Partially Coherent Electromagnetic Beam Propagation in Random Media

TL;DR

This paper develops a theoretical framework for analyzing the fourth moment of partially coherent electromagnetic beams propagating through random media, providing explicit solutions in the scintillation regime and applications to imaging.

Contribution

It introduces a new explicit solution for the fourth moment equations of partially coherent beams in random media, extending the Itô-Schrödinger model to this context.

Findings

Explicit fourth moment solutions in the scintillation regime

Characterization of the intensity covariance function

Application to imaging of partially coherent sources

Abstract

A theory for the characterization of the fourth 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 It\^o-Schr\"odinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth order equations are considered. The general fourth 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 wave moment. The fourth moment results for polarized waves is used in an application to imaging of partially coherent sources.