Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence

Based on extended Huygens–Fresnel principle, an analytical expression of M2 factor for partially coherent Hermite–Gaussian (PCHG) beams through non-Kolmogorov turbulence is obtained. Our results show that M2 factor of PCHG beams depends on coherence length, beam order m  , wavelength, exponent value αα, outer scale L0 and inner scale l0. The impact of the exponent's variation on the M2 factor is analyzed in detail. When the propagation distance fixed, the M2 factor of PCHG beams has a maximum for alpha values lower than 11/3.