Spectral changes of radial array beams in inhomogeneous atmospheric turbulence

Based on the generalized Huygens-Fresnel principle, an analytical expression for the spectral intensity of the radial array Gaussian Schell mode beam (RAGSM) in inhomogeneous atmospheric turbulence is derived using the theory of partially coherent light. The variation of the normalized spectral intensity and the on-axis relative spectral shift are investigated. The effects of beam parameters and turbulent parameters on the spectra are numerically calculated. The results show that there is a critical position where a rapid transition of the spectrum takes place. The critical position becomes greater with an increase in the number of sub-beams, the radial distance, initial coherence length. At the longer propagation distance, the effect of structural constants of refractive index is weaker. The spectral transition distances are proportional to the turbulence parameters.