The Expanded Form of Complex Gaussian Functions for Hard-Edge Aperture and an Application in the Gaussian Beam

By expanding the rectangular function into a finite sum of complex Gaussian functions, the propagation of Gaussian beams through an aperture optical ABCD system in the rectangular coordinates system,we derive approximate analytical propagation formulas of Gaussian beams and illumincte the signification of physics of expanded form. As an application,numerical calculations have been performed for the Gaussian beams by an apertured lens. The calculation was made with two sets of data and their results were compared to those of the diffracted integral. The result shows that our method can improve the calculation efficiency and the data updates is better than reference data.