Plane waves in a layered weakly dissipative randomly inhomogeneous medium

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Statistical modelling of the backscattered field in a one-dimensional non-stationary stochastic problem

Abstract

Within the framework of an exact wave approach in the spatial-time domain, the one-dimensional stochastic problem of sound pulse scattering by a layered random medium is considered. On the basis of a unification of methods which has been developed by the authors, previously applied to the investigation of non-stationary deterministic wave problems and stochastic stationary wave problems, an analytical-numerical simulation of the behaviour of the backscattered field stochastic characteristics was carried out. Several forms of incident pulses and signals are analysed. We assume that random fluctuations of a medium are described by virtue of the Gaussian Markov process with an exponential correlation function. The most important parameters appearing in the problem are discussed; namely, the time scales of diffusion, pulse durations, the medium layer thickness or the largest observation time scale in comparison with the time scale of one correlation length for the case of a half-space. An exact pattern of the pulse backscattering processes is obtained. It is illustrated by the behaviour of the backscattered field statistical moments for all observation times which are of interest. It is shown that during the time interval when the main part of the pulse energy leaves the medium, the backscattered field is a substantially non-stationary process, having a non-zero mean value and an average intensity that decays according to a power law. There are various power indices for the different duration incident pulses, however, they are not the same as those of previous papers, which were obtained on the basis of an approximate and asymptotic analysis. We have also verified that the Gaussian law is valid for the probability density function of the backscattered field in the case of any incident pulse duration.     

The final states in photoemission and field emission

For a semiinfinite medium and for a slab it is shown how the final state functions describing photoemission and field emission are to be defined if more than one solution of the Schrödinger equation for a fixed value of the energyE and the parallel componentk of the wave vectork exist. As by-product some interesting statements concerning complexband structure and the solutions of the Schrödinger equation for a semiinfinite medium or a crystalline slab are derived.     

Interference simulation in a cold collisionless moving magnetized plasma slab and (free surface of plasma slab)

Abstract

The pattern of intensity due to the interference in a cold collisionless magnetized moving plasma slab is investigated. Theoretically, it is assumed the mentioned layer has been located as a thin layer in an etalon Fabry–Perot interferometer surrounded by vacuum. The direction of external magnetic field is normal to the plasma surface and the plasma slab moves parallel with external constant magnetic field. By taking into account the relativistic considerations, the functions of transmitted intensity are presented coincident with the Airy function form in laboratory and plasma slab frames, respectively. The effects of plasma frequency, cyclotron frequency, thickness of plasma slab, and velocity of the plasma slab on band width, finesse factor, and visibility are simulated. Finally with the assumption that there are two wavelengths near together in incident electromagnetic beam the power resolution for this configuration are analyzed. All studies mentioned above have been done for S-polarized and P-polarized electromagnetic beams separately.     

Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

Dynamics of a Peierls system in a light field

Equations describing the temporal dynamics of the order parameter ξ(t) of a metal-semiconductor phase transition and the density n(t) of electron-hole pairs in a Peierls system in a light field are obtained on the basis of the Lagrange equation for the phonon mode and the Liouville equation for the density matrix of the electronic subsystem. The equations obtained are analyzed for a stationary state (with adiabatically slow variation of the light intensity I) and for a transient process near the initial and final states of dynamic equilibrium (with the light field switched on abruptly). It is shown that for adiabatically slow growth of the intensity I up to a certain critical value I _c the band gap of the electronic spectrum decreases but the semiconductor phase of the Peierls system remains stable. For I>I _c the stationary semiconductor state (ξ≠0) becomes unstable. When the light is switched on abruptly, the deviation of the system parameters from the initial values is described by an exponential law with a characteristic reciprocal of the rise time of the process linearly dependent on the irradiation intensity I. As a new position of equilibrium is approached, three qualitatively different regimes of behavior of the order parameter ξ and density n are possible. For low intensities I(I< I ₁) a purely relaxational aperiodic process occurs. For intermediate intensities I(I ₁<I<I _c) damped oscillations of ξ and n are observed near a new stationary semiconductor state with a smaller band gap. For I>I _c the stationary semiconductor state with ξ≠0 is absent. The experimental data on the irradiation of a vanadium dioxide film with a powerful laser pulse is interpreted on the basis of the theory developed. Zh. éksp. Teor. Fiz. 116, 2154–2175 (December 1999)     

Existence and uniqueness for nonlinear boundary value problems in kinetic theory

A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies.     

Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particle Bath

We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host medium with a fixed distribution. This is achieved by controlling the L ^p -norms, the moments and the regularity of the solutions to the Cauchy problem together with arguments related to a dynamical proof for the existence of stationary states.     

Influence of boundary conditions on statistical characteristics of the wavefield in a layered randomly inhomogeneous medium

Abstract

We consider the problem of the oblique incidence of a wave on the half-space of a layered randomly inhomogeneous medium without absorption and analyse the influence of boundary conditions on the probability distribution of the reflection coefficient phase, and the statistical behaviour of the wavefield intensity moments inside the medium.     

线性剖面克尔材料分层板波导中光波的传播

对三层板波导中光波传播问题进行了讨论.芯材料是克尔型介质,其折射率平方(n²)剖面分布随x作线性变化.此时芯区的亥姆霍兹方程约化为Painleve方程,利用Laurant级数可得到其近似解.     

Knudsen Layer for Gas Mixtures

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math. 39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.     

Effects of Self-Correlation Time and Cross-Correlation Time of Additive and Multiplicative Colored Noises for Dynamical Properties of a Bistable System

Considering a bistable system driven by additive and multiplicative colored noises with colored cross-correlation, we obtain the analytic expressions of the stationary probability distribution P _st(x), the linear relaxation time T _c , and the correlated function C(s). The effects of the noise intensity, the self-correlation time and the cross-correlation time for the bistable system are discussed. The noise intensity D speeds up relaxation of the system from unstable points, which when D < Q, the effects are the most obvious; when D > Q, the effects are damped. The self-correlation time τ₁ and τ₂ make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x. On the contrary, the cross-correlation time τ₃ makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x. The effect of the self-correlation time is more projecting than the effect of the cross-correlation time. PACS number: 05.40.−a, 02.50.−r, 05.10.Gg.     

One-and two-front states of equilibrium in a thin superconducting film

Two-phase states of equilibrium of a thin superconducting film carrying a current under conditions of convective heat exchange at the free surface of the film are studied. It is shown that for a classical superconductor the two-phase state of the film remains a single-front state over a wide range of parameters of the system. For high-T _c superconductors there exists a maximum value of the Steckl number above which weakly nonequilibrium stationary states can only be multifront states. The solutions of the boundary-value problem modeling a two-front state of equilibrium are investigated, and the conditions under which they obtain are examined. Zh. Tekh. Fiz. 68, 84–87 (March 1998)     

Propagation of a beam of gamma rays in the field of a monochromatic laser wave

The head-on propagation of a beam of γ grays through the field of a laser wave is investigated. The optical properties of the laser wave (as a medium) are described by the dielectric tensor. The refractive indices are determined, and the polarization characteristics of electromagnetic normal modes capable of propagating in such a medium are investigated. Relations are derived to describe the variation of the initial polarization and intensity of a γ-ray beam as it propagates in a laser field. The influence of laser intensity on the investigated process is discussed. Zh. éksp. Teor. Fiz. 112, 2016–2029 (December 1997)     

Coherent backscattering of a light pulse by a slab of disordered medium

We obtain an exact analytical solution to the problem of the enhanced backscattering of a short pulsed signal from a two- and three-dimensional medium with isotropically scattering centres. The angular spectrum is expressed in terms of the solution to the corresponding stationary problem. The intensity oscillations are shown to appear on the tails of the angular spectrum. The origin of these oscillations is associated with the ballistic phase shift between the interfering waves arriving at the detector. It is shown that the finiteness of the slab thickness influences the magnitude of the backscattering intensity and does not change the shape of the angular spectrum. The range of validity for the diffusion approximation is pointed out.

