数值法研究光的圆孔衍射实验现象

在平行平面波近似的情况下,数值法求解菲涅耳-基尔霍夫衍射积分公式,得到平行平面光波通过圆孔衍射后的光强分布图.通过对纵向及横向光强分布图的数值分析,验证了轴上点光强由菲涅耳数决定,菲涅耳数大于1时为菲涅耳衍射区,菲涅耳数小于1时为夫琅禾费衍射区.在近场,光强分布为明暗相间的环形条纹;在远场,光束演化成束腰位置在圆孔处的高斯光束,仿真结果与理论和实验结果基本一致.本仿真结果将光衍射的抽象理论直观化、可视化.     

高斯光束菲涅耳圆孔衍射轴上的光强分布

本文从惠更斯－菲涅耳原理的数学表达式出发，在菲涅耳圆孔衍射的情况下求出了高斯光束入射时轴上光强分布的解析表达式，并对比平面波和球面波入射的情况进行了分折讨论．     

高斯光束圆孔衍射光强分布的解析解

本文从菲涅尔-基尔霍夫衍射公式出发,结合贝塞耳函数等特殊函数的性质,计算了正入射高斯光束圆孔衍射的光强分布,并以洛默尔函数的形式表示了焦点附近的光强分布.之后选取了几何焦平面、光轴以及几何阴影区域边界这三个特殊区域,理论结合数值方法给出了光强分布的解析表达式以及数值结果,并发现高斯光束束腰半径越小,艾里斑半径越大,同时焦深也越大.最后计算了焦平面上的光强积分强度,结果表明束腰半径越小,光强就越向中心集中.同时高斯光束相较于平面波的衍射,不会改变光强分布的整体轮廓,但会使得光强向焦点处集中.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

余弦平方高斯光束通过无光栏透镜的梯度力

基于Collins公式推导了余弦平方高斯光束通过无光栏透镜光学系统聚焦后的光强分布及梯度力,采用数值模拟分析梯度力分布及光阱的数量、位置及尺度随光束参数、光束入射距离及系统菲涅耳数的变化。结果表明:光束相关参数b越大光阱的数量越多,光阱的位置随光束入射距离而改变,大小随系统菲涅耳数的增加而减小,但不影响其位置。     

初级球差对矢量柱状贝塞耳-高斯光束聚焦场的影响

通过柱坐标下的的分析方法,获得径向偏振和方位角偏振贝塞耳-高斯光束经具有球差的高数值孔径系统聚焦后的三维光场分布函数,根据光场分布函数模拟了不同球差系数下贝塞耳-高斯光束在焦平面和通过焦点的纵向切面上的光场分布.结果表明,在球差系数增加时,方位角偏振贝塞耳-高斯光束在焦平面上的圆环状光斑内半径逐渐变小到趋于恒定,而外环半径先减小后增大;而衍射焦点偏离高斯焦点的距离越来越大,纵向光强不再对衍射焦平面呈对称分布,调整离焦距离无法完全消除球差的影响;径向偏振贝塞耳-高斯光束会聚场的光强随初级球差的变化规律与方位角偏振贝塞耳-高斯光束的一致.     

用环围功率法研究双曲正弦高斯光束的焦移

 从Collins公式出发研究了无光阑双曲正弦高斯光束的聚焦特性。研究发现聚焦双曲正弦高斯光束的轴上光强为零，因此Li和Wolf二人研究焦移的方法不再适用。使用环围功率法定义束宽和实际焦面，由此可以决定聚焦双曲正弦高斯光束的焦移。数值计算表明，聚焦双曲正弦高斯光束的焦移与偏心参数和菲涅耳数有关，焦移随偏心参数和菲涅耳数的减小而增大。此外，还分析了双曲正弦高斯光束的最佳聚焦问题。     

双曲正弦-高斯光束的像散透镜聚焦性质与暗空心光束产生

基于广义惠更斯-菲涅耳衍射积分公式,推导了双曲正弦-高斯光束通过像散透镜聚焦的场分布解析表达式,并用数值计算研究了双曲正弦-高斯光束在像散透镜焦平面上或焦平面附近的光强分布与相位特性。理论分析与数值计算结果表明,选择适当的光束参数与像散透镜结构参数,可以使双曲正弦-高斯光束经像散透镜后转换为具有涡旋的暗空心光束,其拓扑荷指数为1。此外,还对影响场强度分布与相位分布的光束参数与透镜参数进行了分析讨论。特别地,透镜的像散是双曲正弦-高斯光束经像散透镜聚焦产生暗空心涡旋光束的关键控制因素,利用合适的像散透镜可获得相当长度的理想暗空心光管。     

复变几何光学

本文在复平面上描述高斯光束的特性，并利用复数分式线性变换及其几何反演点对研究高斯光束的传输与变换，推导出几何光学的高斯光束类牛顿公式和类高斯公式，同时阐明了高斯光束菲涅耳数与焦移概念的本性．     

