Propagation of rectangular multi-Gaussian Schell-model vortex beams in turbulent atmosphere

Based on the extended Huygens-Fresnel integral, the analytical expression of average intensity of a rectangular multi-Gaussian Schell-model vortex (RMGSMV) beam propagating in turbulent atmosphere is derived, the effects of turbulent atmosphere on the average intensity and effective beam widths of a RMGSMV beam are analyzed. The numerical results indicate that the RMGSMV beam propagating in turbulent atmosphere will gradually evolve from the dark hollow beam into a solid beam with Gaussian-like distribution, and the effective beam width W-xz of a RMGSMV beam propagating in turbulent atmosphere with larger C-n(2) will have a larger beam width. The results also show that the effective beam width of a RMGSMV beam with smaller sigma, larger M and N-1 = N-2 will have a larger effective beam width as the propagation distance increases.