M² factor of disturbed Bessel-Gaussian beam propagating in turbulent atmosphere

In order to study the propagation properties of the disturbed Bessel-Gaussian beam in turbulent atmosphere, based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function, the formulas of M² factor for the disturbed Bessel-Gaussian beam were derived by theoretical calculation analysis, and the corresponding numerical calculation was carried out. The results show that, when the size of obstruction is not more than 0.4 times of beam width, the propagation factor of Bessel-Gaussian beam in turbulent atmosphere would increase with the increasing of the propagation distance and atmospheric structure constant, and decrease with the increasing of the inner scale of turbulence and topological charge indexes. Under the same condition, the propagation factor of Bessel-Gaussian beam in turbulent atmosphere increases with the increase of the size of obstruction. These results have certain reference value in free space optical communication and actual laser transmission.