拉盖尔高斯光的衍射和轨道角动量的弥散

根据菲涅耳衍射积分和拉盖尔高斯光束场强分布,对拉盖高斯光束中的圆孔衍射、单缝衍射和方孔衍射进行了研究,并分析了拉盖高斯光束的相位结构对光束衍射后场分布的影响。拉盖高斯光束的相位奇点落在衍射孔中心时,由螺旋谱计算出拉盖高斯光束通过单缝和方孔衍射后的轨道角动量的弥散程度,从理论上证明了拉盖尔高斯光束通过圆孔衍射后,轨道角动量不发生弥散。     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Experimental realization of an optical one-way barrier for neutral atoms

We demonstrate an asymmetric optical potential barrier for ultracold 87Rb atoms using laser light tuned near the D2 optical transition. Such a one-way barrier, where atoms incident on one side are transmitted but reflected from the other, is a realization of Maxwell's demon and has important implications for cooling atoms and molecules not amenable to standard laser-cooling techniques. In our experiment, atoms are confined to a far-detuned dipole trap consisting of a single focused Gaussian beam, which is divided near the focus by the barrier. The one-way barrier consists of two focused laser beams oriented almost normal to the dipole-trap axis. The first beam is tuned to present either a potential well or barrier, depending on the state of the incident atoms. On the reflecting side of the barrier, the second beam optically pumps the atoms to the reflecting (barrier) state, thus producing the asymmetry.     

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.     

Generation of the basis sets for multi-Gaussian ultrasonic beam models--an overview

By using a small number of Gaussian basis functions, one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of Gaussian beams. Since Gaussian beams can be transmitted through complex geometries and media, such multi-Gaussian beam models have become powerful simulation tools. In previous studies the basis function expansion coefficients of multi-Gaussian beam models have been obtained by both spatial domain and k-space domain methods. Here, we will give an overview of these two methods and relate their expansion coefficients. We will demonstrate that the expansion coefficients that have been optimized for circular piston transducers can also be used to generate improved field simulations for rectangular probes. It will also be shown that because Gaussian beams are only approximate (paraxial) solutions to the wave equation, a multi-Gaussian beam model is ultimately limited in the accuracy it can obtain in the very near field.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

一维线阵离轴高斯光束通过湍流大气的传输特性

研究了一维(1D)线阵离轴高斯光束通过湍流大气的传输特性，推导出了其光强传输方程. 研究表明，1D线阵离轴高斯光束通过湍流大气传输经历了三个阶段，即在近场其光强分布为类似于入射光的锯齿状分布，随着传输距离的增加逐渐变为平顶分布，最后在远场成为类高斯分布. 湍流的增强会使光束传输经历三阶段的进程加快. 并且，湍流使得不同子光束数的1D线阵离轴高斯光束的归一化光强分布相接近. 此外，子光束数越多的1D线阵离轴高斯光束受到湍流的影响越小；1D线阵离轴高斯光束较高斯光束受到湍流的影响要小. 关键词： 一维(1D)线阵离轴高斯光束 湍流大气 传输特性     

The Effect of the Spin Angular Momentum on the Tight-Focusing Vortex Hollow Gaussian Beams

The propagation properties of a hollow Gaussian beam (HGB) carrying on-axis and off-axis vortices through a high numerical aperture lens are investigated. The intensity of the focused beam in the focal plane can be controlled by choosing the different topological charges, the beam order, and the semi-aperture angle. As intrinsic properties, vortex beams possess both spin and orbital angular momenta. The spin angular momenta (SAM) density can be treated as a vector in 3D since it exists in arbitrary orientation during the beam propagation. The vectors of SAM density orientation of the focused beam in 3D rotate around the central axis whose locations mainly rely on the vortices. The magnitude of the SAM density near the focus plane abruptly varies by altering the focal length of the lens. Under tightly focusing condition, two new pairs of vortices generate alternately on x and y axes in the vectorial electric fields, while the topological charges increase by one.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

Anomalies in the field of a gaussian beam near focus

A theoretical analysis of the electromagnetic field of a focused gaussian beam, like that produced by some lasers, indicates anomalies in the field distribution over the focal region. The transverse component of the electric field is shown graphically in this region using data obtained through the numerical integration of an expression that is exact according to Maxwell's equations. These data agree with the standard paraxial theories used to describe gaussian beams only asymtotically, in the limit of zero beam divergence about focus. As the divergence is increased, so that the beam is brought more sharply to focus, the gaussian beam evolves toward a dipole field from which all evanescent plane waves have been removed. Gaussian beams observed in nature should show some evidence of the associated anomalies, even if the beam is almost collimated.     

Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–H?nchen shift for all the spots of a higher-order Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.