Propagation properties of partially coherent four-petal Gaussian vortex beams in turbulent atmosphere

The partially coherent four-petal Gaussian vortex beam is introduced and described by analytical expressions. The analytical propagation equation for partially coherent four-petal Gaussian vortex beam in turbulent atmosphere is derived by using the extended Huygens-Fresnel diffraction integral formula. The influences of refraction index structure, beam order n, topological charge M and the coherence length on the average intensity distributions of beam are investigated by numerical examples.