Expansion and angular spread of partially coherent beam propagating in atmospheric turbulence

The generalized Huygens-Fresnel principle and the cross-spectral density function were used to derive the expressions of beam width and angular spread of partially coherent Gaussian-Schell beam when it was propagating in the atmosphere on the basis of the model of the modified Von Karmon spectrum and the atmospheric refractive-index structure constant issued by ITU-R. And then, the impact on the beam propagating in the slant and horizontal ways, caused by the zenith, the transmission distance, the turbulent intensity, the coherent length of the beam and other parameters, were discussed and compared. The impact of the parameters on the ability of anti-turbulence of the beam was analyzed from the perspective of the relative expansion and the relative angular spread respectively and a series of concrete explanations were given. The research results demonstrate that the expansion and the angular spread of the beam suffer little effect from the turbulence during slant path when the zenith is less than /3, which is close to vertical transmission. The beam width and the relative beam width of the beam increase with the increasing transmission distance significantly when the distance is greater than 1 km. The larger the coherent length of the beam is, the greater the impact of the turbulence suffers, while the expansion and the angular spread decrease.