Complex coherent square Gaussian Schell-model beams

A class of random sources with complex multi-Gaussian coherence states producing a square flat topped far field with transverse self-shifting properties is introduced. The beams generated by such sources are called complex coherent square Gaussian Schell-model beams (GSM). The analytic propagating formulas of the cross-spectral density function of such beams propagating in isotropic random medium are derived. With the help of the analytic formulas, the evolutions of statistical characteristics for such beams in linear medium are illustrated numerically and interpreted physically. The effect of turbulence parameters on the beam propagation properties is stressed.