Fourth-order moments analysis for partially coherent electromagnetic beams in random media

• Published in: Waves in random and complex media Vol. 33; no. 5-6; pp. 1346 - 1365
• Main Authors: Garnier, Josselin, Sølna, Knut
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 06-11-2023; Taylor & Francis Ltd
• Subjects: Beams (radiation); Coherence; Correlation; Covariance; Electromagnetic radiation; electromagnetic waves; Gauss-Schell model; Mathematics; multiple scattering; Random media; Schrodinger equation; Schrödinger equation; scintillation; source imaging; Transport equations; Wave propagation; Wigner distribution
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2022.2096272

A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources.