Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M-2-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M-2-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M-2-factor. However, for the superposition of the intensity the M-2-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M-2-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M-2-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M-2-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams. (C) 2009 Elsevier B.V. All rights reserved.