Effective radius of curvature of rectangular Gaussian Schell-model array beams

The analytical expression for the effective radius of curvature of rectangular Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the effective radius of curvature depends on the strength of turbulence, the beam parameters and the type of beam superposition. The effective radius of curvature decreases due to turbulence. However, for the superposition of the cross-spectral density function, effective radius of curvature is more sensitive to turbulence than that for the superposition of the intensity. In free space effective radius of curvature for the superposition of the cross-spectral density function is always larger than that for the superposition of the intensity. However, when the strength of turbulence increases, effective