Laser arrays of partially coherent beams with multi-Gaussian correlation function

We study the laser arrays which are constructed by partially coherent beams with multi-Gaussian correlation function, i.e., circular, rectangular and elliptical multi-Gaussian Schell-model (MGSM) beam arrays. Analytical propagation formulas for circular, rectangular and elliptical MGSM beam arrays through a stigmatic ABCD optical system and in turbulent atmosphere are derived, with which the propagation properties of such laser arrays may be easily determined. It is found that in the near field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays are mainly controlled by the distribution of beam arrays in the source plane. In the far field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays in free space are determined by their correlation functions respectively; while in turbulent atmosphere, the correlation functions and turbulent atmosphere all influence the irradiance distributions, especially after enough long distance propagation, the turbulent atmosphere may change the irradiance distributions from non-circular symmetry to circular symmetry.