• Advanced Photonics
  • Vol. 1, Issue 1, 014001 (2019)
Jingjing Zhang1, John B. Pendry2、*, and Yu Luo1、*
Author Affiliations
  • 1Nanyang Technological University, School of Electrical and Electronic Engineering, Singapore
  • 2Imperial College London, Blackett Laboratory, Department of Physics, London, United Kingdom
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    DOI: 10.1117/1.AP.1.1.014001 Cite this Article Set citation alerts
    Jingjing Zhang, John B. Pendry, Yu Luo. Transformation optics from macroscopic to nanoscale regimes: a review[J]. Advanced Photonics, 2019, 1(1): 014001 Copy Citation Text show less

    Abstract

    Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations. This technique enables a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence, providing a powerful and intuitive design tool for the control of EM fields on all length scales. With the unprecedented design flexibility offered by transformation optics (TO), researchers have demonstrated a host of interesting devices, such as invisibility cloaks, field concentrators, and optical illusion devices. Recently, the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena, where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena, such as nonlocal effects, Casimir interactions, and compact dimensions. We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.
    εy=μy=εz=μz=α1.(1)

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    μx=εx=α.(2)

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    ε¯¯=Λ¯¯·ε¯¯·Λ¯¯Tdet(Λ¯¯),μ¯¯=Λ¯¯·μ¯¯·Λ¯¯Tdet(Λ¯¯),(3)

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    Λ¯¯=[x/xx/yx/zy/xy/yy/zz/xz/yz/z](1)

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    r=(R2R1R2)r+R1,θ=θ,φ=φ.(4)

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    εr=μr=R2R2R1(rR1r)2,εθ=μθ=εφ=μφ=R2R2R1.(5)

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    f(r)={αr,when  r<R1R2αR1R2R1(rR1)+αR1,when  R1<r<R2,(6)

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    ε¯¯=μ¯¯=Diag[α1,α,(α|Λ|)1].(7)

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    ε¯¯=μ¯¯=[α12+β12(α1β2α2β1)2α1α2+β1β2(α1β2α2β)2α1α2+β1β2(α1β2α2β)2α12+β12(α1β2α2β1)2],(8)

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    x=x,y=H2H1H2y+Dxsgn(x)DH1,z=z.(9)

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    ε¯¯xy=ε[(H2H2H1)2H1H22(H2H1)2dsgn(x)H1H22(H2H1)2dsgn(x)1+(H2H2H1)2(H1d)2].(10)

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    2ϕx2+2ϕy2=0.(11)

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    2ϕx2+2ϕy2=0,(12)

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    ϕ(x,y)=ϕ(x,y).(13)

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    ε(x,y)=ε(x,y).(14)

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    σ=4π2k0(ρ1ρ)2Do2Re[ε1ε2(ε1ε+1)2DiDoDiln(ε1ε+1)],(15)

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    σ=π2k0D12D22(D1+D2)2Re{[(ε1ε+1)D1D2D1+D2+(ε1ε+1)D2D1D1+D2+2]ln(ε1ε+1)},(16)

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    (ε1ε+1)2{exp[nπ(2πθ)l1+l2]exp(nπθl1+l2)}2[exp(2π2nl1+l2)1]2=0,(17)

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    ε(r¯)=RT2|r¯R¯0|2ε,(18)

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    ϕ(r,θ,φ)=l=0m=ll|r¯R¯0|[alm+(r/R0)l+alm(R0/r)l+1]Ylm(θ,φ),(19)

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    Jingjing Zhang, John B. Pendry, Yu Luo. Transformation optics from macroscopic to nanoscale regimes: a review[J]. Advanced Photonics, 2019, 1(1): 014001
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