Cantor fractal zone plates: numerical simulation and experimental characterization

Abstract

We study experimentally and by numerical simulation the Fresnel diffraction on the recently introduced fractal zone plates (ZPs) associated with Cantor sets'. The focusing properties of these ZPs and the evolution of the intensity patterns at the plane transversal to the propagation direction are discussed. As it follows from numerical simulation the series of conventional and doughnut-like secondary focuses are observed around the principal focus. The position, depth and the size of these focuses depends on the type of Cantor set and the level of the fractal, which are directly related to the number of the corresponding Fresnel zones. The results obtained by numerical simulations are verified in the experiments. The fractal Cantor ZPs of different levels are implemented with a liquid crystal display and with the diapositives. The experimental results obtained by both types of the dispositives are in good agreement with the theory and numerical simulations.