Propagation factors of laser array beams in turbulent atmosphere

The propagation factors of phased locked laser array beams of radial and rectangular symmetries in a turbulent atmosphere are investigated based on the extended Huygens–Fresnel integral and the Wigner distribution function. Analytical propagation formulae for the propagation factors are derived and numerical examples are illustrated. We find that unlike their propagation invariant properties in free space, the propagation factors of laser array beams increase when propagating in turbulent atmosphere, and are closely related to the parameters of initial beams and the atmosphere.