Rotation of elliptic optical beams in anisotropic media

We investigate the linear propagation of a paraxial optical beam in anisotropic media. We start from the eigenmode solution of the plane wave in the media, then subsequently derive the wave equation for the beam propagating along a general direction except the optic axes. The wave equation contains a second-order mixed derivative term originating from the anisotropy, and this term can result in the rotation of the beam-spot. The rotation effect is investigated by solving analytically the wave equation with an initial elliptical Gaussian beam for both uniaxial and biaxial media. For both media, it is found that there exists a specific direction, which is dependent on anisotropy of the media, on the cross-section perpendicular to propagation direction to determine the rotation of the beam-spot. When the major axes of the elliptical beam-spot of the input beam are parallel to the specific direction, the beam-spot will not rotate during propagation, otherwise, it will rotate with the direction and the velocity determined by input parameters of the beam.     

A FDTD formulation for high order dispersive media of muscle-equivalent

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) is expressed in terms of E(t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.     

New Characterizations of the Region of Complete Localization for Random Schrödinger Operators

We study the region of complete localization in a class of random operators which includes random Schrödinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity.     

On the dual symmetry between absorbing and amplifying random media

We re-examine the dual symmetry between absorbing and amplifying random media. By analysing the physically allowed choice of the sign of the square root to determine the complex wave vector in a medium, we draw a broad set of conclusions that enables us to resolve the apparent paradox of the dual symmetry and also to anticipate the large local electromagnetic field enhancements in amplifying random media.     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

Wave Interaction with an Emerged Porous Media

In this paper, we study wave interaction with an emerged porous media. The governing equation is shallow water equations with a friction term of the linearized Dupuit-Forcheimer's formula. From the continuity of surface and horizontal flux, we derived the wave reflection and transmission coefficient formulas. They are similar to the corresponding formulas of the submerged solid bar breakwater. We solve the equations numerically using finite volume method on a staggered grid. The numerical wave reduction in the porous media confirms the analytical wave transmission curve.     

Detonation waves in bubble-drop media

Wave processes in chemically active multicomponent media: liquid — gas bubbles — liquid drops have been studied experimentally. Existence of detonation waves in multicomponent (bubble-drop) media has been proved. Structure of detonation waves in bubble-drop and bubble media is qualitatively identical: detonation waves are solitary waves with pulsation profile the pressure behind which is close in value to the one in unperturbed medium. Propagation velocity of detonation waves in bubble and bubble-drop media drops with the increase in medium gas phase concentration and with the decrease in carrier liquid viscosity. Presence of liquid drops decreases detonation wave velocity compared with bubble medium that does not contain liquid drops. Detonation wave propagation in multicomponent media causes gas bubbles fragmentation as well as fragmentation of individual liquid drops. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 04-03-33106).     

Frequency-domain wave equation and its time-domain solutions in attenuating media

Our purpose in this paper is to describe the wave propagation in media whose attenuation obeys a frequency power law. To achieve this, a frequency-domain wave equation was developed using previously derived causal dispersion relations. An inverse space and time Fourier transform of the solution to this algebraic equation results in a time-domain solution. It is shown that this solution satisfies the convolutional time-domain wave equation proposed by Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)]. The form of the convolutional loss operator contained in this wave equation is obtained. Solutions representing the propagation of both plane sinusoidal and transient waves propagating in media with specific power law attenuation coefficients are investigated as special cases of our solution. Using our solution, comparisons are made for transient one-dimensional propagation in a medium whose attenuation is proportional to frequency with recently obtained numerical solutions of Szabo's equation. These show good agreement.     

波动方程深度偏移的局部裂步Fourier传播算子

针对裂步Fourier传播算子在速度强横向变化介质中的不足,将算子的框架展开方法应用于Fourier传播算子中的相移算子,提出了一种波场传播的局部裂步Fourier传播算子,并把它应用于波动方程叠前深度偏移成像.这个局部裂步Fourier传播算子是由相空间(空间-波数)-频率域的相移算子和空间-频率域的窗口时移算子两部分组成.与波数-频率域的空间全局性相移算子不同,相空间-频率域的相移算子具有很好的空间局部性.通过在国际标准的SEG-EAGE二维盐丘模型的波动方程叠前深度偏移成像数值试验,证明局部Fourier传播算子不仅具有很好的稳定性,而且还特别适用于速度强横向变化介质.     

Including dispersion and attenuation directly in the time domain for wave propagation in isotropic media

When sound propagates in a lossy fluid, causality dictates that in most cases the presence of attenuation is accompanied by dispersion. The ability to incorporate attenuation and its causal companion, dispersion, directly in the time domain has received little attention. Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)] showed that attenuation and dispersion in a linear medium can be accounted for in the linear wave equation by the inclusion of a causal convolutional propagation operator that includes both phenomena. Szabo's work was restricted to media with a power-law attenuation. Waters et al. [J. Acoust. Soc. Am. 108, 2114-2119 (2000)] showed that Szabo's approach could be used in a broader class of media. Direct application of Szabo's formalism is still lacking. To evaluate the concept of the causal convolutional propagation operator as introduced by Szabo, the operator is applied to pulse propagation in an isotropic lossy medium directly in the time domain. The generalized linear wave equation containing the operator is solved via a finite-difference-time-domain scheme. Two functional forms for the attenuation often encountered in acoustics are examined. It is shown that the presence of the operator correctly incorporates both, attenuation and dispersion.     

