Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam

Analytical formula is derived for the propagation factor (known asM(2)-factor) of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in free space and in turbulent atmosphere. In free space, the M(2)-factor of an EGSM beam is mainly determined by its initial degree of polarization, r.m.s. widths of the spectral densities and correlation coefficients, and its value remains invariant on propagation. In turbulent atmosphere, the M(2)-factor of an EGSM beam is also determined by the parameters of the turbulent atmosphere, and its value increases on propagation. The relative M(2)-factor of an EGSM beam with lower correlation factors, larger r.m.s. widths of the spectral densities and longer wavelength is less affected by the atmospheric turbulence. Under suitable conditions, an EGSM beam is less affected by the atmospheric turbulence than a scalar GSM beam (i.e. fully polarized GSM beam). Our results will be useful in long-distance free-space optical communications.