Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

超短THz脉冲在随机散射介质中的传播

用Monte-Carlo方法模拟了超短THz脉冲在随机散射介质中的传播.根据Mie理论计算出随机散射介质的散射系数和各向异性因子，研究了随机散射颗粒及介质厚度的大小对透射脉冲的影响.结果表明在Mie散射范围内，在相同的浓度下，颗粒尺寸越小，散射介质越厚，THz散射越严重，对透射脉冲的影响越大.散射同时降低了THz脉冲在随机散射介质中的成像分辨率. 关键词： 超短THz脉冲 随机散射介质 Mie理论 Monte-Carlo方法     

Multiple scattering in random media. III. Coherent potential propagators and fluctuations

An earlier microscopic approach to the theory of the averaged resolvent operator for an electron interacting with impurities is formulated in terms of coherent propagators. We study the corrections to the coherent potential approximation arising from fluctuations. For uncorrelated positions of the impurities, the linear, restricted, and general two-body additive approximations to the treatments of fluctuations are studied. For general correlations, the linear and restricted two-body additive approximations are studied. For both coherent and bare propagators, corresponding treatments of fluctuations involve the same correlation functions for impurities.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

A hierarchical model for random walks in random media

We show that the random walk generated by a hierarchical Laplacian in ^d has standard diffusive behavior. Moreover, we show that this behavior is stable under a class of random perturbations that resemble an off-diagonal disordered lattice Laplacian. The density of states and its asymptotic behavior around zero energy are computed: singularities appear in one and two dimensions.     

Microwave propagation in dense random media

Summary Using simple, approximate arguments, we obtain a formula that relates the average spacing between peaks in the transmitted intensityvs. wave frequency distribution of a single configuration of a random distribution of scatterers to the diffusion constant, sample thickness, and effective absorption length. The value of the diffusion constant obtained this way is found to be within 20% of the value obtained via intensity-intensity autocorrelation function techniques. The author of this paper has agreed to not receive the proofs for correction.     

Long time tails in stationary random media. I. Theory

Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t^–(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket ^–d/2 for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ^d/2 contribution to the low-frequency part of the frequency-dependent electrical conductivity.     

光在随机增益介质中的放大

结合环形腔理论,运用蒙特卡罗法模拟了光子在介质中的随机行走。研究了倍频Nd:YAG（脉宽6 ns,频率20 Hz）脉冲激光器作为泵浦光,在TiO2 / 若丹明 B有机增益介质中,散射微粒的颗粒密度和泵浦光面积对随机激光器阈值强度的影响。模拟结果表明：随机激光阈值和光子在增益介质中的随机行走路程长度和光子通过边界返回增益区和非增益区的几率有关。随着泵浦光面积的增加,随机激光器阈值降低;增益介质中散射颗粒密度的增加降低了随机激光器的阈值。     

Dielectric polarization in random media

The theory of dielectric polarization in random media is systematically formulated in terms of response kernels. The primary response kernel K(12) governs the mean dielectric response at the pointr ₁ to the external electric field at the pointr ₂ in an infinite system. The inverse of K(12) is denoted by L(12); it is simpler and more fundamental than K(12) itself. Rigorous expressions are obtained for the effective dielectric constant ^* in terms of L(12) and K(12). The latter expression involves the Onsager-Kirkwood function ( ^*– ₀)(2 ^*+ ₀) /₀^* (where ₀ is an arbitrary reference value), and appears to be new to the random medium context. A wide variety of series representations for ^* are generated by means of general perturbation expansions for K(12) and L(12). A discussion is given of certain pitfalls in the theory, most of which are related to the fact that the response kernels are long ranged. It is shown how the dielectric behavior of nonpolar molecular fluids may be treated as a special case of the general theory. The present results for ^* apply equally well to other effective phenomenological coefficients of the same generic type, such as thermal and electrical conductivity, magnetic susceptibility, and diffusion coefficients.Work performed under the auspices of the United States Department of Energy. A preliminary report on this work was given at the Eighth West Coast Statistical Mechanics Conference, University of California, Berkeley, 22 June 1982.     

