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.     

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.     

Experimental study of electromagnetic wave propagation in dense random media

Controlled experiments have been conducted to measure the propagation of synthetically generated pulses in dense random media. The dense media were prepared by embedding spherical dielectric scatterers in a homogeneous background medium: the size and volume fraction of the scatterers were the controlled parameters. A network analyser-based system operating in the frequency domain was used to measure the electric field reflected and transmitted by slab-shaped samples of dense media as the source signal was swept from 26.5 to 40 GHz. An inverse Fourier transform was used to convert the frequency domain response into time domain pulse waveforms. The time domain response was then used to obtain pulse propagation velocity and attenuation in the controlled samples. The experimental results are shown to be in general agreement with dense medium theories.     

Low-frequency surface wave propagation along plane boundaries in fluid-saturated porous media

A method of the mechanics of a fluid-saturated porous medium is used to study the propagation of harmonic surface waves along the free boundary of such a medium, along the boundary between a porous medium and a fluid, and along the boundary between two porous half-spaces. It is shown that, at low frequencies (i.e., for waves with frequencies lower than the Biot characteristic frequency), the corresponding dispersion equations in zero-order approximation are reduced to the equations for an “equivalent” elastic medium. For the wave numbers of surface waves, corrections taking into account the generation of longitudinal waves of the second kind at the boundary are calculated. Examples of numerical solutions of dispersion equations for rock are presented.     

Functional Fokker-Planck formalism for wave propagation in random media under delocalized and weak localized regimes

The functional Fokker-Planck equation is used to obtain the phenomenological radiative transfer theory in the form of the modified Ambarzumian-Chandrasekhar equation which takes into account the backscattering enhancement effect from the 3D slab of a randomly inhomogeneous medium.     

Theory of wave propagation in one-dimensional random media containing two-scale inhomogeneities

Pacific Oceanographic Institute, Far-Eastern Branch of the Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 3, pp. 274–279, March, 1991.     

Path integral solution of the time-domain progressive wave equation and wave propagation in random media

A time-domain progressive wave equation is derived from the usual linear acoustic wave equation, and it is shown that the solution to this new equation can be expressed as a Feynman path integral. This path integral representation is used to derive the time-dependent statistics of acoustic fields propagating through random media.     

The effect of total internal reflection of wave beams in nonlinear media

The recent papers that consider new effects attributed to the total refection of a weak beam at a more powerful beam with another frequency in nonlinear media are reviewed. As an example, the dynamics of the beam reflection in media with thermal nonlinearity and photorefractive crystals are analyzed.     

Statistical temporal behaviour of pulse wave propagation through continuous random media

Pulse waves propagating through random media suffer distortions, such as fluctuation of arrival time, temporal broadening, and alteration of skewness and kurtosis, due to both the background medium and embedded irregularities. We carry out a study on the temporal behaviour of electromagnetic pulses propagating through random media using temporal moments and an analytic solution of a two-frequency mutual coherence function recently obtained by iteration. We treat the temporal characteristics sequentially, with general expressions obtained first. Then the concise forms are given for pulse propagation in the turbulent non-dispersive atmosphere and the ionosphere, with numerical calculations for the latter. The results show that the mean arrival time is dominated by the term propagating at group velocity, and small corrections arise from higher-order dispersion of the background medium and random scattering of irregularities, but the correction from dispersion of irregularities is neglected as it is so small. As for pulse broadening in trans-ionospheric propagation, the results show that contributions are mainly from the dispersion of the background ionosphere and scattering of electron density irregularities in most cases, and the contribution of dispersion of irregularities is so small that it can be neglected. Finally, we find that the temporal skewness of a trans-ionospheric pulse is negative and its energy is shifted to the leading edge, and the contributions from scattering and dispersion of irregularities dominate over those of background, so the latter can be neglected in most cases.     

Effects of nondiffusive wave propagation upon coherent backscattering by turbid media

The nondiffusive contribution to the coherent backscattering intensity is calculated for the media with relatively large particles (size a is greater than wavelength λ). The results are in good agreement with the experimental data at the wings of the angular spectrum of the coherent backscattering. The shape of the backscattering peak is analyzed for strongly absorbing media. The correlation function of the intensity fluctuations is calculated for the scattering by Brownian particles at relatively large time shifts.     

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.     

Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations

We survey research on radiation propagation or ballistic particle motion through media with randomly variable material density, and we investigate the topic with an emphasis on very high spatial frequencies. Our new results are based on a specific variability model consisting of a zero-mean Gaussian scaling noise riding on a constant value that is large enough with respect to the amplitude of the noise to yield overwhelmingly non-negative density. We first generalize known results about sub-exponential transmission from regular functions, which are almost everywhere continuous, to merely “measurable” ones, which are almost everywhere discontinuous (akin to statistically stationary noises), with positively correlated fluctuations. We then use the generalized measure-theoretic formulation to address negatively correlated stochastic media without leaving the framework of conventional (continuum-limit) transport theory. We thus resolve a controversy about recent claims that only discrete-point process approaches can accommodate negative correlations, i.e., anti-clustering of the material particles. We obtain in this case the predicted super-exponential behavior, but it is rather weak. Physically, and much like the alternative discrete-point process approach, the new model applies most naturally to scales commensurate with the inter-particle distance in the material, i.e., when the notion of particle density breaks down due to Poissonian—or maybe not-so-Poissonian—number-count fluctuations occur in the sample volume. At the same time, the noisy structure must prevail up to scales commensurate with the mean-free-path to be of practical significance. Possible applications are discussed.