By using wave optics numerical simulation, the intensity-hole effect, beam spreading and wandering properties of Gaussian vortex beam propagation in atmospheric turbulence are investigated quantitatively. It is found that an intensity hole in the center of the beam pattern appears gradually as a Gaussian vortex beam propagates. The size of the intensity hole increases with the increase of the topological charge of the vortex phase. However, the intensity hole could to some extent be filled with optical energy by atmospheric turbulence, especially in strong turbulence. The radius of the intensity hole first decreases and then increases with the growth of turbulence strength. The effective radius of vortex beam with larger topological charge is greater than with a smaller topological charge. But the topological charge has no evident influence on beam wandering.
The number of return photons from sodium laser beacon（SLB） greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.
