硬边光阑的复高斯函数展开及在高斯光束中的应用

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

将硬边光阑门函数展开成复高斯函数后,利用高斯光阑和薄透镜的ABCD矩阵形式,推导出了高斯光束通过内含硬边光阑的近轴ABCD光学系统传输的解析表达式,说明了展开式的物理含义.通过二组复高斯函数展开系数与直接对Collins公式数值积分结果进行比较,说明所得的解析结果和新数据的优点.

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.