The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

We propose the backward phase flow method to implement the Fourier–Bros–Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.     

Non-paraxial Elliptical Gaussian Beam

By using the methods of Hertz vector and angular spectrum transormation, the exact solution of non-paraxial elliptical Gaussion beam with general astigmatism based on Maxwell′s equations is obtained. We discussed its propagation characteristics. The results show that the orientation of the elliptical beam spot changes continuously as the beam propagates through isotropic media. Splitting or coupling of beam spots may occur for different initial spot size. This is very different from that of paraxial elliptical Gaussian beam.     

Non-paraxial Elliptical Gaussian Beam

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｆｕｎｄａｍｅｎｔａｌＧａｕｓｓｉａｎｂｅａｍｉｓｎｏｔｔｈｅｅｘａｃｔｓｏｌｕｔｉｏｎｏｆＭａｘｗｅｌｌ′ｓｅｑｕａｔｉｏｎｓ,ｂｕｔａｎａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｏｆｔｈｅｗａｖｅｅｑｕａｔｉｏｎｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｏｆｓｌｏｗｌｙ ｖａｒｙｉｎｇｅｎｖｅｌｏｐｅａｐｐｒｏｘｉｍａｔｉｏｎ[1] .Ｔｈｅｐａｒａｘｉａｌａｐｐｒｏｘｉｍａｔｉｏｎｉｓｎｏｌｏｎｇｅｒｖａｌｉｄｗｈｅｎｔｈｅｂｅａｍｗａｉ…     

高斯初始能量分布下自由电子激光饱和状态的统计理论求解

基于高增益自由电子激光饱和状态的统计物理方法,在不同的电子束相空间初始分布下对原有理论进行了发展和推广,借助于多重数值积分技术解决了粒子束一般动量初始分布带来的计算困难,并以更接近实际的高斯动量分布为例进行计算。作为对比验证编写高斯初始动量分布下的直接数值模拟程序,将高斯初始分布同"水袋"两种初始分布的"暖电子束"入射情形下自由电子激光达到饱和时系统的光强、聚束因子和粒子相空间分布均进行相应计算和比较。结果表明:数值模拟和统计计算结果相一致;在目前选取的参数范围内,两种初始分布的相应结果差异并不显著。     

高斯光束的数值模拟新方法

基于高斯光束的单叶双曲面特征,给出了一种新的模拟高斯光束的数值方法.该方法将高斯光束视为由无数个共轴单叶双曲面构成的双曲线体,由束腰截面发射的光子传播方向是在经过该光子发射点的双曲面内两条直母线中等概率选择.这不仅符合光子沿直线传播,而且意味着大量光子的“平均”传播方向与相应高斯光束的波印廷矢量相同.数值模拟结果表明：该方法可高准确度地模拟高斯光束的几何构形、光强分布、光子的光程分布和波前曲率半径,而且模拟效率与现有的方法相近.     

Far-field structural property of a Gaussian beam diffracted by a phase aperture

Based on the angular spectrum representation of an arbitrary electromagnetic beam and the method of stationary phase, an analytically vectorial structure of a Gaussian beam diffracted by a phase aperture has been derived in the far-field. Moreover, the derivation is performed without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured Gaussian beam are also presented in the far-field, respectively. The influence of the phase delay on the energy flux distributions of the TE term, the TM term, and the apertured Gaussian beam is discussed in the far-field.     

非球面系统中高斯光束传输的数值计算

高斯光束的理论公式从整体上描述了光束的传输特性,但并没有描述光束内每一光子的传播行为。基于高斯光束的单叶双曲面特性,建立了一个新的高斯光束光子传输模型。该模型将高斯光束视为由无数个共轴单叶双曲面构成的双曲线体,光子传播方向是在过该光子初始发射点的双曲面的两条直母线中等概率选择。基于该模型,通过计算大量光子经光学系统的传播轨迹可获得高斯光束的几何构形、光强分布、光子光程分布及其传播方向。对实际非球面光学系统的计算结果充分验证了该方法可全面、准确地模拟高斯光束的传输特性,且数值计算效率高。     

Conditional and unconditional Gaussian quantum dynamics

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as ‘general-dyne’) quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.     

