We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian–Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.
© 2011 Optical Society of America
Atmospheric and Oceanic Optics
Original Manuscript: December 20, 2010
Revised Manuscript: March 24, 2011
Manuscript Accepted: May 20, 2011
Published: July 12, 2011
Xiuxiang Chu, Chunhong Qiao, Xiaoxing Feng, and Ruipin Chen, "Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model," Appl. Opt. 50, 3871-3878 (2011)