Effect on Wave Propagation in Random Media of Fluctuations in Dielectric Constant Having Finite Longitudinal Correlation Radius within the Framework of the Parabolic Wave Equation

Abstract

Abstract Within the framework of the parabolic wave equation, we consider the effect on wave propagation in random media of fluctuations in dielectric constant that are correlated over a finite longitudinal distance. The corresponding equations for the averaged correlators are derived and applied to propagation of plane-wave packets and Gaussian beams. The non-Markovian corrections are discussed. These corrections result in some novel features such as the appearance of phase shifts due to fluctuations of dielectric constant and a much stronger dependence of the effective attenuation on the transverse wave-vectors. This may result in a redistribution of intensity of the periphery of axial beams and formation of an intensity depression at the beam centre, and may also change the various asymptotic features. We consider Gaussian fluctuations in the course of most of our discussions while the general, non-Gaussian, case is considered at the end of the paper, and illustrated with the specific example of Poisso...