Fourth-Moment Analysis for Wave Propagation in the White-Noise Paraxial Regime

• Published in: Archive for rational mechanics and analysis Vol. 220; no. 1; pp. 37 - 81
• Main Authors: Garnier, Josselin, Sølna, Knut
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-04-2016; Springer Nature B.V
• Subjects: Beams (radiation); Classical Mechanics; Complex Systems; Covariance; Fluid- and Aerodynamics; Gaussian; Gaussian beams (optics); Mathematical analysis; Mathematical and Computational Physics; Mathematical models; Noise propagation; Physics; Physics and Astronomy; Propagation; Theoretical; Transforms; Wave propagation; Transmitted Beam; Propagation Distance; Random Medium; Scintillation Index; Turbulent Atmosphere
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/s00205-015-0926-2

In this paper we consider the Itô–Schrödinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width. In terms of applications we prove that the centered fourth-order moments of the field satisfy the Gaussian summation rule, we derive the covariance function of the intensity of the transmitted beam, and the variance of the smoothed Wigner transform of the transmitted field. The second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the Wigner transform.