Propagation factors of Hermite-Gaussian beams in turbulent atmosphere

Abstract

Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, an analytical formulae for the propagation factors (M-2-factors) of coherent and partially coherent one-dimensional Hermite-Gaussian beams in a turbulent atmosphere are derived. Evolution properties of the M-2-factor of the Hermite-Gaussian beam in a turbulent atmosphere are studied numerically in detail. Our results show that the M-2-factor of the Hermite-Gaussian beam increases upon propagation in a turbulent atmosphere. The M-2-factor of the Hermite-Gaussian beam with larger beam order (or lower coherence) increases slower that of the Hermite-Gaussian beam with smaller beam order (or higher coherence) in a turbulent atmosphere, which means that the Hermite-Gaussian beam with a larger beam order and lower coherence is less affected by a turbulent atmosphere. Our results will be useful in long-distance free-space optical communications