A General Framework for Localization of Classical Waves: II. Random Media

We study localization of classical waves in random media in the general framework introduced in Part I of this work. This framework allows for two random coefficients, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, electromagnetic waves with random position dependent magnetic permeability and dielectric constant, and allows for anisotropy. We show exponential localization (Anderson localization) and strong Hilbert–Schmidt dynamical localization for random perturbations of periodic media with a spectral gap. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.     

Dynamics of generalized sine-Gordon soliton in inhomogeneous media

In this paper we introduce a few novel generalized sine-Gordon equations and study the dynamics of its solitons in inhomogeneous media. We consider length, mass, gravitational acceleration and spring stiffness of a coupled pendulums chain as a function of position x. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation in the inhomogeneous media. The obtained results confirm that the behavior of solitons in these media is similar to that of a classical point particle moved in an external potential.     

Between right- and left-handed media

We report analytical calculations for the propagation of electromagnetic radiation through an inhomogeneous layer whose refractive index varies in one-dimension situated between bulk right- and left-handed media. Significant field localization is generated in the layer that is caused by the coherent superposition of evanescent waves. The strength of the field localization and the transmission properties of the layer are investigated as a function of the layer width, losses and defects in the refractive index; the former two being modelled by continuous changes, and the latter by discontinuous changes, in the index profile.     

Reflection and transmission of waves near the localization threshold

A theory is presented for propagation of waves in bounded media near the mobility edge, based on the self-consistent theory for localization. It predicts a spatially inhomogeneous diffusion constant that leads to scale dependence in enhanced backscattering and transmission.     

Contribution to the statistical theory of wave localization in a two-layered medium

A very simple system of stochastic boundary-value wave equations that describes the interaction of two types of waves in a randomly inhomogeneous medium is studied. The statistics of the reflection and transmission coefficients for the incident and excited waves are discussed. It is shown that the excitation of waves is statistically equivalent to switching on damping for the initial incident waves which are localized in separate specific realizations. The parameters of the length of such localization are estimated in terms of the spectral density of the variations of the medium. It is also shown that for excited waves there is no dynamical localization, and the transmission coefficients for them are estimated. Zh. éksp. Teor. Fiz. 111, 2030–2043 (June 1997)     

Localization of Classical Waves II: Electromagnetic Waves

We consider electromagnetic waves in a medium described by a position dependent dielectric constant . We assume that is a random perturbation of a periodic function and that the periodic Maxwell operator has a gap in the spectrum, where . We prove the existence of localized waves, i.e., finite energy solutions of Maxwell's equations with the property that almost all of the wave's energy remains in a fixed bounded region of space at all times. Localization of electromagnetic waves is a consequence of Anderson localization for the self-adjoint operators . We prove that, in the random medium described by , the random operator exhibits Anderson localization inside the gap in the spectrum of . This is shown even in situations when the gap is totally filled by the spectrum of the random operator; we can prescribe random environments that ensure localization in almost the whole gap. Received: 1 July 1996 / Accepted: 15 August 1996     

Fractional hydrodynamic equations for fractal media

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the “fractional” continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered.     

TM Nonlinear electromagnetic waves guided by an inhomogeneous medium

Analytical dispersion relations and the power flow expression for TM (polarized) nonlinear electromagnetic surface waves propagating along the interface of an inhomogeneous and dielectric nonlinear media have been investigated theoretically. An inhomogeneous dielectric cover has the dielectric permittivity=a+bz, which is contacted with a strongly nonlinear Kerr like layer. The existence conditions for these waves to be propagated are studied. These waves have no counterpart in the linear isotropic regime. The power flow versus the wave index, and the consequence interface nonlinearity might be evaluated for a variety of inhomogeneity parameters, which are found to be inhomogeneity dependent, and could lead to optical hysterisis and bistability.On leave from: Department of Electrical Engineering and Electronics, UMIST, P.O. Box 88, Manchester M60 1QD, U.K.     

Regions of high correlation of acoustic waves in oceanic waveguides

We discuss the role of weakly divergent rays in the formation of regions with high correlation of waves in inhomogeneous stationary random media. The geometrical-acoustic approximation is used. Theoretical study is supported by numerical calculations.     

Volume and surface longitudinal waves in a cold inhomogeneous magnetoplasma

We study analytically and numerically volume and surface longitudinal waves in a dense weakly magnetized inhomogeneous plasma. First, the well-known results for volume and surface waves in homogeneous and semi-bounded magnetoplasmas are presented for reference. Problems with similar geometry are then studied for plasmas with nonuniform density distributions close to those observed in experiments. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 234–254, March 2007.     

