Changes in the spectrum of radial array beams through turbulent atmosphere

According to the extended HuygensFresnel principle, the propagation formulas of the spectrum for correlated superposition radial array Gaussian Schell-model (RAGSM) beams in a turbulent atmosphere have been derived. The spectral properties of correlated superposition RAGSM beams in free space and in turbulence have also been compared and analyzed. The results show that there exist two identical spectral maxima for the normalized on-axis spectrum of RAGSM beams at one critical position against propagation distance. When the propagation distance is large enough, the on-axis relative spectral shifts in free space and those in turbulence tend to a steady nonzero and zero value, respectively. The off-axis relative spectral shift in free space exhibits a blue-shift alternating with red-shift against off-axis distance, and it depends on the array radius and the beamlet number; whereas the spectral shift has a rapid transition in turbulence. In addition, the on-axis and off-axis relative spectral shifts also depend on the characteristic parameters of turbulence, the beam parameters, and the array parameters.