Propagation properties based on second-order moments for correlated combination partially coherent Hermite–Gaussian linear array beams in non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle, the definition of second-order moments of the Wigner distribution function (WDF), and the non-Kolmogorov turbulence spectrum, analytical expressions for the M 2-factor and Rayleigh range of correlated combination partially coherent Hermite–Gaussian linear array (PCHGLA) beams propagating through non-Kolmogorov turbulence have been derived. The effect of non-Kolmogorov turbulence and array beam parameters on the M 2-factor and Rayleigh range is discussed in detail. The results show that the M 2-factor and Rayleigh range, as well as their corresponding relative quantities of the PCHGLA beams, vary non-monotonically with increasing generalized exponent parameter α of the turbulence, and M 2-factor exists a maximum whereas Rayleigh range exists a minimum at α = 3.11, respectively. The M 2-factor and Rayleigh range of PCHGLA beams increase with increasing beam number but oscillate with increasing relative beam separation distance for < 1 and then increase monotonically as increases for > 1. The PCHGLA beams are less affected than the GSM linear array beam under the same conditions.