Study on focusing properties of annular beams through circular lens

The model of the annular beams under the cylindrical coordinate system was proposed. According to the theory of generalized diffraction integration, the formula for the annular beams propagating through paraxial ABCD optical systems was derived. Using the method of numerical simulation, the focusing intensity distribution of annular beams and the power in the bucket (PIB) in the focal plane of annular beams were analyzed quantitatively. The numerical calculation results show that the focusing properties of the annular beams depend on the beam orders of the annular beams and the Fresnel number of the system. The powers in the bucket in the geometrical and real focal planes of annular beams decreases with the increasing obstruct ratio while increases with the increase of the Fresnel number of the system. In practical applications, the beam quality of the focused annular laser beams can be effectively controlled through the proper selection of Fresnel number and obstruct ratio.