Propagation of coherently combined flattened laser beam array in turbulent atmosphere

The analytical expression for the propagation of a flattened laser beam array in a turbulent atmosphere is derived based on extended Huygens–Fresnel principle. The influence of beam order and turbulent atmosphere on beam quality is studied. It is revealed that the beam quality of a coherently combined laser beam array with higher order is better than its lower order counterpart when propagating in free-space, weak and medium turbulence (i.e. Cn2<10−13 m−2/3). The beam quality of higher order beam arrays degrades faster as the intensity of turbulence gets stronger. In the case of propagating in strong turbulence, the beam order has no influence on coherently combined beam quality.