光束分数傅里叶变换的Wigner分布函数分析方法

利用Wigner分布函数(WDF)方法，对光束的分数傅里叶变换特性进行了研究.以厄米 高斯(H G)光束为例，导出了H G光束在分数傅里叶变换面上光强分布的解析公式和H G光束在分数傅里叶变换面上束宽的解析计算公式.通过数值计算研究了H G光束光强随分数傅里叶变换阶数变化的规律.研究表明：选取适当的分数傅里叶变换阶数p，在x，y方向可以得到相等束宽的对称光强分布. 关键词： Wigner分布函数 厄米 高斯(H G)光束 分数傅里叶变换     

基于柱坐标系下的空心高斯光束的分数傅里叶变换

推导出分数傅里叶变换基于柱坐标系下的解析表达式,应用此解析表达式对空心高斯光束进行分析,得到其分数傅里叶变换的解析表达式。讨论其在分数傅里叶变换平面的光强分布与各种光束参数之间的变换关系,并进行数值计算,从而得出基于柱坐标系下的空心高斯光束的分数傅里叶变换的传输性质。所得结果为分析和计算这种光束的分数傅里叶变换提供了方便,同时对此类光束的传输控制提供了基础理论支持。     

向列相液晶中的(1+1)维呼吸子解

理论分析了(1+1)维呼吸子在向列相液晶中传输时的情况,通过对原始方程作归一化计算和相应的傅里叶变换,得到了特定情况下的强非局域非线性薛定谔方程,并且通过此方程最终求到了呼吸子解。在未作近似时可以计算出呼吸子的周期和最大(最小)束宽,在平衡点处将势函数近似展开到二阶,此时不仅得出了呼吸子解的周期和最大(最小)束宽,而且解出了波动振幅的解析解。通过数值模拟与解析解的比较,结果表明,解析结果成立于非局域程度较强的情况,并且未作近似的解析解始终比较接近模拟解。     

傅里叶变换、拉普拉斯变换和伽博变换的关系

傅里叶变换、拉普拉斯变换和伽博变换,作为三种常见的积分变换,无论在数学物理的理论研究中还是在各种工程应用中,都有着极重要的价值.本文以傅里叶变换为中心,从逐级修正的角度,详细阐明了三者的理论渊源.     

分数傅里叶变换面上余弦-高斯光束的变换特性

 利用Wigner分布函数的方法，研究了余弦-高斯光束的分数傅里叶变换特性。导出了余弦-高斯光束在分数傅里叶变换面上光强分布和束宽的解析计算公式，并对此进行了数值模拟计算。研究表明：分数傅里叶变换阶数对余弦-高斯光束的光强分布有明显影响，余弦-高斯光束的轴上光强随分数傅里叶变换阶数呈周期性变化，束宽随分数傅里叶变换阶数也呈周期性变化，周期为2；对给定调制参数的余弦-高斯光束，通过适当选取分数傅里叶变化阶数可以获得平顶的光强分布。     

光学信息处理讲座 第六讲 光学Mellin变换

以傅里叶光学为基础的相干光处理器,能够进行微分、积分、卷积和相关等多种模拟运算.这种运算的实现,是利用一个理想的薄的正透镜的前后焦平面互为傅里叶变换关系进行的.函数f(x,y)的傅里叶变换F(u,v)定义为用傅里叶透镜组成的相干光处理系统,主要通过正逆傅里叶变换和空间滤波来完成多种运算的.同电子计算机比较,它具有信息容量大,计算速度快两大优点.但是,这种光学处理系统只能解决那些空间平移不变的物理问题,也就是只能解决在数学上用这种卷积积分描述的问题.这是因为设叶G(u,叶,F(。,。)和0(。,。)分别是g(X,y),八X,叫和h(X,y)的傅…     

用Wigner分布函数方法研究平顶多高斯光束的分数傅里叶变换

本文用Wigner分布函数方法分析了平顶多高斯光束的分数傅里叶变换。导出了分数傅里叶变换面上光的强度、束宽、远场发散角、M2因子和K参数的解析表达式。通过数值模拟研究了分数傅里叶变换阶数对平顶多高斯光束传输性质的影响。     

用MATLAB解决线性三自由度系统微振动问题

借助教学软件MATLAB,用矩阵方法,傅里叶频谱分析和拉普拉斯变换法对线性三自由度系统微振动问题进行计算和讨论,并模拟力学系统的运行。     

三能级钾原子气体三维傅里叶变换频谱的解析解

利用投影切片定理、傅里叶位移定理和误差函数给出三能级钾原子气体三维傅里叶变换频谱在T=0界面的解析解.固定均匀线宽,非均匀展宽和对角线相关系数可以定量地识别,通过在适当方向上拟合三维傅里叶变换频谱谱峰的切片来确定.结果表明,非均匀展宽增大,频谱图沿着对角线方向延伸,对角线相关系数增大,频谱图逐渐变圆,振幅也逐渐变小.     