The results obtained in the paper also contain a generalization of the well known solution to the problem of incoherent transfer to a pulsed signal to the case of two-dimensional disordered media.     

Enhancement of the backscattered intensity from fractal aggregates

Abstract

Comparative measurements were conducted for the backscattered intensities of light from uniform random and fractal aggregated media. Different features are found for the backscattered intensity peak shapes. A crossover between the θ^1?D and θ^?2 dependences of the backscattered intensity occurs in the case of fractal aggregated medium, where D indicates the fractal dimension.     

Phase fluctuations and localization length in layered randomly inhomogeneous media

Abstract

We consider the problem of the inclined incidence of a plane wave on the halfspace of a randomly inhomogeneous layered medium without absorption. The probability distribution of the reflection coefficient phase with respect to the incidence angle is calculated. With the help of this distribution we analyse the quantities connected with localisation effects—the length localization and moments of the intensity inside the medium.     

Diffuse reflection of light from a dense random medium using fibres dipped into the medium

Abstract

Diffuse reflection of a narrow collimated light beam from a slab of a dense random medium is considered theoretically and experimentally for the case of the source and the detector fibres dipped into the random medium, as is the case for an endoscopic catheter. By use of the diffusion approximation, a simple and physically clear analytical expression is derived for the distribution of the diffuse reflectance of the light beam along the surface of the random medium slab. We include the effects of reflections from the top and bottom surfaces of the slab. The analytical expression derived predicts that, in the case of small absorption, the relative reflectance is a universal function defined by the geometrical parameters and is independent of specific properties of the random medium. The theoretical prediction is found to show good agreement with the results of measurements.     

磁单负材料板附近的原子的自发辐射场分布

本文研究了磁单负材料板附近的两能级原子通过自发辐射激发的表面模式及场强分布. 磁单负材料是有效介电常数大于零而磁导率小于零的人工微结构材料. 根据麦克斯韦方程及边界条件, 这种材料板只支持TE极化的表面模式. 本文分析了具有不同磁导率和厚度的磁单负材料板所支持的表面模的性质, 如模式数目和模式的对称性, 进而讨论了这些特性对原子自发辐射场的空间分布的影响. 结果表明原子与磁单负材料板的距离可影响辐射场中表面模的比重, 当表面模起主要贡献时, 在材料板左表面上原子辐射场呈定向发射的分布. 而材料板右表面的辐射场分布取决于表面模的对称性和比重, 如果同时存在对称和反对称的表面模, 右表面的场很弱甚至完全消失, 而如果只存在对称或反对称的表面模, 右表面会有与左表面等强度的辐射场分布. 这些性质与原子在金属表面的辐射场分布明显不同, 我们的结果对原子辐射场的空间控制以及实现简单结构的单光子源有积极意义.     

Backscattering of stationary radiation in time-dependent random media: average intensity and intensity fluctuations

We consider backscattering of stationary radiation in a random medium whose wavespeed fluctuations depend on time and on space. We modify a previous derivation of the equations that govern the range-evolution of the spectra of the ensemble-averaged forward-and back-propagating components of the field and their second-order statistics, and extend the approach to treat the fourth-order statistics. The latter are governed by integro-difference equations that account for the broadening of the signal spectra due to the time-dependence of the random fluctuations. In the quasi-monochromatic regime, where spectra owing to a monochromatic excitation remain confined to a narrow band over extensive ranges, the integro-difference equations transform into ordinary differential equations that govern the time-dependence of the quantities of interest. We use this simplification to track the power fluxes and their fluctuations (scintillation) in a one-dimensionally stratified slab, where the wave-speed fluctuations depend on the range-coordinate normal to the planes of stratification, and also to treat modal propagation in a duct, where the wave-speed fluctuations depend on all three spatial dimensions. The results suggest that a Gaussian equilibrium is approached at large ranges, on a suitably defined backscattering scale that depends on the medium parameters and the geometry.