Evolution of the angular power spectrum of scattered radiation from a point source upon propagation in a turbid medium

The propagation of radiation from a point source through a plane layer of an absorbing medium with smooth random permittivity inhomogeneities is considered for the case in which the source and a receiver are spaced by different distances from the layer boundaries. The angular power spectra of the scattered radiation are calculated by the method of statistical modeling for different values of the layer thickness, positions of the source and the receiver relative to the layer, and absorption in the layer. The results for the moments of the angular power distribution obtained earlier in the small-angle approximation are fully confirmed. The transformation of the angular power spectrum upon variation of the source or receiver position with respect to the layer is analyzed for the first time.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Beam propagation in a randomly inhomogeneous medium

An integrodifferential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the “3/2 law.”     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Reflection of waves from a strong scatterer buried in a random medium

Reflection of waves from a mirror covered by a random layer of isotropic, absorbing scatterers is studied and the angular distribution of the scattered intensity is calculated both analytically and numerically. It is shown that backscattering enhancement as well as an enhancement of the incoherent signal in the specular direction take place even in the singly scattered random field. The dependence of the retroreflected intensity is shown to be a non-monotonic function of the depth of the mirror, with a maximum at a depth of the order of the scattering mean free path. Possibilities for employing the results obtained to detect buried strong scatterers and to retrieve parameters of the random media are discussed. In particular, it is shown that in the case of strong absorption the reflecting plane manifests itself by the presence of a peak in the retroreflected intensity which is missing from the scattering diagram of a free-standing or an infinitely thick random layer.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Simulation of wave transmission and reception with phased arrays near the sea shelf bottom

The wave field excited by both single sources and a vertically directed phased transmitting array in a shallow-water waveguide with a layered elastic bottom is numerically simulated. The receivers are equispaced vertical arrays with different apertures, which are positioned at different depths in the water layer. The type of vertical distribution and the transformation of the vertical angular spectrum of pulsed signals arriving at a receiving array are demonstrated for different parameters of the medium, different carrier frequencies, and different distances from the source. It is shown that a selective angular reception ensures a better resolution of the travel-time curves of waves used for sounding the bottom. As an example, the possibility of singling out the shear wave refracted by a deep-seated bottom layer from the tone pattern of the travel-time curves is demonstrated. This possibility can be realized by means of angular scanning in the course of transmission and reception with the use of vertically oriented arrays.     

Multiple scattering of light by a layer of discrete random medium: backscattering

The problem of multiple scattering of light by a layer of discrete random medium is considered. The medium is supposed to be rarefied with scatterers randomly positioned in the layer. Backscattering of light incident normal to the plane of the layer is considered. The scattering matrix is presented as a sum of three matrices, one of them corresponding to incoherent scattering of light and difference of the other two matrices describing coherent scattering. Equations for the calculation of these matrices are given.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

Abstract

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Long-range correlations upon wave propagation in random media under the conditions of strong internal reflection from their boundaries

The large-scale behavior of the spatial distribution of radiation in a random medium is investigated under the assumption of strong internal reflection from its boundaries. The qualitative variations of the angular coherent backscattering spectrum and long-range spatial intensity correlations in the transmitted and reflected radiation fluxes are predicted. Zh. éksp. Teor. Fiz. 113, 291–312 (January 1998)     

Exact solution for coherent backscattering of polarized light from a random medium of Rayleigh scatterers

We discuss a rigorous vectorial theory as a model to represent the enhanced backscattering of polarized light from a random medium. The theory is based on the well known relation between the contributions of the ladder and cyclical diagrams to the intensity which allows to express these contributions in terms of radiative transfer theory. The tensor transfer equation for the electromagnetic field in a half-space occupied by point-like scatterers is explicitly solved with the aid of the Wiener-Hopf method. For the case of normal incidence the angular distribution of the backscattered intensity and the enhancement factor are found for arbitrary angles between the incident and detected linear polarizations and the scanning plane. To describe spatial anisotropy of the backscattering cone the half width at half maximum of the intensity is calculated as a function of these angles. Coherent backscattering of circularly polarized light is also considered.     

