Close-Form Equation for the Transformation of Hermit-Gaussian Beams through a Optical System with Hard-Edged Apertures

By expanding the rectangular function into a finite sum of complex Gaussian functions,the propagation of Hermit-Gaussian beams through an apertured optical ABCD system is studied in the rectangular coordinates system,and approximate analytical propagation formulas of Hermit-Gaussian beams are derived and the signification of physics of expanded form is illuminated.As an application example,numerical calculations have been performed for the Hermit-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.