Open AccessThree-dimensional array diffraction-limited foci from Greek ladders to generalized Fibonacci sequences
Author(s) -
Junyong Zhang
Publication year - 2015
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.23.030308
Subject(s) - fibonacci number , diffraction , binary number , sequence (biology) , integer (computer science) , optics , photonics , ternary operation , algebraic number , integer sequence , physics , mathematics , combinatorics , computer science , mathematical analysis , arithmetic , biology , genetics , programming language , generating function
Greek ladder is a technique for approximating Cn by rational numbers where n is a positive integer and C is a positive real number. For the classical Greek ladder, the value isC. 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 diffraction-limited array foci are freely designed or distributed under the requirement at the desired multiple focal planes.