Wave Propagation In Random Media Research Articles

Universal fluctuations and long-range correlations for wave propagation in random media

The last few years, a large amount of effort has been devoted to the study of coherent effects in disordered systems. They essentially dealt with average values over a whole ensemble of samples and gave rise to the so-called coherent corrections of the weak localization regime. Recently, the transport properties of small disordered (mesoscopic) samples were considered from the view-point of the exact wave configuration (speckle pattern) of a given realization of the random impurity potential. A new kind of coherent effects appeared in the statistics of various properties of disordered samples like for example the universal conductance fluctuations in metals which are size-independent. These properties are shown to come from the long-range correlations in the fluctuations due to the underlying wave-field.

The ground field of arbitrarily shaped linear antennas of geostationary satellites in polar regions taking into account a stochastic and anisotropic ionosphere

The propagation of electromagnetic waves from satellites to the earth is influenced by the electrically anisotropic behavior of the ionosphere. Fluctuating ionospheric parameters cause perturbations in the signal. To calculate the ground field of arbitrarily shaped linear antennas of geostationary satellites for polar regions, the passage of a carrier wave through a homogeneous, electrically anisotropic, stochastic ionosphere imbedded in a two-dimensional three-layer model (near-earth space, ionosphere, atmosphere) is considered. Perturbations due to the ionospheric fluctuations are treated using B.J. Uscinski's multiple scatter theory (see The Elements of Wave Propagation in Random Media, McGraw Hill, 1977) which has been extended to anisotropic media. Finally, the theory of E. Arbel and L.B. Felsen (see Electromagnetic Theory and Antennas Part I, Pergamon, 1963, p.391-420) is applied to derive field representations for the more realistic case of a homogeneously stratified anisotropic ionosphere.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Chaotic wave propagation in random media

Under certain conditions, wave propagation in a random medium can become chaotic, i.e., display extreme sensitivity to initial conditions and complex behavior. This problem has been treated by both ray and wave theory as well as simulations. Chaos is shown by the presence of a positive Lyapunov exponent. For some random media (irregularity spectra), the Lyapunov exponent can be theoretically calculated and agrees with the simulation results. In a ray model, a positive Lyapunov exponent results in the exponential divergence of nearby rays. In the wave case, narrow beams diverge exponentially with range, provided other effects (e.g., diffraction and scattering by small-scale irregularities) do not dominate. In both ray and wave cases, the local exponential divergence results in tangling of the global portraits of the wave fields in phase space. In regimes where it dominates, chaotic wave propagation has wide ranging implications for underwater acoustics, including the proliferation of caustics and uncertainties in predicting long-range propagation. Environments that produce multiple scattering (volume, surface, or bottom) by fluctuations with a large length scale are most likely to show chaotic wave propagation.

Effects of random heterogeneity on wave fields

A theory of wave propagation in random media must actually refer to a suite of predictive models of the effects of a random heterogeneity. This is because a single general formalism, suitable for all stochastic experiments, would be too complicated for realistic scenarios to have any computational capability. Thus predictive models expressed in partial descriptors of a propagating radiation field, intended for specific experiments are acceptable. In this talk, a number of thought experiments for the propagation of waves in random media will be presented. The point of this is to highlight a richness in the observations one might expect to obtain as a result of random heterogeneity, and to provide a discussion of the possible physical bases for these observations. Appropriate descriptors of the radiation field for each of the thought experiments will be considered, as will be the derivation of prediction models expressed in these measures. A number of specific issues to be addressed are: the possibility of ...

Wave propagation in random media having spatial variation of the mean refractive index: a complete set of moment equations with different wavenumbers

Propagation of waves in random media having spatial variation of their mean refractive index is studied, when the frequencies of the waves are high and the "small angle scattering around the ray" and the "Markov random process" approximations are valid. A special coordinate system is introduced, which follows the ray path of the deterministic wave that would propagate in the absence of randomness. The stochastic differential equation for the wave field, which the phase accumulation along the ray is extracted from, is given in the local coordinates around the curved ray paths connecting a source with an arbitrary located observer in back ground media with spatial variation of their mean refractive index. A Fokker-Planck equation satisfied by the characteristic functional of the wave field, with the phase accumulation along the ray extracted, is derived. A complete set of moment equations of waves with different wave numbers and different positions is obtained from the Fokker-Planck equation of the characteristic functional. When the wave has a straight-line ray, our moment equations can degenerate to the moment equations of Tatarskii and the moment equations of Lee. The application of our results to the study of problems related to waves in the atmosphere or in a turbulent ocean are briefly discussed.

