The behavior of four angular parameters describing polarization ellipse is analyzed in the vicinity of Poincare sphere
poles. It is shown that the phenomenon of step-wise change of azimuthal angle of polarization ellipse at π/2 near poles s3 = ±1 is not accompanied by discontinuities in other parameters of polarization ellipse. In particular the dual system of angular parameters “amplitude-ratio angle and phase difference” do not experience any discontinuities near the poles s3 = ±1. The same is true for the area of polarization ellipse, which is shown to be continuous on the whole Poincare sphere. Analogously, step-wise change of phase difference at π near poles s1 = ±1 is not accompanied by any discontinuities in basic system of angular parameters “azimuth-ellipticity”. General features of angular parameters behavior are illustrated by the results of numerical modelling.
The evolution of polarization along the ray in homogeneous plasma is analyzed in situation when Faraday and
Cotton-Mouton effects are not small and comparable with each other. On the basis of the quasi-isotropic
approximation of geometrical optics method authors find the numerical solution for azimuthal and ellipticity
angles of polarization ellipse and analyze how the initial state of the incident beam affects obtained results.
Numerical modeling is performed for plasma parameters comparable with those acceptable for the ITER project.
New method in plasma polarimetry is considered, which is based on the phenomenon of normal wave transformation in
the vicinity of orthogonality point, where the probing beam is perpendicular to the static magnetic. Phenomenon of
normal wave transformation near orthogonality point is analyzed in the frame of quasi-isotropic approximation of
geometrical optics, both theoretically and numerically. It is shown that measuring polarization state of the beam, passing
through the orthogonality point allows estimating local electron density in the vicinity of that point. This property seems
to be great advantage of the method under consideration as compared with traditional plasma polarimetry, which deals
with line averaged measurements.
In this paper we study the small scale inhomogeneities at the thin 1D phase screen, using weighted Fourier transform (WFT), which contains quadratic in phase weighted function and represents a simplified version of double weighted Fourier transform (DWFT), suggested earlier [1,2]. The phase screen is assumed to be illuminated by the point source, and the wave field, scattered by the phase screen, is measured by the set of receivers. Integral, performing weighted Fourier transform is shown to contain delta-like function, which localizes inhomogeneities at the thin phase screen and allows their reconstructing. Such tomography-like measurement scheme is shown to provide super Fresnel resolution, close to diffraction limit. These results may serve as basis for developing 2D and 3D tomography system in IR or microwave bands for studying small-scale turbulent inhomogeneities in thermonuclear devices like tokamaks and stellarators.
The method of paraxial complex geometrical optics is presented to describe Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like media. The method modifies and specifies the results by Babic' (1968), Kirpichnikova (1971), Cerveny, Popov, Psencik (1982), Cerveny (1983, 2001), Timofeev (1995) and Pereverzev (1996) as applied to the optical problems. The method of paraxial complex geometrical optics reduces the problem of Gaussian beam diffraction in inhomogeneous media to the solution of the system of the ordinary differential equations of first order, which can be readily calculated numerically by the Runge-Kutta method. Thereby the paraxial complex geometrical optics radically simplifies description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. By the way of example the known analytical solution for Gaussianbeam diffraction both in a free space and in lens-like medium (Bornatici, Maj 2003) are presented. It is pointed out, that the method of paraxial complex geometrical optics turns out to be equivalent to the solutions of the abridged parabolic wave equation.
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.
New method for wave propagation description in multi-scale random media is suggested. The method uses double Fourier transform of the observed wave field both in coordinates of receivers and those of the moving source (satellite). It is shown, that the suggested approach is consistent with known partial solutions: geometrical optics method and Born approximation in areas of their applicability. The method under consideration is valid in the case of strong fluctuation, caused by large-scale focusing inhomogeneities and in the same time describes backscattering effects. Characteristic for wave propagation in small-scale random media.
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