Changes of Beam Parameters of Modified Partially Coherent Flat-Topped Beams Propagating in Turbulence

Based on the extended Huygens-Fresnel principle, the second-order moments of modified partially coherent flat-topped (PCFT) beams in a turbulent atmosphere have been derived. The analytical expressions for the beam propagation factor (M²-factor), the root-mean-square (rms) spatial width, the rms angular width, the radius of curvature of PCFT beams have been given. The effects of turbulence on propagation properties of PCFT beams have been analyzed quantitatively. Finally, a study for the structure constant of the turbulence related to the M²-factor has been proposed. The results show that the M²-factor depends on the beam order and the spatial coherence parameter of PCFT beams, as well as the structure constant, the inner scale and the spatial power spectra of the refractive index fluctuations of the atmospheric turbulence. The radius of curvature exhibits a minimum upon propagation, and the increased refractive index structure constant tends to lower the radius of curvature. The variation of M²-factor of laser beams through a turbulent atmosphere is related to the properties of the turbulence, and the structure constant of the turbulence can be estimated by the use of the M²-factor measured by experiments.