基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

随机介质中的矢量辐射传输理论

本文讨论了极化电磁波在随机介质中多次散射,传输和热辐射的斯托克斯矢量的辐射传输理论。其中包括随机分布离散的球形和非球形粒子的矢量辐射传输方程,离散坐标-特征分析法,付利叶变换,迭代法等数值解。讨论了非球形粒子的穆勒矩阵。并研究了密集分布的散射粒子介质的辐射传输理论,考虑了密集粒子散射的相干性,计算了有效传播常数。理论及数值结果与实验作了很好的比较。     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Guided wave topological imaging of isotropic plates

Topological imaging is a recent method. So far, it has been applied to bulk waves, and high resolution has been demonstrated for imaging scatterers even with a single ultrasonic insonification of the inspected medium. This method consists of (i) emitting waves and measuring the response of the medium; (ii) solving two propagation problems: the direct problem, where the experimental source is simulated, and the adjoint problem, where the source is the time-reversed difference between the measured wave field and that obtained from the direct problem; (iii) computing the image by simply multiplying both wave fields together in the frequency domain, and integrating over the frequency. The speed of the method depends only on the cost of the field computations that are performed in the defect-free medium. The present work deals with the application of topological imaging to plate guided waves. Combining modal theory and Fourier analysis, the computations are performed in a very short time. In the investigated cases, two-dimensional in-plane imaging is based on propagation of the single S0 Lamb mode. Despite very high dispersion of that mode, scatterers are accurately located and the spatial resolution is equal to about one wavelength.     

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 of acoustic waves by a half-space of distributed discrete scatterers with modified T-matrix approach

In studying the multiple scattering of acoustic waves by a half-space of distributed discrete scatterers, the quasicrystalline approximation(QCA) approach together with the hole correction (HC) or the pair distribution functions (PDF) have been used extensively, in which a system of simultaneous equations must be solved to determine the effective propagation constant and the expansion coefficients of the coherent exciting field. In this paper, we analyse the same problem under Foldy's approximation (EFA) by using the so-called modified T-matrix approach (MTMA) which was first proposed by Twersky. Two equations in a considerably simple and clear form are obtained for determining the effective propagation constant and the amplitude of the coherent transmitted field, as the scatterers are identical spheres. The numerical results in the low-frequency limit are also discussed in brief.     

随机非球形粒子全极化散射的时间相关Mueller矩阵解

从与时间相关的矢量辐射传输方程推导一阶Mueller矩阵解,用来模拟Gauss型平面脉冲波入射下,一层随机、非均匀取向非球形粒子的全极化双站散射.数值计算了同极化和去极化脉冲响应,与入射脉冲进行了比较,说明了随机介质的物理参数,如粒子的取向和占空比、入射角、极化以及层厚等对脉冲响应的影响 关键词： 平面脉冲波 非球形粒子 Mueller矩阵     

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.     

含金属散射体的中红外无序介质的光子定域化理论研究

基于Mie散射理论发现,各种金属在中红外区的各个频率点上的散射行为均极为相近,是一种在中红外区反照率高但散射效率较低的散射体.在浓度为10%时,介质的定域化参量最小只能达到6.6,并且与体系的常用基质材料无关.数值研究揭示了这种金属散射体系统与低吸收、高折射率散射体系统间的内在联系 关键词： 光子定域化 无序介质 中红外 Mie散射 金属     

Effect of pulse entrapping on diffuse reflection from a resonant random medium: exact solution to the scalar albedo problem

A recently derived radiative transfer equation with three Lorentzian delay kernels is applied to an albedo problem of the scalar wave field produced by the diffuse reflection of a quasi-monochromatic pulse from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function H(μλ), extended analytically into the complex single-scattering albedo λ plane. The resulting analytic solution for the time evolution of a diffusely reflected short pulse is used to study on the whole time axis the effect of the redistribution of the energy of the propagated pulse from the front to the rear of the pulse in cases where the pulse may for most of the propagation time through the medium be 'entrapped' inside resonant scatterers. By considering the power flux through unit area of the boundary of the medium and unit solid angle, it is shown that the relative shift of an 'energy centroid' ('centre of mass') of the pulse diffusely reflected from the resonant random medium (compared with the pulse energy centriod in the non-resonant case) is equal to the parameter describing the energy accumulation inside the scatterers. This result may be used for experimental study of resonant random media with the aid of a short-pulse technique.     

Scattering of electromagnetic waves from a half-space of randomly distributed discrete scatterers and polarized backscattering ratio law

Summary The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.     

Modeling of high-frequency propagation in inhomogeneous background random media

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.     

Control of the tunnel current flowing though nonuniform heterogeneous barriers with spherically symmetric inclusions

The effect of spherical quantum objects (scatterers) embedded into semiconductor barriers on the tunnel current flowing through them has been studied. For this purpose, the problem of the scattering of incident and reflected wave functions (damping if their energy is less than the barrier potential) of the electron by the stepwise spherically symmetric scattering potential has been solved.     

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.     

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.     

Long-range intensity correlations for the multiple scattering of waves in unordered media

The long-range correlations in the reflected and transmitted fluxes in the case of the coherent transport of waves in an unordered medium with discrete inhomogeneities are considered. The correlator and spectrum of the intensity fluctuations are expressed in a general form in terms of the one-center scattering amplitude and the propagators of the mean radiated intensity. The random interference of the waves and the fluctuations of the number of scattering centers in a microvolume of the medium are taken into account simultaneously. Detailed calculations are performed for two limiting radiation propagation regimes, viz., spatial diffusion and small-angle multiple scattering. It is shown that the conservation of the total flux upon elastic scattering leads to the formation of a dip in the spectrum and, accordingly, a negative correlation between the intensities at large distances. In the case of spatial diffusion this feature is displayed upon reflection, and in the case of small-angle multiple scattering it is displayed upon transmission through a slab. The relative roles of the various sources of intensity fluctuations, as well as the sensitivity of the correlations to factors that influence the wave propagation regime, viz., the finite size of the scattering sample, absorption in the medium, and the presence of a frequency shift in the incident waves, are analyzed. We find that fluctuations in the distribution of the scatterers show up most strongly in a medium with strong, i.e., “non-Born,” centers, especially if they exhibit absorption. Zh. éksp. Teor. Fiz. 111, 1674–1716 (May 1997)     

Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions

In a previous paper, Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] obtained two formulas for the effective wavenumber in a dilute random array of circular scatterers. They emerged from a study of the problem of the reflection of a plane wave at oblique incidence to a half-space containing the scatterers. Here, their study is extended to obtain formulas for the reflection and transmission coefficients and to investigate the average fields near the boundary of the half-space. Comparisons with previous work are made.