Love waves excited by a moving source

The study analyzes the characteristics of surface Love waves excited by the moment of an oscillating torsional force with a point of action that moves uniformly and rectilinearly along the free flat boundary of a medium having the structure of a “layer on a half-space.” The azimuthal–angular distribution of the amplitude and Doppler shift in frequency of the wave modes is studied as a function of the motion velocity of a vibrating source and the parameters of the medium.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

Randomly layered active medium as a broadband amplifier

A flat-layered active medium in which two types of layers with different refractive indices alternate is considered. The thickness of a layer is assumed to be random and large as compared to the wavelength of propagating radiation. A wave propagating along the normal to the layers in such a medium is exponentially enhanced over lengths of the order of many layer thicknesses. In contrast to the familiar case of a periodic flat-layered active medium, waves with any (not necessarily definite resonant) frequency are amplified identically in a wide frequency range. By way of an example, convective instability of space-charge waves in a flow of charged particles moving through a randomly layered medium is considered. The predicted effect can be regarded as an analogue of Anderson’s localization, when increasing solutions rather than exponentially ecreasing ones are selected in view of the activity of the medium.     

Time-resolved phase-space distributions for light backscattered from a disordered medium

We demonstrate time-resolved measurement of optical phase-space distributions as a new probe for investigating the propagation of light in disordered media. Phase-space techniques measure the joint transverse position and momentum distribution of the scattered light, and are sensitive to the spatially varying phase and amplitude of the field. Using this method we investigate light backscattered from a random medium. The measurements indicate that the weakly localized component is a phase conjugate of the incident light field. A new model of backscatter, based on Wigner phase-space distributions, elucidates the spatial and angular behavior of the localized and unlocalized components.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

具有二维fBm特征的分层介质粗糙面电磁散射的特性研究

运用微扰法研究了平面波入射分层介质粗糙面的电磁散射,推出了不同极化状态下的双站散射系数公式.采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合二维fBm分形粗糙面的功率谱导出了平面波入射二维fBm分形分层介质粗糙面的散射系数计算公式.通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线,讨论了分维、底层介质介电常数、中间介质介电常数和厚度及入射波频率对双站散射系数的影响,得到了二维fBm分形分层介质粗糙面散射系数的分维特征、基本特征、分区特征和随频率变化的特征. 关键词： 电磁散射 二维fBm分形粗糙面 分层介质 微扰法     

Röntgenstreuung in Körpern mit regelloser Struktur

It is shown how small angle scattering can be used to get information on the gross structure of a medium with non-crystalline matter distribution. Explicit formulae are derived for the special case of a gel with hole structure, where X-ray analysis will be appropriate. The scattering intensity is expressed in terms of a correlation functionC (r) which determines, byC′(0), the specific surface of the gel. If the hole sizes are random, the correlation function takes on the analytic form of a simple exponential, containing a correlation length a. This correlation length can be measured directly by observing the angular distribution of the scattering intensity.     

Influence of Coating Layer on Acoustic Wave Propagation in a Random Complex Medium with Resonant Scatterers

We investigate the influence of coating layer on acoustic wave propagation in a dispersed random medium consisting of coa.ted fibers.In the strong-scattering regime, the characteristics of wave scattering resonances are found to evolve regularly with the properties of the coating layer.By theoretical calculation,frequency gaps are found in acoustic excitation spectra in a random medium.The scattering cross section results present the evolution of scattering resonances with the properties of the coating layer,which offers a good explanation for the change of the frequency gaps.The velocity of the propagation quasi-mode is also shown to depend on the filling fraction of the coating layer.We use the generalized coherent potential-approximation approach to solve acoustic wave dispersion relations in a complicated random medium consisting of coating-structure scatterers.It is shown that our model reveals subtle changes in the behavior of the acoustic wave propagating quasi-modes.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey-Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.