Propagation properties of Gaussian Schell-model array beams in non-Kolmogorov turbulence

A stochastic beam generated by a recently introduced Gaussian Schell-model array (GSMA) source (2015 Opt. Lett. 40 5662) is investigated. We derive the analytical propagation formulae for the spectral density and the propagation factor in non-Kolmogorov turbulence by utilizing the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function. Numerical results show that the lattice patterns of GSMA beams, which keep propagation-invariant in free space, are destroyed by the turbulence at sufficiently large distances. The GSMA beams have significant advantage over the Gaussian Schell-model beam in the robustness of the destructive effect of non-Kolmogorov turbulence, especially for the GSMA beam with more lattice elements and bigger relative separation distance of each lattice element. The effects of beam parameters and non-Kolmogorov turbulence on the propagation factor are analyzed in detail.