  We propose a family of zone plates which are produced by the generalized
Fibonacci sequences and their axial focusing properties are analyzed in detail.
Compared with traditional Fresnel zone plates, the generalized Fibonacci zone
plates present two axial foci with equal intensity. Besides, we propose an
approach to adjust the axial locations of the two foci by means of different
optical path difference, and further give the deterministic ratio of the two
focal distances which attributes to their own generalized Fibonacci sequences.
The generalized Fibonacci zone plates may allow for new applications in micro
and nanophotonics.
