Fractal Generalized Zone Plates

TL;DR

This paper introduces fractal generalized zone plates (FraGZPs), enhancing the focusing capabilities of traditional fractal zone plates by increasing the number of foci while maintaining self-similarity, supported by analytical and numerical analysis.

Contribution

It proposes a novel method to construct FraGZPs from periodic diffractive elements, expanding the number of foci and analyzing their focusing properties analytically and numerically.

Findings

FraGZPs increase the number of foci compared to FraZPs.

Analytical expressions for irradiance are derived.

Numerical simulations show efficiency and effects of ring area variations.

Abstract

The construction of fractal generalized zone plates (FraGZPs) from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us to increase the number of foci of a conventional fractal zone plate (FraZP), keeping the self-similarity property within the axial irradiance. The focusing properties of these fractal diffractive optical elements for points not only along but also in the close vicinity of the optical axis are investigated. In both cases analytical expressions for the irradiance are derived. Numerical simulations of the energetic efficiency of FraGZPs under plane wave illumination are carried out. In addition, some effects on the axial irradiance caused by the variation in area of their transparent rings are shown.