Focusing light with fractal zone plates

A detailed description of the design procedure of fractal zone plates (FZPs), i.e., zone plates with fractal structure, is given. The focusing properties of these elements are studied analytically and compared with conventional Fresnel zone plates. Some distinctive aspects of the new kind of zone plates are outlined. It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture. In addition, the impact on the axial irradiance produced by the lacunarity of a general FZP is investigated. Several numerical examples that illustrate these features are presented.