  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.
