Abstract It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance z_{c}. For Gaussian array beams, the analytical expressions of z_{c} are derived. For the coherent combination, z_{c} is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.

Fund:Project supported by the National Natural Science Foundation of China (Grant No. 61178070) and the Construction Plan for Scientific Research Innovation Teams of Universities in Sichuan Province, China (Grant No. 12TD008).

Lu Lu,Ji Xiao-Ling,Deng Jin-Ping et al . A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence[J]. Chin. Phys. B, 2014, 23(6):064209.