Partially coherent laser beams propagating in jet engine exhaust induced turbulence

In this work, the propagation properties of an Electromagnetic Multi-Gaussian Schell-model beam (EMGSMB) propagating through a jet engine exhaust are investigated. We derive analytical expressions for the elements of the cross- spectral density matrix, root mean square beam width, root mean square angular width and propagation factor known as the M2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M^{2} -$$\end{document} factor with the help of the extended Huygens-Fresnel diffraction integral and the second order moments of the Wigner distribution function. Based on the derived formulae, we discussed numerically the statistical properties such as the spectral density, the degree of coherence, the beam spreading, and the beam quality. Our main results show that the EMGSMB changes its shapes during their propagation, when the source coherence width is large the spectral density evolves into an elliptical profile. Then, to flat-topped elliptical profile if the source coherence width is lower. It was also found that the EMGSMB spreads faster and less degraded by turbulence-induced from jet engine exhaust when it is compared with Gaussian Schell-model beam (GSMB) and Electromagnetic Gaussian Schell-model beam (EGSMB).