Generation and propagation of a new kind of power-exponent-phase vortex beam

A general analytical formula for the propagation of the new kind of power-exponent-phase vortex beam through a paraxial ABCD optical system is derived. With two different calculation methods, the evolution of the intensity distribution and phase contour of such a beam in free space is investigated. Some experiments are carried out to verify the theoretical predictions. Both of the theoretical and experimental results show that the beam's profile can be modulated by the topological charge and the power order. In addition, the orbital angular momentum (OAM) density and the normalized OAM of such a beam are also studied.