NUMERICAL SIMULATION OF FRAUNHOFER DIFFRACTION OF TYPICAL FRACTAL STRUCTURE GRATINGS

This paper aims to investigate the Fraunhofer diffraction patterns on a screen produced by three self-similar fractal structures: Cantor stripes, Cantor carpet, and Sierpinski carpet, Additionally, it explores the geometric principles underlying these self-similar fractal structures. Mathematical expressions for the relative intensity of light at different positions on the screen are derived through complex integration and the displacement phase theorem. Subsequently, numerical calculations and post-processing are performed using MATLAB to visually present the diffraction patterns. The results reveal that the overall symmetry of the diffraction intensity distribution is determined by the symmetry of the parent diffraction pattern.As the number of fractal offspring increases, the diffraction pattern gradually branches and becomes more complex on the symmetric structure pattern of the parent, eventually converging to the diffraction pattern similar to the parent, and satisfying the inverse diffraction law. The content provides a reference case for teaching extensions of the grating diffraction and displacement-phase shift theorems.