Theoretical Aspects of Wave Propagation in Random Media Based on Quanty and Statistical Field Theory (original) (raw)

Wave propagation in random media: a comparison of two theories

Journal of the Optical Society of America, 1983

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.

Wave propagation in non-Gaussian random media

Journal of Physics A: Mathematical and Theoretical, 2015

We develop a compact perturbative series for accoustic wave propagation in a medium with a non Gaussian stochastic speed of sound. We use Martin -Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a "quantum" field theory one, and then frame this problem within so-called Schwinger -Keldysh of closed time-path (CTP) formalism. Variation of the so-called two-particle irreducible (2PI) effective action (EA), whose arguments are both the mean fields and the irreducible two point correlations, yields the Schwinger-Dyson and the Bethe-Salpeter equations. We work out the loop expansion of the 2PI CTP EA and show that, in the paradigmatic problem of overlapping spherical intrusions in an otherwise homogeneous medium, non Gaussian corrections may be much larger than Gaussian ones at the same order of loops

Statistics of waves propagating in a random medium

Foundations of Physics, 1996

The statistics of coherent radiation propagating in a random medium is analyzed in the framework of diagrammatic techniques. The distribution function for radiation intensity is calculated and it is shown that only for small values of intensity is the distribution function a simple exponential, as predicted by Rayleigh statistics. For larger values of intensity, the distribution function differs drastically from a simple exponential, and exhibits the asymptotic behavior of a stretched exponential. The results obtained are con6rmed by numerical simulations.

Statistics of Wave Dynamics in Random Media

Physical Review Letters, 1999

We measure the joint distribution of the energy transmission coefficient´a b and the single channel delay time t ab for microwave radiation propagating through a random medium in the limit of zero pulse bandwidth. For fixed´a b the distribution of t ab is Gaussian with variance inversely proportional to´a b . In contradistinction to t ab , the dynamic matrix element´a b t ab has substantial long-range correlation with frequency shift. We present a new dynamic theory for a Gaussian process, which is in excellent agreement with experiment. [S0031-9007 08297-0] PACS numbers: 42.25.Dd

Wave propagation in random media

Journal of Fluid Mechanics, 1971

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

Coherent propagation of waves in intrinsically nonuniform random media

Physical Review B, 1991

We develop a theoretical framework in which to study coherent propagation of waves in a random medium, which is also characterized by an intrinsic nonuniformity such as stratification. We show that the coherent efFects are preserved in such a medium and can be readily treated by making a straightforward extension of the method used for a uniformly random medium. To illustrate the general formalism, we study in detail the problem of backscattering in a stratified medium.

Propagation in random media with stationary temporal fluctuations

Radio Science, 1975

Born's method is applied to the time-dependent wave equation. Exact solutions, valid for all wavelengths, are obtained for the first-order perturbation terms for monochromatic plane and spherical waves propagating in random media with stationary temporal fluctuations. It is shown that the temporal fluctuations of the medium can be neglected if the temporal frequencies of the fluctuations are much less than the frequency of the propagating wave and if the propagation time from the transmitter to receiver is much less than the coherence time of the medium. In the atmosphere for the case where (•k30//40)L • 1, where l 0 is the inner scale of turbulence, log-amplitude and phase covariance functions were calculated for the polarized and depolarized fluctuations of plane waves propagating in slightly different directions. Numerical evaluation revealed that the polarized log-amplitude fluctuations decorrelate for angular separations on the order of tan-• [(h 0 / L) •/2 ] while phase fluctuations decorrelate for angular separations on the order of tan -• (Lo/L), where L 0 is the outer scale of turbulence. E•z(r,t) = -(1/2'tr) f dr' [exp(ik0 Jr-r' I)/Ir -r' l] ß {(1/c2)(02/Ot2)[n•(r',t -Jr -r' I/c)] -E0 ß (r',t-Jr-r'J/c)(O2/oz'2)n•(r',,)l,=,_l,_,,i/c} (•)

Velocity and attenuation of scalar and elastic waves in random media: A spectral function approach

This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green’s function in the frequency-wavenumber domain (x, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves

Transport equations for elastic and other waves in random media

Wave Motion, 1996

We derive and analyze transport equations for the energy density of waves of any kind in a random medium. The equations take account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization e ects, coupling of di erent types of waves, etc. We also show that di usive behavior occurs on long time and distance scales and we determine the di usion coe cients. The results are specialized to acoustic, electromagnetic, and elastic waves. The analysis is based on the governing equations of motion and uses the Wigner distribution.

Two-scale solution for the intensity fluctuations of two-frequency wave propagation in a random medium

Journal of the Optical Society of America A, 1985

We have solved the equation for the two-frequency fourth-order moment of two parallel monochromatic plane waves having different frequencies and propagating through a randomly inhomogeneous medium. The solution procedure uses a two-scale expansion based on the smallness of a new parameter whose magnitude does not depend on the scattering strength. The results are shown to be valid for all values of the scattering parameter. The multidimensional integral expression for the bichromatic correlation was evaluated for a two-dimensional random medium characterized by a Gaussian correlation function. Further simplification was carried out in the strongscattering regime, using asymptotic techniques. It is shown that the bichromatic correlation decreases with the wavelength separation. Its dependence on range is more complicated: Initially it increases with increasing range, only to level off to zero for large enough scattering strength, wavelength separation, and range.