Doping profile effects on modulation-doped single nonabrupt GaAs/AlxGa1 − xAs quantum wells

We study inhomogeneous doping effects on the confinement properties of modulation-doped single nonabrupt GaAs/Al_xGa_1 − xAs quantum wells. We describe the inhomogeneous doping using error function profiles, and we solve self-consistently the coupled Schrödinger (with a position dependent kinetic energy operator) and Poisson equations to obtain the electron energy levels. When the nonabrupt interfaces (spacer layer) are 10Å(100Å) wide and the presence of Si-dopant density in a 100 Å GaAs well region is only 10% of the Si-dopant density in the Al_0.3Ga_0.7As barriers, the lowest intersubband transition energy increases 37 meV in comparison with that calculated within the homogeneous doping-abrupt interface picture.     

非均匀波导中的声聚焦

理论研究了声波在非均匀波导中的空间聚焦问题,利用多模态导纳法构建波导内任意位置处声压与入射声压在模态域的映射关系,计算使声波聚焦于空间某位置时的最佳入射波,并画出了相应的聚焦声场.研究了三种非均匀情况:水平变截面波导、含散射体波导以及声速垂直变化波导.结果表明,当输入最佳入射波时,在非均匀波导中可以产生良好的单点或多点声聚焦效果,声波的聚焦过程充分地利用了波导结构及介质非均匀性对声波的散射作用.     

Metabolism-enhanced tumor localization by fluorescence imaging: in vivo animal studies

We present a high-sensitivity near-infrared optical imaging system for noninvasive cancer detection and localization based on molecularly labeled fluorescent contrast agents. This frequency-domain system utilizes the interferencelike pattern of diffuse photon density waves to achieve high detection sensitivity and localization accuracy for the fluorescent heterogeneity embedded inside the scattering media. A two-dimensional localization map is obtained through reflectance probe geometry and goniometric reconstruction. In vivo measurements with a tumor-bearing mouse model by use of the novel Cypate-mono-2-deoxy-glucose fluorescent contrast agent, which targets the enhanced tumor glycolysis, demonstrate the feasibility of detection of a 2-cm-deep subsurface tumor in the tissuelike medium, with a localization accuracy within 2-3 mm.     

Electromagnetic waves in isotropic and gyrotropic media

Maxwell’s equations are considered for waves in transparent inhomogeneous anisotropic and gyrotropic media with time dispersion. A uniaxial inhomogeneous crystal is taken for an anisotropic medium and an isotropic heterogeneous medium in a constant electric field for a gyrotropic medium. The solutions for flat-layered and cylindrical media are presented in terms of Hertz potentials. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 82–86, March, 2008.     

海洋声学环境下水中声源的时延估计法定位精度分析

水中声源的定位精度受到海洋声学环境的重要影响。结合海上试验的实际应用,分析了水下观测平台采用时延估计法对声源的定位精度问题。根据理论分析,计算了时延估计误差、海洋中声速不均匀、平台非稳性、及声传播起伏等因素引起的俯仰角和方位角误差。利用误差传递公式,获得了上述因素引起的不同平台深度下,不同距离声源的定位误差。比较了采用平面阵与立体阵、是否补偿声线弯曲效应等条件下定位误差的变化,并通过海上试验结果进行了部分验证。研究结果表明,海洋声速不均匀对定位误差的贡献最大。采用立体阵代替平面阵、测量海洋声速剖面并补偿声线弯曲引起的定位误差,在1000m距离上可使定位相对误差从最大30%降低到约10%,有效提高了较远距离上的定位精度。研究结果对于采取措施提高水中声源的定位精度有指导意义。      

The Prediction of Wave Competitions in Inhomogeneous Brusselator Systems

The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.     

Anomalous transparency of water-air interface for low-frequency sound

Sound transmission through a water-air interface is normally weak because of a strong mass density contrast. We show that the transparency of the interface increases dramatically at low frequencies. Almost all acoustic energy emitted by a sufficiently shallow monopole source under water is predicted to be radiated into air. Increased transparency at lower frequencies is due to the increasing role of inhomogeneous waves. For sources symmetric with respect to a horizontal plane, transparency is further increased by a destructive interference of direct and surface-reflected waves under water. The phenomenon of anomalous transparency has significant geophysical and biological implications.