推导出了高斯-谢尔(GSM)光束通过非Kolmogorov湍流大气传输的瑞利区间zR和湍流距离zT解析表达式,并研究了湍流参量(广义指数α、内尺度l0及外尺度L0)对部分相干光扩展的影响。研究表明,随着α的增大,zR先减小而后增大,且在α=3.11处时存在极小值,即光束扩展的极大值。zR随L0的减小而增大(仅当3.6<α<4时);zR随l0的增大而增大。当α>3.11时,α越大,l0对于zR的影响越小。值得指出的是:若相干参数β或束腰半径w0较小时,不论α取何值,在瑞利范围之内,湍流大气对光束扩展几乎不构成影响;相反,β或w0取较大值,不论α取何值,在瑞利区间范围内湍流大气对光束扩展都会产生明显的影响。此外,若β或w0取值在一定范围内,湍流大气是否能在瑞利区间范围内对光束扩展构成影响将与广义指数α相关。 The analytical expressions of zR and turbulent distance zT in the Rayleigh range of Gaussian-Sheer (GSM) beams propagating through non-Kolmogorov turbulent atmosphere are deduced. The effects of turbulent parameters (generalized exponent α, inner scale l0 and outer scale L0) The effect of coherent light expansion. The results show that zR decreases first and then increases with the increase of α, and there exists a minimum at α = 3.11, which is the maximal value of beam expansion. zR increases with decreasing L0 (only when 3.6 <α <4); zR increases with increasing l0. When α> 3.11, the larger α is, the smaller the influence of l0 on zR is. It is worth pointing out that if the coherence parameter β or the waist radius w0 is small, no matter what the value of α, within the Rayleigh range, the turbulent atmosphere hardly affects the beam expansion; on the contrary, β or w0 takes a larger value, No matter what the value of α, the turbulent atmosphere in Rayleigh range will have a significant effect on the beam expansion. In addition, if the value of β or w0 is within a certain range, whether the turbulent atmosphere can affect the beam expansion in the Rayleigh range will be related to the generalized index α.