二维各向同性均匀随机介质中平面波的传播及其局域性

讨论了二维各向同性均匀随机介质中平面波的传播及其局域性.假设二维随机介质具有各向同性窄带高斯谱,运用随机泛函理论给出了二维介质中随机平面驻波的解析近似解及其幅度和相位的定量统计特性.计算结果证实了波在随机介质中传播时的局域性.将二维介质中的平面波和柱面波的传播特性作了对比.数值结果模拟了二维随机介质场及平面驻波,并验证了本文结果的正确性. 关键词： 随机介质 随机泛函 平面波 局域性     

随机激光器中准态腔的阈值与其局域化程度的关系

基于光波在有限随机介质中的局域化理论，利用有限时域差分法数值求解Maxwell方程 组，研究了随机介质中的激光现象，分析了准态模的放大与其 空间局域性的关系. 通过研究二维非增益随机介质中光波的局域化，确定了准态模的空间分 布和频谱特征. 通过引入增益，研究了准态模的放大过程和阈值特性. 结果表明空间局域化 强的准态模在增益介质中被优先放大，且有较低的阈值. 关键词： 随机激光器 准态模 随机介质中的光学特性     

变分法研究二维光晶格中玻色-爱因斯坦凝聚的调制不稳定性

利用含时变分法研究了二维光晶格中准二维玻色-爱因斯坦凝聚中的调制不稳定性. 在平均场近似下, 由准二维Gross-Pitaevskii方程出发, 利用变分法给出了调制波振幅和相位所满足的时间演化方程, 通过求解时间演化方程和能量分析法给出了发生调制不稳定性的条件, 决定于平面波振幅, 晶格强度, 调制波的波矢量和原子之间的两体相互作用.     

线性吸收介质非局域线性电光效应的耦合波理论

本文提出了线性吸收介质非局域线性电光效应的耦合波理论,建立了相应的耦合波方程组,并求解了该方程组.由此,可给出在任意方向外加电场的作用下,光在具有空间非局域响应的线性吸收介质中沿任意方向传播时出射光场的表达式.据此,研究了线性吸收是如何改变出射光场的两个偏振分量的振幅、相位和波形的.进一步讨论了线性吸收对电光强度调制的影响,以及如何测量一阶线性和二阶非线性极化率非局域响应的特征长度和介质的线性吸收系数.     

随机介质介电常量的涨落与光波的空间分布

采用随机介质统计模型和时域有限差分方法模拟了二维随机介质中光场的空间分布及其同介电常量涨落的关系。模拟中,散射微粒随机地分布在均匀介质中以增加光子在介质中滞留时间。不同随机强度α,形成不同空间结构的随机介质。通过小心地调节入射光波长,得到了不同随机介质中的场强分布。结果表明,随机介质介电常量的涨落导致在介质的某些区域形成一些特殊结构。这些结构延长了光子在其中的滞留时间,产生了光波的局域态,起到了光腔的作用,使得随机介质在抽运激励下能够产生激光辐射。这样的光腔在介质中是随机分布的,其数量与分布特征与介电常量涨落的强弱有关。     

布里渊增强四波混频时域特性的理论研究

通过对布里渊增强四波混频(BEFWM)瞬态耦合波方程的数值求解，描述了共轭输出光的时域调制行为.同时，对能量耦合过程中起决定性作用的声学波的时空演化特征进行了模拟与分析，由此给出BEFWM时域特性物理机理的解释.研究表明，共轭光输出强度的波动与介质内声波场的分布和起伏相关联，共轭光波形调制现象的强弱取决于介质声子寿命、信号及抽运光强度、有效作用长度等诸多参数.     

二维相对论运动等离子体的介电率张量

定义了相对论性运动等离子体的物理模型.利用荷流体的微扰理论，研究了该系统二维扰动现象及背景离子下的束-波互作用问题，导出了该系统的介电率张量.研究表明，相对论运动等离子体系统属复杂的色散荷流体介质并呈复杂的空间电磁不均匀性.数值模拟计算给出了相对论运动等离子体系统的介电率对波频率、电子能量以及空间坐标的响应. 关键词： 等离子体 荷流体 介质 电磁理论     

对全入射角负折射二维光子晶体结构和电磁参量的研究

利用二维光子晶体的等频线分析原理和平面波展开方法,得到了使二维光子晶体产生全入射角负折射(All-Angle Negative Refraction,AANR)现象时,入射电磁波的频率取值范围.同时,分析了AANR频率范围随着结构参量(晶格类型、介质棒半径与晶格周期的比值)和电磁参量(介质柱介电常量、本底介电常量、入射电磁波偏振方向)变化的行为.结果表明:固定组成光子晶体的一种介质的介电常量,另一介质的介电常量只有达到一定阈值,才有可能使光子晶体出现AANR现象.在给定两种介质介电常量的条件下,存在使AANR频率范围最大化的结构参量和电磁参量.     

