We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

Abstract. New integral representation of a wave field ,in a continuously inhomogeneous random medium is suggested in the form of double-weighted Fourier transformation, performed simultaneously with respect to coordinates of the source and the observer. The integral representation under consideration takes into account both the diffraction effects and the multiray effects. It incorporates many results of known techniques of wave propagation description in continuously inhomogeneous media: the methods of geometrical optics, smooth perturbations, phase screen, and two-scale expansions. The method delivers new opportunities to retrieve small-scale inhomogeneous structure of ionosphere plasma from radio-sounding data and can serve as the basis for diffraction tomography of the ionosphere.

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Influence of enhanced backscattering effect on laser measurements of dust and aerosols content in a turbulent atmosphere is discussed. It is shown that doubling of the backscattered light intensity, characteristic for enhanced backscattering, leads to overestimating dust content in the air. To avoid undesirable effect of overestimation, it is recommended to displace receiving aperture sidewise relatively to laser source. Other method to eliminate overestimation is to use wider laser beam and extended receiving aperture as compared to coherence radius of the scattered wave field.