• Photonics Research
  • Vol. 6, Issue 6, 630 (2018)
Jinhua Li and Xiangdong Zhang*
Author Affiliations
  • Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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    DOI: 10.1364/PRJ.6.000630 Cite this Article Set citation alerts
    Jinhua Li, Xiangdong Zhang. Electric field tunable strong transverse light current from nanoparticles embedded in liquid crystal[J]. Photonics Research, 2018, 6(6): 630 Copy Citation Text show less

    Abstract

    We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed. The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is anticipated.
    ϵ=ϵL0ϵ^=ϵL0(no2+Δϵcos2α0Δϵcosαsinα0no20Δϵcosαsinα0no2+Δϵsin2α),(1)

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    Es(j0)=n=1m=nniE¯mn[amnNmn(3)(k0,rj0)+bmnMmn(3)(k0,rj0)],(2)

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    Hs(j0)=k0wμ0n=1m=nnE¯mn[bmnNmn(3)(k0,rj0)+amnMmn(3)(k0,rj0)],(3)

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    Cmn=[2n+1n(n+1)(nm)!(n+m)!]1/2,(4)

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    Ein(j0)=n=1m=nniE¯mn[pmnNmn(1)(k0,rj0)+qmnMmn(1)(k0,rj0)],(5)

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    Hin(j0)=k0ωμ0n=1m=nnE¯mn[qmnNmn(1)(k0,rj0)+pmnMmn(1)(k0,rj0)].(6)

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    pmn=[pθτ˜mn(cosθk)ipϕπ˜mn(cosθk)]eimϕk,(7)

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    qmn=[pθπ˜mn(cosθk)ipϕτ˜mn(cosθk)]eimϕk,(8)

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    EI0(j0)=n=1m=nniE¯mnlγlj0[cmn,lMmn(1)(kl,rj0)+dmn,lNmn(1)(kl,rj0)+w¯mn,lλlLmn(1)(kl,rj0)]ilγlj0kl2ω2μL0w¯00,lL00(1)(kl,rj0),(9)

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    HI0(j0)=n=1m=nn1ωμL0E¯mnlklγlj0×[dmn,lMmn(1)(kl,rj0)+cmn,lNmn(1)(kl,rj0)],(10)

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    EI(j0)=Et(j0)+j(1,N)Essj(j,j0),(11)

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    HI(j0)=Ht(j0)+j(1,N)Hssj(j,j0),(12)

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    Et(j0)=n,miE¯mnlαlj0[cmn,lMmn(1)(kl,rj0)+dmn,lNmn(1)(kl,rj0)+w¯mn,lλlLmn(1)(kl,rj0)]ilαlj0kl2ω2μL0w¯00,lL00(1)(kl,rj0),(13)

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    Ht(j0)=n,m1ωμL0E¯mnlklαlj0×[dmn,lMmn(1)(kl,rj0)+cmn,lNmn(1)(kl,rj0)].(14)

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    Essj(j)=n,miE¯mnlβlj[cmn,lMmn(3)(kl,rj)+dmn,lNmn(3)(kl,rj)+w¯mn,lλlLmn(3)(kl,rj)]ilβljkl2ω2μL0w¯00,lL00(3)(kl,rj),(15)

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    Hssj(j)=n,m1ωμL0E¯mnlklβlj×[dmn,lMmn(3)(kl,rj)+cmn,lNmn(3)(kl,rj)].(16)

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    EsIj(j)=n,miE¯mn×[emnjNmn(1)(kj,rj)+fmnjMmn(1)(kj,rj)],(17)

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    HsIj(j)=kjωμjn,mE¯mn×[fmnjNmn(1)(kj,rj)+emnjMmn(1)(kj,rj)],(18)

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    Esinj(j)=Et(j0,j)+ij(1,N)Essi(i,j),(19)

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    Hsinj(j)=Ht(j0,j)+ij(1,N)Hssi(i,j).(20)

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    Mmn=ν=0μ=νν(A0μνmnMμν+B0μνmnNμν),(21)

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    Nmn=ν=0μ=νν(B0μνmnMμν+A0μνmnNμν),(22)

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    Lmn=ν=0μ=ννΓ0μνmnLμν,(23)

