Effective radius of curvature of partially coherent flat-topped beam propagating through atmospheric turbulence

The analytical expression for the effective radius of curvature R of a partially coherent flat-topped beam propagating through atmospheric turbulence is derived. It is shown that R decreases due to turbulence. However, position z(min) where R reaches its minimum will change due to the turbulence when the strength of turbulence is strong enough. The effective radius of curvature R increases with the increase of beam coherence parameter beta when the strength of turbulence is weak, while R decreases with beta increasing when the strength of turbulence is strong. The R decreases slowly with the increase of beam order M(N) The R of partially coherent flat-topped beam with larger beta and smaller M ( N) is more sensitive to turbulence. In addition, in free space the wavefront of partially coherent flat-topped beam can be regarded as a spherical surface in the far-field, which is independent of the beam parameters However, in turbulence the effective radius of curvature depends on the beam parameters in the near field and also in the far field.