Propagation properties of partially coherent anomalous hollow beams in quadratic-index media

Based on the generalized diffraction integral formula, analytical propagation expressions for a partially coherent anomalous hollow beam (AHB) propagating through a quadratic-index medium are derived. The distributions of intensity and Poynting vector for a partially coherent AHB through the quadratic-index medium are numerically and theoretically studied. It is found that the intensity and Poynting vector of the partially coherent AHB take on a periodical change. The evolution properties of the partially coherent AHB in a quadratic-index medium are closely relevant to its transverse coherence width and the quadratic-index parameter of media.