Cantor Grating and Spatial Weierstrass Fractal Diffraction

• Main Authors: Jen-Yu Liu, 劉仁宇
• Other Authors: Yih-Yuh Chen
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/68xz6e

碩士 === 國立臺灣大學 === 物理學研究所 === 106 === Cantor set and its grating diffraction pattern are studied both analytically and numerically. Two approaches, coordinate approach as well as recursive approach, are provided to derive Cantor set grating diffraction formula which preserves how the fractal is replicated and separated by a distance to form a double slit. In addition, these methods are applied to generalized Cantor set grating diffraction. Next, Weierstrass-Mandelbrot fractal function is analysed in detail both with deterministic phase and with stochastic phase. For the case with deterministic phase, the trend of this function can be derived by employing Poisson summation formula. For the other case with stochastic phase, its statistical properties are investigated and its increment is shown to be stationary. Finally, a modified spatial Weierstrass fractal plus a plane wave is used as the incident wave for knife edge and single slit diffraction. Their diffraction patterns are studied both analytically and numerically. We also find the effects of varying its fractal dimension and phase. A rigorous proof to estimate the remainder for computational purpose is also developed.