Partially coherent circular and elliptical dark hollow beams and their paraxial propagations

A theoretical model is proposed to describe a partially coherent dark hollow beam (DHB) of circular or elliptical symmetry. The characteristics of the partially coherent circular or elliptical DHB can be easily controlled by properly choosing the beam parameters. Based on the generalized Collins integral, analytical formulas for a partially coherent circular or elliptical DHB propagating through paraxial aligned and misaligned optical systems are derived. Some numerical examples are illustrated. Our model provides a convenient way to describe and treat the propagation of partially coherent circular and elliptical DHBs.