Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere

Cylindrical vector (CV) partially coherent beam was introduced (Dong et al. Opt Express 19:5979–5992, 2011) and generated (Wang et al. Appl Phys Lett 100:051108, 2012) recently. In this paper, we derive the realizability conditions for a CV partially coherent beam, and we derive the analytical formula for the cross-spectral density matrix of a CV partially coherent beam propagating in turbulent atmosphere based on the extended Huygens-Fresnel formula. The statistical properties, such as the average intensity, the complex degree of coherence and the degree of polarization of a CV partially coherent beam in turbulent atmosphere are studied in detail and compared with those in free space. It is found that the statistical properties of a CV partially coherent beam in turbulent atmosphere are much different from those in free space, and are affected by the initial beam parameters.