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    Et(j0,j)=n,miE¯mnlαlj0[cmn,lj0,jMmn(1)(kl,rj)+dmn,lj0,jNmn(1)(kl,rj)+w¯mn,lj0,jλlLmn(1)(kl,rj)]ilαlj0kl2ω2μL0w¯00,lj0,jL00(1)(kl,rj),(24)

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    Ht(j0,j)=n,m1ωμL0E¯mnlklαlj0×[dmn,lj0,jMmn(1)(kl,rj)+cmn,lj0,jNmn(1)(kl,rj)],(25)

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    dmn,lj0,j=μνE¯μνE¯mn×[dμν,lA0mnμν(j0,j)+cμν,lB0mnμν(j0,j)],(26)

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    cmn,lj0,j=μνE¯μνE¯mn×[dμν,lB0mnμν(j0,j)+cμν,lA0mnμν(j0,j)],(27)

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    w¯mn,lj0,j=μνE¯μνE¯mnw¯μν,lΓ0mnμν(j0,j).(28)

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    Ess(i,j)=n,miE¯mnlβli[cmn,li,jMmn(1)(kl,rj)+dmn,li,jNmn(1)(kl,rj)+w¯mn,li,jλlLmn(1)(kl,rj)]ilβlikl2ω2μL0w¯00,li,jL00(1)(kl,rj),(29)

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    Hss(i,j)=n,m1ωμL0E¯mnlklβli×[dmn,li,jMmn(1)(kl,rj)+cmn,li,jNmn(1)(kl,rj)],(30)

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    dmn,li,j=μνE¯μνE¯mn×[dμν,lA0mnμν(i,j)+cμν,lB0mnμν(i,j)],(31)

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    cmn,li,j=μνE¯μνE¯mn×[dμν,lB0mnμν(i,j)+E¯μνE¯mncμν,lA0mnμν(i,j)],(32)

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    w¯mn,li,j=μνE¯μνE¯mnw¯μν,lΓ0mnμν(i,j).(33)

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    [Esinj(j)+Essj(j)]×e^r=EsIj(j)×e^r,(34)

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    [Hsinj(j)+Hssj(j)]×e^r=HsIj(j)×e^r.(35)

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    (emnjfmnj)=(IVJ¯IVJ)α˜lj0+ij(1,N)(SVJ¯SVJ)β˜li+(SVH¯SVH)β˜lj,(36)

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    (emnjfmnj)=(IUJIUJ¯)α˜lj0+ij(1,N)(SUJSUJ¯)β˜li+(SUHSUH¯)β˜lj,(37)

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    IVJ¯mn,l=dmn,lj0,jkjklψn(klaj)ψn(kjaj)+w¯mn,lj0,jλlkjaj(klaj)2ψn(klaj)ψn(kjaj),(38a)

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    IVJmn,l=cmn,lj0,jkjklψn(klaj)ψn(kjaj),(38b)

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    SVJ¯mn,l=dmn,li,jkjklψn(klaj)ψn(kjaj)+w¯mn,li,jλlkjaj(klaj)2ψn(klaj)ψn(kjaj),(38c)

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    SVJmn,l=cmn,li,jkjklψn(klaj)ψn(kjaj),(38d)

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    SVH¯mn,l=dmn,lkjklξn(klaj)ψn(kjaj)+w¯mn,lλlkjaj(klaj)2ξn(klaj)ψn(kjaj),(38e)

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    SVHmn,l=cmn,lkjklξn(klaj)ψn(kjaj),(38f)

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    IUJmn,l=dmn,lj0,jμjμL0ψn(klaj)ψn(kjaj),(38g)

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    IUJ¯mn,l=cmn,lj0,jμjμL0ψn(klaj)ψn(kjaj),(38h)

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    SUJmn,l=dmn,li,jμjμL0ψn(klaj)ψn(kjaj),(38i)

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    SUJ¯mn,l=cmn,li,jμjμL0ψn(klaj)ψn(kjaj),(38j)

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    SUHmn,l=dmn,lμjμL0ξn(klaj)ψn(kjaj),(38k)

