Fraunhofer Diffraction Simulation Of A Vortex Beam Through Any Apertures

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.