Restoration of Decentered Gaussian Beam with the Combination of a Lens and a Gaussian Aperture

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＴｈｅＧａｕｓｓｉａｎｂｅａｍｉｓｔｈｅｆｕｎｄａｍｅｎｔａｌｓｈａｐｅｏｆｔｈｅｌａｓｅｒｗｉｔｈａｓｐｈｅｒｉｃａｌ ｍｉｒｒｏｒｒｅｓｏｎａｔｏｒａｎｄｗｉｄｅｌｙｕｓｅｄｔｏｄｅｓｃｒｉｂｅａｓｉｎｇｌｅｍｏｄｅｌａｓｅｒ.Ｉｎｔｈｅｐａｒａｘｉａｌａｐｐｒｏｘｉｍａｔｉｏｎ ,ｔｈｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｃｏｍｐｌｅｘａｍｐｌｉｔｕｄｅｏｆｉｔｒｅｍａｉｎｓｕｎｃｈａｎｇｅｄｗｈｅｎｉｔｕｎｄｅｒｇｏｅｓｔｈｅＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍｏｒｔｈｅ…     

Small Gaussian laser beam diameter measurement using a quadrant photodiode

A method that uses the quadrant photodiode has been shown to be relatively inexpensive and robust in measuring Gaussian laser beam diameters in two axes. This approach requires neither component rotation nor precision alignment, and it facilitates integration of Gaussian laser beam diameter measurement with laser beam tracking in instruments. The physical gap between sensors in the quadrant photodiode, however, limits laser beam diameter measurements to those in the millimeter range. Here, we describe a modified approach to measure Gaussian laser beam diameters that are significantly smaller.     

Analytical structure of Hermite Gaussian beam in far field

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\     

Entangling two single-mode Gaussian states by use of a beam splitter

Considering two light beams which are in general single-mode Gaussian states and incident on input ports of an ideal beam splitter, respectively, this paper investigates how separability and entanglement of the output lights depend on degrees of nonclassicality and purities of the input states. The minimum and maximum amounts of attainable entanglement in the output state are found.     

大气湍流对部分相干平顶高斯光束的影响

采用相屏近似处理方法对激光通过湍流大气的传输进行了数值模拟。从数值模拟的结果拟合出两个公式:一是通过湍流前后部分相干平顶高斯光束的束宽平方比随阶数、传输距离和湍流强度的变化关系式;一是通过湍流后的相干长度随初始光束相干长度、湍流相干长度的变化关系式。研究发现:部分相干平顶高斯光束分解为相互独立的厄米-高斯光束的叠加;相干性越差的光束受到湍流的影响程度就越小;湍流对光束传输的影响与光束自身相干特性对其传输的影响之间是不相关的。     

基于改进单高斯模型法的交通背景提取

在分析交通背景提取的特点和单高斯模型法的不足的基础上,提出了一种改进的单高斯模型法.该算法利用均值法初始化背景模型,引入判断值进行背景更新,运用邻域判别法实现干扰点抑制.不同天气条件,不同交通场景下的实验表明：与单高斯模型法相比,改进算法在提取背景时可以随车辆的走停及时更新,并且抑制了非静止背景物体的干扰.     

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.     

高斯光束在双层云中传输的蒙特卡罗模拟

基于辐射传输理论, 利用蒙特卡罗方法模拟了无限窄(冲击函数)准直光束入射到典型水云以及冰水双层云时的后向散射特性, 进而将得到的冲击响应与高斯光束卷积, 得到高斯光束在云层中传输的多次散射特性. 文中给出了两种波束入射时水云以及冰水双层云的反射函数随径向r和天顶角α的变化关系, 并给出了光强在云层内部的二维分布图. 计算结果表明, 高斯光束入射时, 云层反射函数的特点与无限窄准直光束入射时有较大区别. 因此在利用激光雷达进行云层探测时需要考虑激光的散斑, 文中的方法可以为此提供理论依据.     

像散椭球高斯光束的理论分析与实验模拟

从理论上讨论了具有简单像散特必的椭 图 束的处理方法,在实验中利用两个正交的柱透镜模拟球面双轴透镜对半导体激光器的输出光束进行变换,得较为理想的结果,即把椭圆高斯光束自理为近似圆高斯光束。     

横向激发线偏振高斯光束的非傍轴传输

文章提出一种横向激发的任意线偏振高斯光束,该光束场量的模与传统的任意线偏振高斯光束具有相同的模,在源场区,其满足自由空间无源场的场方程。同时利用瑞利—索末菲衍射积分对该高斯光束的非傍轴传输特性进行了解析研究,给出了空间光强分布、束腰和远场发散角的解析通式,发现该类光束的远场光强呈一平顶空心光束。     

偏离束腰入射对非局域非线性介质中高斯光束演化的影响

从1+1维强非局域模型出发，讨论了偏离束腰入射的高斯光束在非局域非线性介质中的传输 特性，得到了精确的解析解.结果表明，在聚焦介质中偏离束腰入射时，不论入射功率多大 ，光束束宽将发生周期性波动，光孤子不复存在，这与从高斯光束束腰入射的情况有本质的 不同；入射功率决定了光束平均束宽的大小，入射位置决定了光束初始的演化趋势.比较了在入射位置相同的条件下，聚焦介质、散焦介质和线性均匀介质中光束的演化.给出了“空 间啁啾”的定义，偏离束腰入射的物理本质是光束的不同入射位置对应不同的初始空间啁啾 .空间啁啾的概念， 关键词： 非局域非线性介质 空间光孤子 高斯光束