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. (C) 2012 Elsevier B.V. All rights reserved.