用光学傅里叶变换方法对合成孔径雷达海洋波浪图像的频谱分析

本文将介绍应用光学傅里叶变换方法检测海洋波浪的存在、波浪周期及传播方向。原始信息从卫星运载合成孔径雷达的底片上得到。文章将给出傅里叶变换结果,并进行适当的讨论。     

Use of the second dimension in PGSE NMR studies of porous media

2-dimensional methods based on PGSE NMR may be used to correlate or separate molecular dynamical properties, or to elucidate fluctuations. These may utilize either the gradient (q-vector) domain, in which molecular displacements are measured, or the time domain, in which relaxation is measured, and may be analyzed by combinations of inverse Fourier or Laplace transforms. Existing methodologies are reviewed and new experiments proposed. In particular the use of diffusion-diffusion exchange and correlation analysis is demonstrated using the case of water diffusion in a lamellar phase liquid crystal.     

Electro–magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity

A unified mathematical model of Green–Naghdi’s thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.     

Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating

Based upon the coupled thermoelasticity and Green and Lindsay theory, the new governing equations of two-temperature thermoelastic theory with thermal nonlocal parameter is formulated. To more realistically model thermal loading of a half-space surface, a linear temperature ramping function is adopted. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Specific attention is paid to study the effect of thermal nonlocal parameter, ramping time, and two-temperature parameter on the distributions of temperature, displacement and stress distribution.     

On the connection between analyticity and lorentz covariance of wightman functions

We prove a conjecture ofR. Streater [1] on the finite covariance of functions holomorphic in the extended tube which are Laplace transforms of two tempered distributions with supports in the future and past cones. A new, slightly more general proof is given for a theorem of analytic completion of [1].     

Magneto-thermo-elastic interactions in an infinite solid due to some time-dependent heat sources

To determine the distribution of stress, strain, temperature, electric and magnetic fields in an infinite solid when it is subjected to a time-dependent heat source, is the aim of the present paper. The solutions have been achieved by means of Fourier and Laplace transforms.     

Free Energies and Fluctuations for the Unitary Brownian Motion

We show that the Laplace transforms of traces of words in independent unitary Brownian motions converge towards an analytic function on a non trivial disc. These results allow one to study the asymptotic behavior of Wilson loops under the unitary Yang–Mills measure on the plane with a potential. The limiting objects obtained are shown to be characterized by equations analogue to Schwinger–Dyson’s ones, named here after Makeenko and Migdal.     

Pattern formation in superdiffusion Oregonator model

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.     

Solutions of Fractional Partial Differential Equations of Quantum Mechanics

The aim of this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators, occurring in quantum mechanics. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms, in terms of the Fox's $H$-function. Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented. The results given earlier by Saxena et al. [Fract. Calc. Appl. Anal., 13(2) (2010), pp. 177-190] and Purohit and Kalla [J. Phys. A Math. Theor., 44 (4) (2011), 045202] follow as special cases of our findings.     

Generalized analytic signal associated with linear canonical transform

Analytic signal is tightly associated with Hilbert transform and Fourier transform. The linear canonical transform is the generalization of many famous linear integral transforms, such as Fourier transform, fractional Fourier transform and Fresnel transform. Based on the parameter (a, b)-Hilbert transform and the linear canonical transform, in this paper, we develop some issues on generalized analytic signal. The generalized analytic signal can suppress the negative frequency components in the linear canonical transform domain. Furthermore, we prove that the kernel function of the inverse linear canonical transform satisfies the generalized analytic condition and get the generalized analytic pairs. We show the generalized Bedrosian theorem is valid in the linear canonical transform domain.     

Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials,Logan–Shepp ridge polynomials,Chebyshev–Fourier Series,cylindrical Robert functions,Bessel–Fourier expansions,square-to-disk conformal mapping and radial basis functions

We compare seven different strategies for computing spectrally-accurate approximations or differential equation solutions in a disk. Separation of variables for the Laplace operator yields an analytic solution as a Fourier–Bessel series, but this usually converges at an algebraic (sub-spectral) rate. The cylindrical Robert functions converge geometrically but are horribly ill-conditioned. The Zernike and Logan–Shepp polynomials span the same space, that of Cartesian polynomials of a given total degree, but the former allows partial factorization whereas the latter basis facilitates an efficient algorithm for solving the Poisson equation. The Zernike polynomials were independently rediscovered several times as the product of one-sided Jacobi polynomials in radius with a Fourier series in θ. Generically, the Zernike basis requires only half as many degrees of freedom to represent a complicated function on the disk as does a Chebyshev–Fourier basis, but the latter has the great advantage of being summed and interpolated entirely by the Fast Fourier Transform instead of the slower matrix multiplication transforms needed in radius by the Zernike basis. Conformally mapping a square to the disk and employing a bivariate Chebyshev expansion on the square is spectrally accurate, but clustering of grid points near the four singularities of the mapping makes this method less efficient than the rest, meritorious only as a quick-and-dirty way to adapt a solver-for-the-square to the disk. Radial basis functions can match the best other spectral methods in accuracy, but require slow non-tensor interpolation and summation methods. There is no single “best” basis for the disk, but we have laid out the merits and flaws of each spectral option.