Changes of M²-factor for Hermite-Gaussian beams in turbulent atmosphere

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function, the propagation formula for the M2-factor of Hermite-Gaussian(H-G) beams propagating in turbulent atmosphere has been derived. Taking into account the Tatarskii spectrum, major factors affecting the M2-factor of H-G beams have been discussed. The results show that the M2-factor in turbulence depends mainly on the beam order, the waist size and wavelength of the beams, the structure constant of refractive-index fluctuations of turbulence and the propagation distance. The M2-factor of H-G beams in turbulent atmosphere increases obviously as the beam order, the structure constant of refractive-index fluctuations of turbulen