Table of contents

The dependence of beam wandering (random lateral displacement) on distance of a thin beam propagating through strong indoor turbulence is investigated experimentally. In the case of small fluctuations and within the limits of the geometrical-optics approximation, the transverse displacement variance is expected to follow a third-power law dependence on distance. Here we present the results of measurements made over paths of a few metres, both in the laboratory and in a large corridor. Inner scale measured values are also reported.

A new HF propagation mechanism giving rise to a Pedersen mode has been discovered. The boundary frequency dividing the Pedersen mode frequency range into parts with different HF propagation mechanisms is determined. A known sliding propagation mechanism characterized by an exponential decrease in the field with the distance travelled by waves along the layer prevails at frequencies . At the low end of the Pedersen mode frequency range the stable wave formation associated with a field localization effect under HF propagation in a randomly stratified ionosphere appears. The observed phenomenon is described in terms of the wave theory of diffraction. Numerical calculation of the wave field amplitude is performed using the parabolic equation method. The Pedersen mode ducting effect due to multiple re-reflection of a sliding beam at anisotropic irregularities elongated along the F2 layer with characteristic scales from hundreds of metres to several kilometres vertically and tens of kilometres horizontally is demonstrated. The irregularities with anisotropy coefficients also localize waves but the size of the effect is between one and two orders smaller than in a model of strong stratified irregularities with .

For a quasi-homogeneous, random medium with variance, varying along the same direction as tanh, the mean Green function is obtained as an exact solution of Dyson's equation in a bilocal approximation. The coherent part of the field of a plane wave, falling on a bounded, randomly fluctuating medium with a non-sharp boundary, is studied in detail. In the case of small-scale fluctuations, a medium of this kind is shown to be a random analogue of a transient Epstein layer.

This paper presents the formulation of rough-surface scattering theory in which the bounded phase shift factors, , replace the elevation, . Both the Dirichlet and the Neumann problems are considered. The integral equations for secondary surface sources are obtained that contain only this phase function in their kernels.

The Neumann (iterative) series for the solutions of the integral equations thus derived are functional Taylor series in powers of , not in powers of . If we expand in these series in powers of , we obtain the standard perturbation theory series. Thus, the new formulation corresponds to the partial summation of the perturbation series.

Using the Neumann series, we obtain several uniform (with respect to approximate solutions that contain, as limiting cases, Bragg scattering, the Kirchhoff approximation, and most known advanced approximations.

In the case of random surface , these new expansions contain the function only in the exponents, and, therefore, the result of averaging can be expressed only in terms of the characteristic functions of the multivariate probability distribution of elevations.

Radiative transfer in an anisotropically scattering slab with direction-dependent reflectivities at the interfaces is solved using the Pomraning - Eddington variational method. The interfaces are assumed to reflect specularly as a function of angle of incidence according to Fresnel's equation. The quantities of interest, such as the hemispherical reflectivity and transmissivity of the medium, are calculated for different optical thicknesses, single-scattering albedos and refractive indices of the medium. The results are compared with the exact numerical results and with those obtained using the average value of the reflectivities instead of the angle-dependent Fresnel reflectivity. Calculations are also performed for a semi-infinite medium and compared with results calculated using the average reflectivities.

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe - Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton - Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.

We study the statistics of reflection and transmission coefficients of light in randomly layered amplifying media that are periodic on average. We are interested in one-dimensional universal scaling behaviours in such systems. Our study shows that while a homogeneous medium boundary condition is capable of reproducing universal scaling at low frequencies, a periodic medium boundary condition is necessary for high frequencies. Although the statistics depends on the boundary condition, the saturation length, where the reflection coefficient reaches a stationary distribution, and the localization length do not. Implications of these results are discussed.

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.