Propagation Properties of Multi-Gaussian Beams in Turbulent Atmosphere

Many types of light beam, such as flat-topped beams, annular beams and multi-annular beams, are the special cases of multi-Gaussian (MG) beams. Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, the analytical formula for the M2-factor of MG beams in turbulent atmosphere has been derived. Numerical results show that the M2-factor of MG beams in turbulence increases with the propagation distance and depends on the beam order, waist width, wavelength, spatial power spectrum of the refractive index fluctuations.