Two approaches to three-dimensional array foci of generalized Fibonacci structures

We propose two technologies to extend the number of layers in order to complete the three-dimensional (3D) array diffraction-limited foci, which means there are two-dimensional array foci at multi-focal planes. One technology is the diffractive optical lever; the other is multi-hybrid Fibonacci structures. Based on the aperiodic Fibonacci structures and binary phase modulation, various kinds of devices can be designed to produce 3D array foci whose focusing properties approximately satisfy the mathematical characteristics of the Fibonacci sequences. With those technologies, the diffraction-limited array foci are freely designed or distributed as required at the desired multiple focal planes.