Yu. A. Kravtsov

Properties of coherent waves reflected in a turbulent medium

The effects of double passages on waves passing through an inhomogeneous turbulent medium before and after being reflected by a scatterer are investigated. The first effect is enhanced backscattering: The average intensity of the backscattered field in a turbulent medium is approximately twice as strong as that in the absence of turbulent inhomogeneities. Among other important effects the partial reversal of a wave in a turbulent medium and the effect of long-range correlations should be mentioned. The influence of moving inhomogeneities on the efficiency of the wave-reversing mechanism is also investigated.

I Theory and Applications of Complex Rays

Publisher Summary This chapter discusses the theory and applications of complex rays. Complex rays are solutions of the ray equations of traditional geometrical optics but correspond to extremals in the six-dimensional complex space. The chapter discusses the basic equations for ordinary and complex geometrical optics, the properties of complex rays, and the selection rules associated with them. These results follow from the application of standard asymptotic methods, such as stationary phase and saddle-point methods, to the Kirchhoff solutions for wave propagation. The chapter presents examples of complex trajectories in different optical and physical problems and a complex ray analysis of Gaussian beam propagation. The chapter also discusses certain distinctive aspects of complex geometrical optics, including nonlocality and applicability. These considerations serve to give some measure of the physical significance of a complex ray.

Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

Super-Fresnel resolution of plasma inhomogeneities by electromagnetic sounding

The application of the double weighted Fourier transform (DWFT) method is suggested for extracting the linear integral of the electron density in the inhomogeneous plasma from microwave or IR sounding data. The virtue of DWFT is its ability to localize the measured linear integral in the area, narrow as compared with the radius of the Fresnel zone, that is to realize super-Fresnel resolution. The advantages of the DWFT method are illustrated, firstly, by numerical simulation of a wave propagation through the Gaussian inhomogeneity in conditions of weak scattering, when a small angle Born approximation is applicable, and secondly, by theoretical estimates of resolution in conditions of strong scattering. The method under discussion promises to be helpful for studying the fine structure of turbulent plasma.

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwells equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable of describing normal mode conversion in inhomogeneous media. Remarkably, evolution of the four-component Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation describing spin precession in ferromagnetic systems. The general theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.

Microwave backscatter from mesoscale breaking waves on the sea surface

Abstract Radar backscatter from mesoscale breaking waves on the sea surface is considered. Breaking waves are shown to be responsible for sea spikes and high Doppler shift with horizontal polarization observed at low grazing angles. The backscatter cross sections for scattering from a single breaking wave are computed for both orthogonal polarizations. An estimate is obtained of the backscatter cross section averaged over the sea surface. It is shown that the main scattering mechanisms are specular backscatter from the steep front of the breaking wave, and backscatter enhancement due to double-bounce scattering from the wave itself and from the foot of the breaking wave. Horizontally polarized backscatter is shown to be considerably higher than vertically polarized backscatter when the angle of incidence is close to the Brewster angle.

Comparative analysis of two formulations of geometrical optics. The effective dielectric tensor

Two apparently diverse formulations of geometrical optics relevant to space- and time-varying dispersive, anisotropic media are shown to be equivalent by virtue of the relationship between the effective dielectric tensor and the plane-wave dielectric tensor. As a counterpart of the wave kinetic equation governing the wave-action density in phase space, the equation for the transport of action density in physical configuration space is obtained, which entails, in particular, a wavepacket adiabatic invariant in the limit of which the effect of both dissipation and (internal and/or external) current-sources is negligible.

IV Radiative Transfer: New Aspects of the Old Theory

Publisher Summary This chapter discusses the new aspects of the radiative transfer theory, and explains the statistical-wave foundation of the radiative transfer theory. The relation between the radiometric radiance and the coherence function of the wave field is discussed, using plane sources and free wave fields as an illustration. The radiative transfer equation is derived, first on the basis of phenomenological energy-balance equations, and then directly from stochastic wave field equations. Radiative transfer equations evolve as a direct sequel of the Bethe-Salpeter equation for the wave-field coherence function. The wave derivation of the radiative transfer equation reveals the diffraction content of the radiative transfer theory. The chapter provides vivid proofs of the diffraction nature of the radiative transfer equation. The new application areas of transfer theory are outlined. The chapter also discusses the use of the transfer theory for analysis of new correlation effects.

Ray Based Diffraction Tomography of the Ionosphere and Laboratory Inhomogeneous Plasma

A new procedure for restoration of the plasma inhomogeneities with improved resolution is suggested. The procedure deals with the double weighted Fourier transform (DWFT) of the observed wavefield in coordinates of both receivers ρ = (x, y) and sources ρ0 = (x0, y0) [1]. Phase increments between the sources and receivers, being found from DWFT representation, can be used for extracting information on small perturbations of the dielectric constant ε~(ρ, z) in a way similar to traditional radio tomography. The resulting resolution of the method is close to the diffraction limit Δρ = λh/D in the horizontal direction and Δz = λ(h/D)2 in the vertical direction, where h is the height of inhomogeneities and D is the length of the ground-based receiving system.

Estimating statistical parameters of an elastic random medium from traveltime fluctuations of refracted waves

Traveltime fluctuations of diving-type refracted waves are studied in the framework of geometrical optics in order to estimate the statistical parameters of an elastic random medium. A stratified background medium is considered in which the velocity increases linearly with depth. Smooth and strongly anisomeric (statistically anisotropic) inhomogeneities are embedded in this medium. The covariance and the variance of traveltime fluctuations are derived and subsequently used to estimate the standard deviation of the medium fluctuations and the inhomogeneity scale lengths in horizontal and vertical directions. The theoretical estimation procedure is verified by performing numerical calculations and it is observed that, under the considered conditions, the traveltime variance decreases at large offsets. This new phenomenon has not been observed before either in acoustics and optics, or in radio wave propagation.