Nonparaxial propagation properties for a partially coherent anomalous hollow beam

Based on the generalized Raleigh-Sommerfeld diffraction integral formula, an analytical nonparaxial propagation expression of a partially coherent anomalous hollow beam (AHB) in free space is derived. The far field and the paraxial result are also presented as special cases, respectively. By using the derived formula, the nonparaxial propagation properties of a partially coherent AHB are studied numerically and are compared with the paraxial results. It is found that the nonparaxiality properties of a partially coherent AHB are closely related to its beam waist, coherent length and the propagation distance.