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.     

Boson peak, flickering noise, backscattering processes and radiative transfer in random media

The method of matrix Green’s functions in the classical theory of electromagnetic waves is stated. This method allows to obtain a closed equation system in the presence of the random media for the calculation both coherent, and incoherent (fluctuating) components of radiation. The density and heterogeneity of scattering media can be arbitrary. The coherent channel is calculated independently. The fluctuating radiation distribution in the medium is developed initially by an interference pattern generated by the coherent channel. The limitations of the processes speed are absent. The theory embraces such phenomena as the boson peak, flickering noise, memory effect, backscattering processes and also conventional radiative transfer equation and Fresnel’s formulae.     

Time and direction of arrival detection and filtering for imaging in strongly scattering random media

We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and overwhelms the arrivals from the small reflectors. Building on the adaptive time-frequency filter of [Borcea et al, SIIMS 2011;4(3)], we propose a robust method for detecting the direction of arrival of the direct echoes from the small reflectors, and suppressing the unwanted clutter backscatter. This improves the resolution of imaging. We illustrate the performance of the method with realistic numerical simulations in a non-destructive testing setup.     

Multiple scattering of light transmission in a smoke layer

The visibility in a fire scene decreases because of the existence of smoke produced by the flammable materials. With the growth of smoke concentration, the relationship between light and smoke becomes complicated due to the multiple scattering. In this paper, the radiative transfer equation (RTE) that considers the multiple scattering was applied to calculate the light transmission in a smoke layer. As input parameters of RTE, the single scattering albedo, asymmetry parameter and extinction cross section of single smoke agglomerate were calculated by the discrete dipole approximation (DDA) method. The effects of smoke agglomerate diameter, number density of smoke layer, and the incident light wavelength were considered. The results show that the light transmitted flux decreases with the growth of smoke diameter and number density, and increases with the growth of wavelength. The smoke diameter is dominant among the three parameters, and the light transmitted flux tends to be stable when the wavelength reaches a certain value.     

Classical diffusion in strong random media

We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.     

ZnO粉末中无序激射现象时间分辨的研究

采用抽运-探测时间分辨方法实验研究了半导体材料ZnO纳米颗粒粉末中的无序激射现象.在2 67nm激光的抽运下，通过精确控制抽运光的能量和样品表面的抽运面积，获得了宽度小于1n m的单模无序激射光谱和多峰的多模无序激射光谱.时间分辨的抽运-探测结果显示，此时样 品的上能级寿命仅为几个皮秒，证明了ZnO粉末的单模无序光谱是受激辐射的结果. 关键词： 高散射介质 多重散射 抽运-探测 无序激射     

McKean-Vlasov limit for interacting random processes in random media

We apply large-deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit. In particular, we describe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its solution and of the finite-size fluctuation around this solution requires some new ingredient as compared to existing techniques for nonrandom interaction.     

Selection of optical radiation in scattering in partially ordered disperse media

Results of theoretical studies of the interaction between optical radiation and partially ordered disperse media are reported. In terms of the amplitude-phase screen model consideration is given to the concentration effects of whitening and darkening in random close-packed systems of optically soft particles. The concentration dependence of transmission of close-packed systems of coarse particles is described with the use of a small-angle solution of the stochastic finite-difference transfer equation. The effects of coherent reirradiation occurring in close-packed monolayers of highly refracting particles are analyzed using a quasicrystalline approximation of the theory of multiple wave scattering and the radial particle distribution function obtained from a solution of the Percus-Yevick equation. This approach extended to multilayer systems is used to describe formation of forbidden photon zones in transmission spectra of one- and three-dimensional disperse systems with a high degree of ordering. Results of quantitative calculations are shown to agree well with experimental data. The possibility of using established regularities for optimization of spectral characteristics of selective elements based on spatially ordered disperse systems with different structural organization is discussed. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 721–733, September–October, 1998.