Nolinear interaction between P-and SV-wave in isotropic elastic media

I.IntroductionInthelinearwavethcory,thestressinaso1idisproportionaltostrainsandthepropagatingwaves(suchasP-,SV-andSH-waves)satisfythehomogeneouswaveequation.Iftherearesomeboundaries,thereflectionandrefractionobeytheSne11'sla.[1l.Inthenon1inearmcdia,ontheotherhand,a11theequationsarenon1inearsoitisverydifficulttoobtainanexactsolu-honingeneral.Usua11y,thepcrturbationmethodsarcinvokedtofindanapproximateso1ution.Sincethenon1ineartermsofthestrainsappearinthestrcsses,two-waveinteractionwilltakep1…     

多层介质对应力波传播特性影响分析

 通过在气炮上进行多层介质的低速冲击实验及相应的数值计算，分析了不同组成的多层介质对应力波传播特性的影响。结果表明：多层介质中的泡沫材料不仅能够改变应力波的幅值与作用时间，而且具有显著的吸能效果，引起应力波在传播过程中在各层介质中能量与动量分配的改变。通过对泡沫铝和泡沫混凝土两种软材料在多层介质中作用的比较表明，在低速冲击的实验条件下，含泡沫混凝土的多层介质具有较好的削波作用，含泡沫铝的多层介质具有较好的吸能性能。     

Random Backscattering in the Parabolic Scaling

In this paper we revisit the parabolic approximation for wave propagation in random media by taking into account backscattering. We obtain a system of transport equations for the moments of the components of reflection and transmission operators. In the regime in which forward scattering is strong and backward scattering is weak, we obtain closed form expressions for physically relevant quantities related to the reflected wave, such as the beam width, the spectral width and the mean spatial power profile. In particular, we analyze the enhanced backscattering phenomenon, that is, we show that the mean power reflected from an incident quasi-plane wave has a maximum in the backscattered direction. This enhancement can be observed in a small cone around the backscattered direction and we compute the enhancement factor as well as the shape of the enhanced backscattering cone.     

纵波的波形与媒质的运动状态

根据媒质疏密程度来分析纵波传播时媒质的运动状态,并能过媒质间相互作用力与媒质运动状态的关系,证明媒质单位面积相互作用力的功率等于能流密度。     

An anomalous non-self-similar infiltration and fractional diffusion equation

Problems of anomalous infiltration in porous media are considered. As follows from the analysis of experimental data, modification of the infiltration equation is necessary. A fractional diffusion equation with variable order of the time-derivative operator for describing the liquid infiltration in porous media is proposed. The physical meaning of this fractional equation is explained. This equation provides good agreement with existing experimental data for both the subdiffusion and the superdiffusion. The treatment of experimental data for the absorption of water in a fired-clay brick and for water infiltration in cement mortar using this fractional equation of diffusion is presented. Various formulae, which can be useful for applications, have been developed.     

一种处理色散介质问题的通用时域有限差分方法

色散介质的介电系数是频率的函数,使本构关系在时域成为卷积关系.这就给用时域有限差分方法计算色散介质中波的散射和传播带来了困难.现有算法往往要针对不同色散介质模型推导相应的递推公式,算法的通用性较差.本文完善和发展了移位算子-时域有限差分方法,使之成为一种处理色散介质电磁问题的通用方法.首先,证明了常见的三种色散介质模型(德拜模型、洛伦兹模型和德鲁模型)的介电系数均可以写成适于移位算子法计算的有理分式函数形式.然后,用/t代替jω,过渡到时域,再引入时域移位算子z_t代替时间微分算子来处理有理分式函数形式的介电系数,给出离散时域本构关系的表示式,进而导出时域有限差分方法当中电位移矢量和电场强度之间的关系.最后,计算了几种色散介质的电磁散射,数值结果表明了本文方法和程序的通用性和正确有效性. 关键词： 时域有限差分方法 色散介质 移位算子     

Wave equation for vectons and magnetic charges

Based on the wave equation for spin-one particles (vectons) proposed earlier by the author, we select an interaction operator and then in the limit go to field variables and the Maxwell equations of classical electrodynamics. Additional terms arising in this case are interpreted as magnetic charges and currents. We discuss the consequences. We conclude that it is possible to find magnetic charges in matter and present some characteristics of such materials. We logically derive free magnetic charges and their currents. We construct an electrodynamics taking into account material media.Karachaevsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 49–54, September, 1994.     

Phase and group velocity considerations for dynamic modulus measurement in anisotropic media

In anisotropic media, the direction of energy propagation does not necessarily coincide with the wave normal, i.e. the energy flux vector does not coincide with the wave normal. Since, experimentally, one measures group velocity not phase velocity, one must therefore be careful in interpreting ultrasonic wave speed measurements in anisotropic media. This is of particular importance in elastic property reconstruction where acoustic velocity measurements are used as the basis for determining anisotropic material properties. In this work, the consequences of energy flux deviation from the wave normal are considered for typical experimental geometries. Particular attention is devoted to developing appropriate relationships between the phase velocity and ultrasonic transit time measurements, as these relations are most useful for elastic property reconstruction. In all the cases considered, it is shown that the phase velocity can be directly calculated from appropriate time delay measurements.     

Wave propagation in locally perturbed periodic media (case with absorption): Numerical aspects

We are interested in the numerical simulation of wave propagation in media which are a local perturbation of an infinite periodic one. The question of finding artificial boundary conditions to reduce the actual numerical computations to a neighborhood of the perturbation via a DtN operator was already developed in [1] at the continuous level. We deal in this article with the numerical aspects associated to the discretization of the problem. In particular, we describe the construction of discrete DtN operators that relies on the numerical solution of local cell problems, non stationary Ricatti equations and the discretization of non standard integral equations in Floquet variables.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.