A general Matlab program is designed to simulate the Fraunhofer diffraction patterns of a vortex beam through any apertures, which are usually used to compare with the experimental results in detecting the topological charge of a vortex beam. Two significant matrices are suggested in the above program: one related to the aperture, the other concerned with the field of vortex beam. Using the fast Fourier transform function provided within the Matlab software itself to process the dot product of the above two matrices, one obtains the field on the observation screen. The program is applied to a rectangular aperture and an annular triangle aperture. The results agree well with the computational analysis of previous references. This paper is to describe how Matlab can be used to perform complex mathematical calculations without bogging down the student with the details of the numerical methods and it may be particularly useful for both upper-level undergraduates and graduate students who engage in the study of topological charge detection and identification.

设计了一个通用的Matlab程序来模拟通过任何孔径的涡旋光束的夫琅禾费衍射图案，通常用于与检测涡旋光束拓扑电荷的实验结果进行比较。上述程序中建议了两个重要的矩阵：一个与孔径有关，另一个与涡旋光束的场有关。利用Matlab软件自带的快速傅里叶变换函数对上述两个矩阵的点积进行处理，得到观察屏上的场。该程序适用于矩形孔径和环形三角形孔径。结果与先前参考文献的计算分析非常吻合。