Scintillations of partially coherent multiple Gaussian beams in turbulence

For an incidence composed of partially coherent multiple Gaussian beams, Huygens-Fresnel principle-based on-axis scintillation index is formulated in a weakly turbulent homogeneous horizontal atmospheric path. Our general formulation is applied to two examples of partially coherent annular and partially coherent flat-topped Gaussian beams. Compared to partially coherent single Gaussian beam scintillations, annular beam scintillations seem to possess higher values for all partial coherence levels, whereas flat-topped Gaussian beam intensity fluctuations are slightly larger, especially at lower coherence levels and at larger source sizes. At the same source partial coherence, annular beams exhibit smaller scintillations for larger ring sizes. For flat-topped Gaussian beams, except for very small and very large source sizes, as the number of Gaussian beams forming the flatness increases, intensity fluctuations also increase, a trend applicable for different degrees of coherence. A trend valid for both single and multiple Gaussian incidence, except for certain annular beams of large primary beam sizes, is that the scintillations decrease as the source becomes less coherent. Being applicable for all degrees of source coherences, for both beams examined, scintillations increase steadily as the Rytov plane wave scintillation index increases.