Changes of propagation characteristic parameters for partially coherent Hermite-Gaussian beams in a turbulent atmosphere

► The propagation characteristic parameters of PCHG beams in turbulence have been studied in detail. ► Use the definition of the second-order moments of WDF not use the quadratic approximation. ► Analytical expressions of the rms spatial and angular widths and the M2-factor for PCHG beams in turbulence are derived. ► The PCHG beams with a higher order, lower coherence and longer wavelength are less affected by the turbulence. ► PCHG beams may be more useful than HG or GSM beams in for potential applications.