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.     

On propagation in continuous random media

Abstract

The analysis of wave propagation in continuous random media typically proceeds from the parabolic wave equation with back scatter neglected. A closed hierarchy of moment equations can be obtained by using the Novikov–Furutsu theorem. When the same procedure is applied in the spatial Fourier domain, one obtains a closed hierarchy of coupled moment equations for the forward- and back-scattered wavefields that is not restricted to narrow scattering angles nor to small local perturbations. The general equations are difficult to solve, but a Markov-like approximation is suggested by the form of the scattering terms. Simple algebraic solutions can be obtained if a narrow-angle-scatter approximation is then invoked. Thus, three distinct approximations are explicit in this analysis, namely closure, Markov and narrow-angle scatter.

The results show that the extinction of the coherent wavefield has a distinctly different form from the corresponding result for propagation in a sparse distribution of discrete scatteres. Furthermore, when the scatter is constrained to narrow forwardand back-scattered cones, there is no back-scatter enhancement. These results are discussed within the context of the extension of the spectral-domain formalism to discrete random media. The general continuous-media moment equations are developed but not solved. The results correct and extend an earlier analysis that used a perturbation approach to compute the scattering functions rather than the Novikov–Furutsu theorem.     

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.     

Electromagnetic wave propagation in random media

The propagation of a narrow frequency band beam of electromagnetic waves in a medium with randomly varying index of refraction is considered. A novel formulation of the governing equation is proposed. An equation for the average Green function (or transition probability) can then be derived. A Fokker-Planck type equation is contained as a limiting case. The results are readily generalized to include the features of the random coupling model and it is argued that the present problem is particularly suited for an analysis of this type.     

On propagation in continuous random media

The analysis of wave propagation in continuous random media typically proceeds from the parabolic wave equation with back scatter neglected. A closed hierarchy of moment equations can be obtained by using the Novikov-Furutsu theorem. When the same procedure is applied in the spatial Fourier domain, one obtains a closed hierarchy of coupled moment equations for the forward- and back-scattered wavefields that is not restricted to narrow scattering angles nor to small local perturbations. The general equations are difficult to solve, but a Markov-like approximation is suggested by the form of the scattering terms. Simple algebraic solutions can be obtained if a narrow-angle-scatter approximation is then invoked. Thus, three distinct approximations are explicit in this analysis, namely closure, Markov and narrow-angle scatter.

The results show that the extinction of the coherent wavefield has a distinctly different form from the corresponding result for propagation in a sparse distribution of discrete scatteres. Furthermore, when the scatter is constrained to narrow forwardand back-scattered cones, there is no back-scatter enhancement. These results are discussed within the context of the extension of the spectral-domain formalism to discrete random media. The general continuous-media moment equations are developed but not solved. The results correct and extend an earlier analysis that used a perturbation approach to compute the scattering functions rather than the Novikov-Furutsu theorem.     

Wigner-Ville distribution for pulse propagation in random media: pulsed plane wave

The time-frequency Wigner-Ville distribution for a pulsed plane-wave signal propagating in a continuous random medium is found, based on the previously derived modal series expression for the two-frequency coherence function. The theory can address propagation in any homogeneous isotropic random medium, but closed-form expressions are specifically derived for a general power-law medium. Two alternative formulations are presented: a modal-wavefront approach wherein each mode is asymptotically transformed to the time domain and a collective approach wherein the mode series is summed collectively and then transformed to the time domain using pole contributions. The physical interpretation of these two different representations in the time-frequency domain as either a superposition of localized wavefronts or collective excitations is established, and their applications to the calculation of local moments are considered.     

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.     

Singularities in forward scattering through random media

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.     

Singular perturbation method for short waves in random media

Abstract

The problem of wave propagation in a randomly inhomogeneous medium is considered on the basis of the parabolic equation approximation. The method of asymptotic expansions construction in powers of the radius of correlation of the random media for the moments of the wave field are proposed.     

Singular perturbation method for short waves in random media

The problem of wave propagation in a randomly inhomogeneous medium is considered on the basis of the parabolic equation approximation. The method of asymptotic expansions construction in powers of the radius of correlation of the random media for the moments of the wave field are proposed.     

Dynamic correlation in wave propagation in random media

Field spectra are analyzed to yield the time-resolved statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth sigma at delay time t is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of kappa(sigma)(t), the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon kappa(sigma)(t). Steady-state statistics are recovered in the limit sigma-->0, in which kappa(sigma=0) is the steady-state degree of correlation.     

Sound propagation and scattering in media with random inhomogeneities of sound speed,density and medium velocity

Abstract

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Optimal beams for propagation through random media

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green's function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green's function.     

Sound propagation and scattering in media with random inhomogeneities of sound speed, density and medium velocity

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

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.     

New phenomena in the propagation of optical waves through random media

A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the 'polarization memory effect'), correlations and statistical fluctuations ('microstatistics'). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.     

New phenomena in the propagation of optical waves through random media

Abstract

A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the ‘polarization memory effect’), correlations and statistical fluctuations (‘microstatistics’). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.     

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