Focusing properties of radially polarized multi-cosine Gaussian correlated Schell-model beams

Scalar partially coherent beams with multi-cosine Gaussian Schell-model correlations were introduced recently (Mei et al., 2015) [9]. In this paper, we introduce a new class of vector multi-cosine Gaussian correlated sources with radial polarization. The realizability conditions for such sources and corresponding beam conditions are established. Analytical formulas for the cross-spectral density matrix of such beam propagating through a stigmatic ABCD optical system are derived and used to examine their focusing properties in detail. The results demonstrate the novel vector sources can generate lattice-like intensity patterns in the focal plane, and possess periodic distribution of the degree of polarization. It is also shown that the initial polarization structure is broken due to the special source coherence and the state of polarization displays in a more complex way in the focal plane. Besides, such characteristics can be flexible modulated by varying the source coherence parameters.