Effect on Wave Propagation in Random Media of Fluctuations in Dielectric Constant Having Finite Longitudinal Correlation Radius within the Framework of the Parabolic Wave Equation

Abstract Within the framework of the parabolic wave equation, we consider the effect on wave propagation in random media of fluctuations in dielectric constant that are correlated over a finite longitudinal distance. The corresponding equations for the averaged correlators are derived and applied to propagation of plane-wave packets and Gaussian beams. The non-Markovian corrections are discussed. These corrections result in some novel features such as the appearance of phase shifts due to fluctuations of dielectric constant and a much stronger dependence of the effective attenuation on the transverse wave-vectors. This may result in a redistribution of intensity of the periphery of axial beams and formation of an intensity depression at the beam centre, and may also change the various asymptotic features. We consider Gaussian fluctuations in the course of most of our discussions while the general, non-Gaussian, case is considered at the end of the paper, and illustrated with the specific example of Poisso...

Dispersion of seismic waves by a causal approach

Basic ideas of the causal approach to wave propagation in random media are first overviewed. This approach appeals from the outset to the linearity, causality, and passivity of the effective medium and is therefore particularly simple from the conceptual viewpoint. The energy analysis and the Kramers-Kronig relations play the major role in this method, which does not resort to ensemble averaging.

Temporal fluctuations in wave propagation in random media.

The effect of time-dependent fluctuations of a medium on the spectral intensity and intensity fluctuations of light scattered from the medium is discussed. In the case that the light is multiply scattered from the medium, it is possible in the diffusion approximation to relate the spectral intensity in the scattered wave to the angular-average structure factor of the medium. The relaxation time depends on the number of scattering events, i.e., on the lengths of the multiple-scattering paths, and the scattered intensity thus exhibits a broad range of relaxation times. The spectral intensity in coherent backscattering is also discussed.

Comment on "Large intensity fluctuations for wave propagation in random media"

Comment on "Large intensity fluctuations for wave propagation in random media"

The long and short of random media: Acoustic Anderson localization

Wave propagation in random media relates to a large number of important current problems in physics and acoustics. For long wavelengths the wave equation is locally approximated by the Laplace equation, and this together with the complex boundary conditions provided by the random medium describes many interesting phenomena involving percolation, fractional dimensionality, etc. An important puzzle in the long wavelength regime was solved just recently; a homework problem once assigned by I. Rudnick provided the key to the solution. In the short wavelength regime, where wavelengths are on the order of the variations in the random medium, one may observe effects of Anderson localization, which is currently receiving much attention in the study of quantum phenomena in disordered solids. Recent experiments on acoustic Anderson localization, including nonlinear effects, will be reported. [Work supported by ONR.]

Large intensity fluctuations for wave propagation in random media.

The intensity pattern generated by a monochromatic point source in a random medium is studied. The intensity-intensity correlation function is calculated and it is shown that the intensity, as a function of coordinate, exhibits large fluctuations (the speckle pattern). The sensitivity of this speckle pattern to small changes in the source frequency is also studied.

A depth, range, and time probability distribution of intensity for wave propagation in random media

The second moment of intensity as a function of depth, range, and time for WPRM can be modeled in terms of a space‐time autocorrelation function, a scattering strength parameter γ, and a scaled range X. The higher moments have not been predicted for all λ and X; however, it is generally accepted that the intensity moments are lognormal at small X and exponential at large X. The generalized gamma distribution function (GGDF) [E. W. Stacy, Ann. Math. Star. 33, 1187 (1962)] forms a large class that includes the lognormal and the exponential pdf's. It is proposed that the GGDF can model the probability distributions of intensity in forward scattering over wide ranges in y and X. The temporal intensity fluctuations measured during MATE and depth‐range results from Monte‐Carlo simulations of WPRM for a medium with a power law autocorrelation function have been used to test the proposition. The “goodness of fit” of the GGDF's fitted to those data sets, and the benefits of using distribution modeling rather than intensity moment will be discussed. The results are convincing; it remains a nontrivial task to test the hypothesis theoretically. [Supported by ONR code 4250A.]

Moment-equation and path-integral techniques for wave propagation in random media

Differential equations for all moments of the field of a wave propagating through a random medium are derived under the parabolic approximation and the Markov approximation, but including anisotropy in the random medium and a deterministic background refractive index. Mathematical equivalence is demonstrated between these moment equations and path-integral expressions for the moments obtained under the same approximations. A discussion of approximations that are weaker than Markov is given.

Splitting methods for time-independent wave propagation in random media

Time-independent wave propagation is treated in media where the index of refraction contains a random component, but its mean is invariant with respect to translation in some direction distinguishing the wave propagation. Abstract splitting operators are used to decompose the wave field into forward and backward traveling components satisfying a coupled pair of equations. Mode-coupled equations follow directly from these after implementing a specific representation for the abstract splitting operators. Here we indicate a formal solution to these equations, concentrating on the diffusion regime, where we estimate the forward- and backscattering contributions to the mode specific diffusion coefficients. We consider, in detail, random media with uniform (random atmosphere) and square law (stochastic lense) mean refractive indices.

