Three dimensional array diffraction limited foci from Greek ladders to generaliz

Greek ladder is a technique for approximating (n)root 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 root 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-phot