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    SUH¯mn,l=cmn,lμjμL0ξn(klaj)ψn(kjaj).(38l)

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    β˜lj+ij(1,N)GS¯i,jβ˜li=GI¯j0,jα˜lj0,(39)

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    GS¯i,j=(SVH¯SUHSVHSUH¯)1(SVJ¯SUJSVJSUJ¯),(40)

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    GI¯j0,j=(SVH¯SUHSVHSUH¯)1(IUJIVJ¯IUJ¯IVJ).(41)

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    β¯Nl=Tαβα˜lj0,(42)

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    β¯Nl=(β˜l1β˜ljβ˜lN),(43a)

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    Tαβ=(I+(GS¯1,1GS¯N,1GS¯1,NGS¯N,N))1(GI¯j0,1GI¯j0,N).(43b)

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    Essj(j,j0)=n,miE¯mnlβlj[cmn,lj,j0Mmn(3)(kl,rj0)+dmn,lj,j0Nmn(3)(kl,rj0)+w¯mn,lj,j0λlLmn(3)(kl,rj0)]ilβljkl2ω2μL0w¯00,lj,j0L00(3)(kl,rj0),(44)

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    Hssj(j,j0)=n,m1ωμL0E¯mnlklβlj×[dmn,lj,j0Mmn(3)(kl,rj0)+cmn,lj,j0Nmn(3)(kl,rj0)],(45)

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    dmn,lj,j0=μνE¯μνE¯mn×[dμν,lA0mnμν(j,j0)+E¯μνE¯mncμν,lB0mnμν(j,j0)],(46)

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    cmn,lj,j0=μνE¯μνE¯mn×[dμν,lB0mnμν(j,j0)+E¯μνE¯mncμν,lA0mnμν(j,j0)],(47)

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    w¯mn,lj,j0=μνE¯μνE¯mnw¯μν,lΓ0mnμν(j,j0).(48)

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    [Ein(j)+Es(j)]×e^r=EI(j)×e^r,(49)

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    [Hin(j)+Hs(j)]×e^r=HI(j)×e^r.(50)

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    (pq)=(Λ¯00Λ)(ab)+(VJ¯VJ)α˜lj0+j=1N(VH¯VH)β˜lj,(51)

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    (pq)=(Λ00Λ¯)(ab)+(UJUJ¯)α˜lj0+j=1N(UHUH¯)β˜lj,(52)

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    Λ¯mn,uv=ξn(k0R)ψn(k0R)δn,vδm,u,Λ=ξn(k0R)ψn(k0R)δn,vδm,u,(53a)

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    VJ¯=dmn,lk0klψn(klR)ψn(k0R)+w¯mn,lλlk0R(klR)2ψn(klR)ψn(k0R),(53b)

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    VJ=cmn,lk0klψn(klR)ψn(k0R),(53c)

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    VH¯=dmn,lk0klξn(klR)ψn(k0R)+w¯mn,lλlk0R(klR)2ξn(klR)ψn(k0R),(53d)

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    VH=cmn,lk0klξn(klR)ψn(k0R),(53e)

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    UJ¯=μ0μL0cmn,lψn(klR)ψn(k0R),UJ=μ0μL0dmn,lψn(klR)ψn(k0R),(53f)

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    UH¯=μ0μL0cmn,lξn(klR)ψn(k0R),UH=μ0μL0dmn,lξn(klR)ψn(k0R).(53g)

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    (ab)=S(pq),(54)

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    Cs=4πk02n=1m=nn(|amn|2+|bmn|2).(55)

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    Qs=4(k0R)2n=1m=nn(|amn|2+|bmn|2).(56)

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    gy=4πF(θ,φ)πR2QssinθsinφdΩ,(57)

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    F(θ,φ)=dσ(θ,φ)dΩ.(58)

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    dσ(θ,φ)dΩ=|f(θ,φ)|2,(59)

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    Es=E0f(θ,φ)eik0rr,r=|r|.(60)

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    ϵj(ω)=1ωp2ω(ω+iγ),(61)

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    Jinhua Li, Xiangdong Zhang. Electric field tunable strong transverse light current from nanoparticles embedded in liquid crystal[J]. Photonics Research, 2018, 6(6): 630
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