Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere

To study the propagation properties of partially coherent Laguerre–Gaussian (PLG) beams through turbulent atmosphere, the analytical formulas are derived for the angular width and the beam-propagation factor (M2-factor) of PLG beams by using the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The corresponding numerical results are also calculated. When propagation distance increases, the angular width is found to spread faster for PLG beams with higher beam order, smaller correlation length and bigger structure constant Cn2 The angular width of PLG beams decreases with increase in waist width (w0).The M2-factor of PLG beams with higher beam order and smaller correlation length is less affected by turbulence with increase in propagation distance. The propagation properties of the M2-factor for PLG beams with the smaller structure constant Cn2 are better than that with bigger structure constant Cn2. The M2-factor of PLG beams decreases with increase in the wavelength λ, and it is also less affected by turbulence for beams with higher order and smaller correlation length. Furthermore, for the PLG beams with the same beam order, the angular width and the M2-factor keep invariable in free space.