Propagation based on second-order moments for partially coherent Laguerre–Gaussian beams through atmospheric turbulence

Abstract

The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.