Statistical properties in Young’s interference pattern formed with a radially polarized beam with controllable spatial coherence

Experimental generation of a radially polarized (RP) beam with controllable spatial coherence (i.e., partially coherent RP beam) was reported recently [Appl. Phys. Lett. 100, 051108 (2012)]. In this paper, we carry out theoretical and experimental studies of the statistical properties in Young's two-slit interference pattern formed with a partially coherent RP beam. An approximate analytical expression for the cross-spectral density matrix of a partially coherent RP beam in the observation plane is obtained, and it is found that the statistical properties, such as the intensity, the degree of coherence and the degree of polarization, are strongly affected by the spatial coherence of the incident beam. Our experimental results are consistent with the theoretical predictions, and may be useful in some applications, where light field with special statistical properties are required.