Spectrum changes of rectangular array beams through turbulent atmosphere

According to the extended Huygens-Fresnel principle, the propagation formulas of the spectrum for correlated and uncorrelated superposition rectangular array Gaussian Schell-model (RAGSM) beams propagating in a turbulent atmosphere have been derived. The results show that for the case of M>1 and N>1, the on-axis relative spectral shift of the RAGSM beam presents the blue-shift alternating with the red-shift with increasing propagation distance, and when the propagation distance is large enough the spectral shifts in free space will only exhibit blue-shift, whereas the spectral shifts will tend to 0 in turbulence due to both the diffraction of atmospheric turbulence and the correlation of the source. The off-axis relative spectral shift for the correlated and uncorrelated RAGSM beams exhibit rapid transitions of the spectrum upon off-axis distance in turbulence. In addition, the spectral shifts also depend on the characteristic parameters of turbulence, the beam parameters and the array parameters.