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

Abstract

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.

Keywords:

• Random media
• electromagnetic waves
• multiple scattering
• Schrödinger equation
• Gauss–Schell model
• scintillation
• source imaging

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

JG was supported by the Agence Nationale pour la Recherche under Grant No. ANR-19-CE46-0007 (project ICCI), and Air Force Office of Scientific Research under grant FA9550-22-1-0176. KS was supported by the Air Force Office of Scientific Research under grant (FA9550-22-1-0176) and the National Science Foundation under grant (DMS-2010046).