are given some special values. The present Part IV studies another special case, namely the one of plane waves viewed as special on-axis axisymmetric beams, and can therefore be viewed as a special case of Part II. Unexpectedly, it is found that, in general, although plane waves are fairly trivial, their expansions require using non trivial beam shape coefficients, exactly as required when dealing with arbitrary shaped beams.     

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     

Partially coherent non-paraxial vectorial Hermite-Gaussian beams and their far-field properities

The far-field theory of partially coherent vectorial non-paraxial beams is expanded and their analytical propagation expressions of the Wigner distribution function matrices and the cross-spectral-density matrices in free space are derived using the far-field approximation. Some interesting cases, in particular the vectorial non-paraxial partially coherent Hermite-Gaussian (HG) beams, are discussed and treated as special cases of our general expressions. It is shown that the f_σ and f parameters play an important role in determining vector and non-paraxiality of partially coherent HG beams. When two parameters are small enough, scalar and paraxial vectorial approximation is allowed; otherwise, non-paraxial vectorial approximation is applied. But the decided parameters additionally affect their far-field divergence angles.     

Phase-flipped Hermite-Gaussian beams and their propagation beyond the paraxial approximation

An extension of phase-flipped Gaussian (PFG) beams to the multi-mode nonparaxial case is made. The recurrence propagation expressions for phase-flipped Hermite-Gaussian (PFHG) beams beyond the paraxial approximation are derived and used to study nonparaxial propagation properties of PFHG beams in free space and through a knife edge and an aperture, and to compare nonparaxial results with paraxial ones. The propagation of paraxial PFHG beams and PFG beams and nonparaxial PFG beams is treated as special cases of nonparaxial PFHG beams. Numerical examples are given to illustrate the theoretical results.     

Propagation of the Wigner distribution function for partially coherent nonparaxial beams

On the basis of the Rayleigh-Sommerfeld diffraction integral, a closed-form propagation expression for the Wigner distribution function of partially coherent nonparaxial beams in free space is derived for what is to our knowledge the first time. The propagation of spatially fully coherent nonparaxial beams is treated as a special case of our general result. Application of the result is illustrated with the nonparaxial propagation of partially coherent anisotropic Gaussian-Schell-model beams and TEM11-mode Hermite-Gaussian beams.     

Fourier treatment of near-field synchrotron radiation theory

In this paper, we couple synchrotron radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical situations (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual “waist” where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions.     

Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature.     

用傅里叶分析法研究艾里光束远场传播特性

为了从理论上深入分析新型无衍射光束艾里光束在有限能量条件下的远场传播特性,首先,从决定光波在自由空间传播的一维旁轴波动方程入手,采用傅里叶分析法,结合艾里函数的特殊性质,并利用经过指数衰减的有限能量初始条件,完整给出了有限能量条件下用于精确描述一维艾里光束在自由空间传播特性的波动方程解析解.然后,利用所得到解析解分别对一维和二维艾里光束在自由空间的传播特性进行了研究,重点分析了不同参量条件对艾里光束进行无衍射传播和横向自加速的影响.研究表明:当任意横向尺度为100μm,衰减系数为0.03、0.05、0.07、0.1、0.2时,二维艾里光束无衍射传播距离分别为1 014、624、455、338、193mm;当横向尺度保持不变时,衰减系数越小,艾里光束保持无衍射传播的距离越大;当衰减系数保持不变时,横向尺度越小,艾里光束横向自加速越大.所采用的研究方法也可用于研究艾里光束在介质中的传播特性.