Scintillation index of a flat-topped beam array in a weakly turbulent atmosphere

An explicit expression for the scintillation index of a phase-locked radial flat-topped beam array propagating in a weakly turbulent atmosphere is derived. By choosing suitable beam parameters, our formula can also be applied to study the scintillation properties of a Gaussian beam, an off-axis Gaussian beam, a flat-topped beam, an off-axis flat-topped beam and a Gaussian beam array. As an application example, the scintillation properties of a flat-topped beam array, a Gaussian beam, a flat-topped beam and a Gaussian beam array in a weakly turbulent atmosphere are studied numerically and comparatively. Our results show that the scintillation index of a flat-topped beam array can be smaller than that of a Gaussian beam, a flat-topped beam and a Gaussian beam array under certain conditions, which will be useful in long-distance free-space optical communication.