Wave propagation in random media: a comparison of two theories

The variance of the irradiance scintillations of a wave that propagates in a random medium is calculated by using the extended Huygens–Fresnel principle (EHFP) and then compared with numerical solutions of the parabolic equation for the fourth-order statistical moment. Results are presented for the propagation of Gaussian beams and plane waves in a two-dimensional random medium with a Gaussian correlation function. Various formulations of the EHFP are considered, with particular emphasis on the often-used phase approximation of the EHFP. It is shown that, although both methods predict saturation, there is a considerable disagreement at moderate ranges.

Direct and inverse wave propagation theories and the factorized Helmholtz equation

The reduced scalar Helmholtz equation for a transversely inhomogeneous half-space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial-value plane defines a direct acoustic propagation model. This elliptic formulation admits a factorization and is subsequently equivalent to a first-order Weyl pseudo-differential equation which is recognized as an extended parabolic propagation model. Perturbation treatments of the appropriate Weyl composition equation result in a systematic development of approximate wave theories while exact inversions for several nontrivial profiles provide for an analysis of strong refractive and diffractive effects. The analysis, in a natural manner, provides for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic, seismic, and optical studies. Backscatter effects in both the direct and inverse problems can be included through weak-backscatter and spatial-dimensional (imbedding) perturbation methods. Moreover, the n-dimensional reduced scalar Helmholtz equation for the transversely inhomogeneous medium is naturally related to parabolic propagation models through (1) the above mentioned n-dimensional extended parabolic (Weyl pseudo-differential) equation and (2) an imbedding in an (n + 1)-dimensional parabolic (Schrödinger) equation. The first relationship provides the basis for the parabolic-based Hamiltonian phase space path integral representation of the half-space propagator. The second relationship provides the basis for the elliptic-based path integral representations associated with Feynman/Fradkin, Feynman/Garrod, and Feynman/Dewitt-Morette. The path integrals allow for a global perspective of the transition from elliptic to parabolic wave theory in addition to providing a unifying framework in the direct and inverse formulations for dynamical approximations, resolution of the square root operator, and the concepts of an underlying stochastic process and free motion on curved spaces, the wave equation and path integral analysis foreshadows computational algorithms, extension to (1) the vector formulation appropriate for elastic media and (2) the bilinear formulation appropriate for acoustic field coherence, and application to wave propagation in random media.

A comparison of the quasi‐Rytov and smoothing methods

Two techniques for studying wave propagation in random media, the quasi‐Rytov method and the smoothing method, have been applied to a problem involving radiation by a point source in a one‐dimensional random medium. Each method was used to calculate the mean field, and the results have been compared. It is found that the results are in substantial agreement outside a small region surrounding the source, but that inside this region they disagree. Some technical difficulties which are associated with the smoothing method, and which are related to this discrepancy, are discussed. It is concluded that, although the two methods yield essentially equivalent results (apart from the discrepancy in the near‐source region, which is generally not of practical importance), the quasi‐Rytov method is easier to apply than is the smoothing method. [Work supported by NORDA.]

The attenuation of sound in a randomly lined duct

The kinetic theory of wave propagation in random media is applied to assess the relative merits of the peripherally segmented, axially segmented and “checkerboard” configured acoustic duct treatments proposed by Mani [1]. It is argued that, in a first approximation, a multisegmented liner involving many discrete and distinct sections may be modelled as a liner whose impedance varies randomly with position. This results in a relatively simple analytical description of the acoustic properties of the liner in terms of a system with axial distance of the acoustic modal intensities. The theory is expected to be valid provided that the variation in the impedance from segment to segment is small, so that the conclusions obtained here are of a preliminary nature, and must be regarded as giving a general indication of features which should be incorporated into the design of efficient acoustic liners. The principal such conclusion is that a checkerboard liner offers the best means of increasing the attenuation over and above that of a uniformly lined duct. On the other hand, only minimal gains are to be derived from the use of strictly peripherally segmented liners.

Effective scattering in strongly heterogeneous media

The radiation transfer theory for wave propagation in random media involves an effective scattering function (or effective differential cross section). This function is calculated by means of a CPA-like single-grain approximation for scalar waves in a multi-component mixture consisting of an irregular arrangement of nearly spherical grains. The strength and angular distribution of effective scattering are discussed for long wavelengths. The results satisfy the optical theorem. For an extremely heterogeneous two-component mixture a particularly strong and nearly isotropic scattering is predicted in the vicinity of the percolation transition of the mixture.

Wave propagation in random media symposium to be held at Cambridge

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