• Photonics Research
  • Vol. 2, Issue 5, 121 (2014)
Carlo Rizza1,2, Elia Palange3, and and Alessandro Ciattoni2,*
Author Affiliations
  • 1Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, via Valleggio 11, 22100 Como, Italy
  • 2Consiglio Nazionale delle Ricerche, CNR-SPIN, 67100 Coppito L’Aquila, Italy
  • 3Dipartimento di Scienze fisiche e chimiche, Università di L’Aquila, via Vetoio, 67100 Coppito L’Aquila, Italy
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    DOI: 10.1364/PRJ.2.000121 Cite this Article Set citation alerts
    Carlo Rizza, Elia Palange, and Alessandro Ciattoni, "Electromagnetic chirality induced by graphene inclusions in multilayered metamaterials," Photonics Res. 2, 121 (2014) Copy Citation Text show less

    Abstract

    We theoretically investigate the electromagnetic response of a novel class of multilayered metamaterials obtained by alternating graphene sheets and dielectric layers, the whole structure not exhibiting a plane of reflection symmetry along the stacking direction. We show that the electromagnetic response of the structure is characterized by a magneto-electric coupling described by an effective chiral parameter. Exploiting the intrinsic tunability of graphene–light coupling, we prove that one can tune both the dielectric and the chiral electromagnetic response by varying the graphene chemical potential through external voltage gating.
    zExxEz=iωμ0Hy,zHy=iωϵ0ϵx(z)Ex,xHy=iωϵ0ϵz(z)Ez,(1)

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    δϵx=n0anexp(in2πzd)=n0anexp(ink0Z),δϵz(1)=n0bnexp(in2πzd)=n0bnexp(ink0Z),(2)

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    Ex(x,z,Z)=E¯x(x,z)+ηδEx(x,z,Z),Ez(x,z,Z)=E¯z(x,z)+δEz(x,z,Z),Hy(x,z,Z)=H¯y(x,z)+ηδHy(x,z,Z),(3)

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    zE¯xxE¯z=iωμ0H¯y,zH¯y=iωϵ0(ϵxE¯x+ηδϵxδEx),E¯z=iωϵ0(ϵz1xH¯y+ηδϵz(1)xδHy)(4)

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    ZδExxδEz=0,ZδHy=iωϵ0δϵxE¯x,δEz=iωϵ0δϵz(1)xH¯y.(5)

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    δEx=1k0ωϵ0n0bnneik0nZx2H¯y,δEz=1iωϵ0n0bneik0nZxH¯y,δHy=ωϵ0k0n0anneik0nZE¯x.(6)

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    zE¯xxE¯z=iωμ0H¯y,zH¯y=iωϵ0(ϵx(eff)E¯xiτ(eff)Z0ϵz(eff)k02x2H¯y),xH¯y=iωϵ0(ϵz(eff)E¯z+τ(eff)k0xE¯x),(7)

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    τ(eff)=iηϵz(eff)n0anbnn.(8)

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    D¯x=ϵ0(ϵx(eff)E¯xτ(eff)k0xE¯zτ(eff)2ϵz(eff)k02x2E¯x),D¯z=ϵ0(ϵz(eff)E¯z+τ(eff)k0xE¯x),(9)

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    D¯x=ϵ0[(ϵx(eff)+τ(eff)2)E¯xτ(eff)2ϵz(eff)k02x2E¯x]+iτ(eff)cH¯y,D¯z=ϵ0ϵz(eff)E¯zB¯y=μ0H¯yiτ(eff)cEx.(10)

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    ϵx(eff)=1d(d1ϵ1+d2ϵ2+iσ1ωϵ0),ϵz(eff)=d(d1ϵ1+d2ϵ2)1,τ(eff)=id1d22cϵ0d2ϵz(eff)σ1(1ϵ21ϵ1),(11)

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    Carlo Rizza, Elia Palange, and Alessandro Ciattoni, "Electromagnetic chirality induced by graphene inclusions in multilayered metamaterials," Photonics Res. 2, 121 (2014)
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