Greek ladder is a technique for approximating n C by rational numbers where n is a positive integer and C is a positive real number. For the classical Greek ladder, the value is C . Based on the continued fraction theory and algebraic equation, the classical Greek ladder in a special case can be reduced to the generalized Fibonacci sequence. By means of proper switching and binary, ternary or quaternary phase modulation, here we have successfully designed the various kinds of nano-photonic devices to produce three-dimensional array foci whose focusing properties satisfy the above mathematical characteristics. With this technology, the diffractionlimited array foci are freely designed or distributed under the requirement at the desired multiple focal planes.