Kurtosis parameter of partially coherent Lorentz-Gauss beam in turbulent atmosphere

Based on the generalized Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, an analytical propagation expression for the kurtosis parameter of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system has been derived in turbulent atmosphere, and the kurtosis parameter was numerically calculated. The results show that the influences of the spatial coherence length and the structure constant of the atmospheric turbulence on the kurtosis parameter are related to the beam parameters. When the spatial coherence length is smaller than the beam parameters, the influence of the spatial coherence length is remarkable. When the beam parameter of the Lorentzian part is relatively large or the beam parameter of the Gaussian part is relatively small, the influence of the structure constant is distinct. Moreover, the influence of the structure constant augments with increasing the propagation distance.