Self-similar focusing with generalized devilís lenses

We introduce the generalized devilís lenses (GDLs) as a new family of diffractive kinoform lenses whose structure is based on the generalized Cantor set. The focusing properties of different members of this family are analyzed. It is shown that under plane wave illumination the GDLs give a single main focus surrounded by many subsidiary foci. It is shown that the total number of subsidiary foci is higher than the number of foci corresponding to conventional devilís lenses; however, the self-similar behavior of the axial irradiance is preserved to some extent.