The variance of angle-of-arrival fluctuation of partially coherent Gaussian-Schell Model beam propagations in slant atmospheric turbulence

The variance of angle-of-arrival fluctuation of the partially coherent Gaussian-Schell Model (GSM) beam propagations in the slant path, based on the extended Huygens-Fresnel principle and the model of atmospheric refraction index structural constant proposed by the international telecommunication union-radio (ITU-R), has been investigated under the modified Hill turbulence model. The expression of that has been obtained. Firstly, the effects of optical wavelength, the inner-and-outer scale of the turbulence and turbulence intensity on the variance of angle-of-arrival fluctuation have been analyzed by comparing with the partially coherent GSM beam and the completely coherent Gaussian beam. Secondly, the variance of angle-of-arrival fluctuation has been compared with the von Karman spectrum and the modified Hill spectrum under the partially coherent GSM beam. Finally, the effects of beam waist radius and partial coherence length on the variance of angle-of-arrival of the collimated (focused) beam have been analyzed under the modified Hill turbulence model. The results show that the influence of the variance of angle-of-arrival fluctuation for the inner scale effect is larger than that of the outer scale effect. The variance of angle-of-arrival fluctuation under the modified Hill spectrum is larger than that of the von Karman spectrum. The influence of the waist radius on the variance of angle-of-arrival for the collimated beam is less than focused the beam. This study will provide a necessary theoretical basis for the experiments of partially coherent GSM beam propagation through atmosphere turbulence.