大尺度介观电学输运在纳米结构石墨烯中的实现

Anderson局域化是量子波动性导致的最重要的物理现象之一。Anderson局域化理论原是对电子体系提出的,但是由于电子波动性只在很小的范围内(即相位相干长度内)有效,使得Anderson局域化的观测成为一个难点。在文章中,作者报道了在纳米结构石墨烯中首次观测到的二维Anderson强局域化现象。更重要的是作者找到了使电子相位相干长度增长至少一个量级的方法,使得电子的相位可以更容易地被操控。作者用尺寸标度方法得到三组局域化长度分别为1.1,2.0和3.4mm。局域化长度随磁场的变化和理论预测符合得非常好。大尺度介观电学输运,表现为并行于二维变程跳跃电导的另一通道。低温下(T<25 K)观测到费米能级附近存在的库仑准能隙抑制了电子与电子间的非弹性散射,从而使得相位相干长度增长到10mm。     

含噪声包裹相位图的加权最小二乘相位展开算法研究

二维相位展开广泛应用在精密光学测量、自适应光学、合成孔径雷达、图像处理等领域中。为处理含噪声包裹相位图,以预条件共轭斜量法求解权重最小二乘相位展开方程。引入非加权二维离散余弦变换求解泊松方程得到的最小二乘相位解作为共轭斜量法的初始解,从而加快了收敛速度,同时提出一种新质量图确定算法求解过程中的权重项。计算机模拟和试验表明算法计算速度快,能有效地消除传统路径积分法在处理信噪比低包裹相位图时的"拉线"现象,是一种有效的相位展开方法。     

Stochastic functional analysis of propagation and localisation of cylindrical waves in a two-dimensional random medium

Propagation and localisation of cylindrical waves in a two-dimensional (2D) isotropic and homogeneous random medium is studied using the stochastic functional approach. By expanding the random permittivity fluctuation in the form of a Wiener integral equation, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved in the cylindrical coordinates system. An analytical expression of the cylindrical wave is derived and demonstrates the localisation phenomenon, as well as the wavenumber fluctuation in the random medium. Comparing with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effect owing to the medium randomness in both the amplitude and phase. Numerical simulations are presented to illustrate the functional dependence of the localisation phenomena.     

Enhanced and specular backscattering in random media

We study scalar waves probing a heterogeneous medium whose parameters are modeled in terms of a statistically isotropic random field. The medium is terminated by an oblique interface at one end (the bottom) and pressure release type boundary conditions at the other end (the top). The tilt of the bottom interface is relatively small so that the dominant contributions to the wave field are confined to a paraxial tube. This study generalizes the basic formulation in terms of Itô–Schrödinger equations in a one-dimensional deterministic background, describing the macrostructure, to one in which the background is more complicated. It provides the first step toward the analysis of scattered waves in general background media modulated by a random microstructure. We discuss in detail the enhanced backscattering phenomenon or weak localization in this setting, with a tilted interface imbedded in the random medium, and find that the backscattering cone does not depend on the tilt. We also find that the enhanced backscattering phenomenon is not affected by the replacement of a specular interface with a diffusive interface.     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

柱面Love波频散分析与SH波场的数值计算

对贴井壁环型剪切源在柱状双层弹性介质中激发的SH波场进行了理论求解,导出了柱面Love波频散方程,讨论了柱面Love波存在的条件及其区域.通过数值计算考察了柱面Love波的频散特性和激发强度,发现最低阶柱面Love波具有截止频率,这与平面半空间双层弹性介质模型下的Love波无截止频率的特征不同.渐近分析与数值考察都表明,井径r₁→∞时,柱面Love波频散方程趋向平面双层半空间的Love波方程,柱面Love波的截止频率趋于零.全波计算还显示用激发SH波来探测侵入带外原状地层的横波信息是一个十分简洁的途径..     

One-dimensional numerical simulations of random sound impulses

Abstract

We perform one-dimensional numerical simulations of small-amplitude acoustic pulses in space- and time-dependent random mass density and time-dependent velocity fields. Numerical results reveal that: (a) random fields affect the speeds, amplitudes and, consequently, shapes of sound pulses; (b) for weak random fields and short propagation times the numerical data converge with the analytical results of the mean field theory which says that a space-dependent (time-dependent) random field leads to wave attenuation (amplification) and all random fields speed up sound pulses; (c) for sufficiently strong random fields and long propagation times numerical simulations reveal pulse splitting into smaller components, parts of which propagate much slower than a wave pulse in a non-random medium. These slow waves build an initial stage of a wave localization phenomenon. However, this effect can be very weak in a real three-dimensional medium.     

WAVE PROPAGATION THROUGH A CYLINDRICAL BORE CONTAINED IN A MICROSTRETCH ELASTIC MEDIUM

Propagation of waves in a cylindrical bore filled with viscous liquid embedded in a microstretch elastic medium is investigated. Frequency equation for the surface wave propagation near the surface of the cylindrical bore is obtained, characterizing the dispersive nature of the wave. Significant effects of viscosity, microstretch and micropolarity are observed. Some special cases have been deduced.     

Propagation of longitudinal waves in a random binary rod

Propagation of waves in a composite elastic rod consisting of rods with alternating properties of random length is considered. We calculate exactly the Lyapunov exponent and find its short and long wave asymptotics. Finally, we discuss conditions for propagation and localization of waves in a binary random medium.     

Propagation of longitudinal waves in a random binary rod

Propagation of waves in a composite elastic rod consisting of rods with alternating properties of random length is considered. We calculate exactly the Lyapunov exponent and find its short and long wave asymptotics. Finally, we discuss conditions for propagation and localization of waves in a binary random medium.