Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices

Taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the analytical expressions for the cross-spectral density, average intensity and root mean square (rms) width of a GSM vortex beam with topological charge m = ± 1 propagating through atmospheric turbulence are derived, which enable us to study the propagation properties of GSM vortex beams through atmospheric turbulence and evolution behavior of their coherent vortices. The propagation of GSM vortex beams undergoes several stages of evolution of the intensity profile in both free space and turbulence, and is different from that of GSM non-vortex beams. An increase of the refraction index structure constant Cn2 and a decrease of the spatial correlation length σ0 speed up the evolution process. The beam-width spreading of GSM vortex beams is less than that of GSM non-vortex beams. The smaller the correlation length σ0 is, the less the beam-width spreading of GSM vortex beams is affected by turbulence. The position and number of coherent vortices depend on the structure constant Cn2, correlation length σ0 and topological charge m. The smaller Cn2 and larger σ0 result in a larger propagation distance for the conservation of the topological charge in turbulence.

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