Atmospheric turbulence effects on hollow Gaussian Schell-model array beams

Abstract

Two types of hollow array beams with circular and rectangular distributions on propagating in atmospheric turbulence are investigated and analyzed comparatively with that in free space. Analytical formulas for the cross-spectral density function of two kinds of hollow array beam propagation in linear isotropic random media are derived and used to examine the behavior of the spectral densities. It is found that such beams possess stable hollow arrays with any dimension and lobes in free space, while such distributions only maintain small distances in atmospheric turbulence and ultimately tend to a Gaussian shape due to the turbulence destroying the hollow array profiles. The effects of the turbulence parameters on the behavior of the spectral density are analyzed in depth.