• Collection Of theses on high power laser and plasma physics
  • Vol. 14, Issue 1, 60501 (2016)
Jie Ke1,2, Junyong Zhang1,*, and Zhiyuan Ren1
Author Affiliations
  • 1National Laboratory on High Power Laser and Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • 2University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/col201614.060501 Cite this Article
    Jie Ke, Junyong Zhang, Zhiyuan Ren. Two approaches to three-dimensional array foci of generalized Fibonacci structures[J]. Collection Of theses on high power laser and plasma physics, 2016, 14(1): 60501 Copy Citation Text show less

    Abstract

    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.
    {F1=a,F2=b,(a,bN)Fn=pFn1+qFn2,(p,qN,n3,nN).(1)

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    γ=limjFj/Fj1.(2)

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    E1(x,y,z)=12πE0(ξ,η,0)t(ξ,η)z[exp(ikR)R]dξdη,(3)

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    fm=f0×K[m12]+|mod(m1,2)mod(m,2)(γ+1)1γ1+1|,fm<<f1,(4)

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    Jie Ke, Junyong Zhang, Zhiyuan Ren. Two approaches to three-dimensional array foci of generalized Fibonacci structures[J]. Collection Of theses on high power laser and plasma physics, 2016, 14(1): 60501
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