• Photonics Research
  • Vol. 1, Issue 2, 77 (2013)
Raphael Tsu1 and Michael A. Fiddy2、*
Author Affiliations
  • 1Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, USA
  • 2Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, USA
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    DOI: 10.1364/PRJ.1.000077 Cite this Article Set citation alerts
    Raphael Tsu, Michael A. Fiddy. Generalization of the effects of high Q for metamaterials[J]. Photonics Research, 2013, 1(2): 77 Copy Citation Text show less

    Abstract

    We revisit the electrodynamics of resonant high-Q interactions in atomic systems with a view to gaining insights into the design of meta-atoms and hence bulk metamaterials with profoundly different electromagnetic responses. The relevance of phase coherence and nonlinearity in charged systems is emphasized, as is the need to take care over defining how one specifies effective boundaries and cavities that ultimately determine light–matter interactions. Radically new material properties become apparent once one designs organized clusters of small numbers of atoms or meta-atoms for which the usually applied random phase approximation (RPA) does not apply. The RPA relies on averages in sufficiently large volumes consisting of large numbers of interacting systems, while our model assumes a small volume with averages in time, i.e., ergodicity. New meaning is given to the concept of effective and practically useful constitutive parameters, based on this very fundamental point of view, which is important to metamaterials.
    E(x)=E0exp(ikx)=m=m=imJm(kr)exp(imφ).(1)

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    kθ2+kr2=εω2c2,(2)

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    dv/dt+γv=emE(3)

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    dv/dt+(·)v+γv=em(E+v×B)β2·n,(4)

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    x ¨+γx˙+ω02x=eE/m(5)

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    P=Nex=(Ne2/mϵ0)E/[ω02ω2iγω].(6)

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    ϵ(ω)=1+(ωes2)/[ω02ω2iγω].(7)

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    ϵ1(ω)=1+(ωes2){(ω02ω2)/[(ω02ω2)2+(γω)2]},(8a)

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    ϵ2(ω)=(ωes2){γω/[(ω02ω2)2+(γω)2]}.(8b)

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    ω2p1sspon=ω2p1s3d2p1s2/3πϵ0c3=γ=(2/3)8α5(mc2/)=6.3×108s1(9)

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    100|x|2,1,±1=±(27/35)a0,(10a)

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    100|y|2,1,±1=i(27/35)a0,(10b)

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    100|z|2,1,0=2(27/35)a0,(10c)

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    E(r,ω)=E0(r,ω)+iωμ0μr(ω)VG(r,r,ω)js(r)d3r,(11)

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    js(r)=iωqδ(rr).(12)

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    β2(·J)+(ω2+iγω)J=iωωp2ε0E,(13)

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    ε(ω)=1[ωp2/(ω2+iγω)],(14)

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    εL(k,ω)=1ωp2ω2+iγωβ2|k|2,(15)

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    Raphael Tsu, Michael A. Fiddy. Generalization of the effects of high Q for metamaterials[J]. Photonics Research, 2013, 1(2): 77
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