• Advanced Photonics
  • Vol. 1, Issue 6, 066003 (2019)
Shimon Rubin* and Yeshaiahu Fainman
Author Affiliations
  • University of California, Department of Electrical and Computer Engineering, San Diego, La Jolla, California, United States
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    DOI: 10.1117/1.AP.1.6.066003 Cite this Article Set citation alerts
    Shimon Rubin, Yeshaiahu Fainman. Nonlinear, tunable, and active optical metasurface with liquid film[J]. Advanced Photonics, 2019, 1(6): 066003 Copy Citation Text show less

    Abstract

    Optical metamaterials and metasurfaces, which emerged in the course of the last few decades, have revolutionized our understanding of light and light–matter interaction. While solid materials are naturally employed as key building elements for construction of optical metamaterials mainly due to their structural stability, practically no attention was given to study of liquid-made optical two-dimensional (2-D) metasurfaces and the underlying interaction regimes between surface optical modes and liquids. We theoretically demonstrate that surface plasmon polaritons and slab waveguide modes that propagate within a thin liquid dielectric film trigger optical self-induced interaction facilitated by surface tension effects, which leads to the formation of 2-D optical liquid-made lattices/metasurfaces with tunable symmetry and can be leveraged for tuning of lasing modes. Furthermore, we show that the symmetry breaking of the 2-D optical liquid lattice leads to phase transition and tuning of its topological properties, which allows the formation, destruction, and movement of Dirac-points in the k-space. Our results indicate that optical liquid lattices support extremely low lasing threshold relative to solid dielectric films and have the potential to serve as configurable analogous computation platform.
    ΔϵD(r,t)=bη(r,t)/h0.(1)

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    η(r,t)/h0=Mdrdt1τthGl(rr,tt)I(r,t)/I0,(2)

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    η(r,t)/h0=Mcdrdt1τonGl(rr,tt)I(r,t)/I0,(3)

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    2iβ0Az+2Ay2V[A(r)]A+iΓA=0,V[A(r)]Δεd[A(r)]=χTC/SCdrGl(r,r)|A(r)|2.(4)

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    I=|n=0N1aneikn·r|2=IN+2nmN1anamcos[(knkm)·r];INn=0N1|an|2.(5)

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    ηh0=2Mτthλn¯cos[K(θ)x];K(θ)=2kcos(θ);Λ(θ)2πK(θ)=πkcos(θ),(6)

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    η(r,t)h0=ηmax3[cos(4πyΔy)+2cos(2πyΔy)cos(2πzΔz)].(7)

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    Δy=λcos(θ);Δz=λ1+sin(θ),(8)

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    ηmax(3q¯M)/(λn¯,0τth);q¯=2λ2n¯,0/λm¯,n¯,(9)

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    η(r,t)h0=ηmax3[cos(2πyΔy)+cos(2πzΔz)+cos(2πyΔy)cos(2πzΔz)].(10)

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    Δy=λ2[cos(α)sin(α)];Δz=λ2[cos(α)+sin(α)];(11)

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    2Δk+LkLqK=0,(12)

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    κ0=kM¯h0;M¯=2MaτthλN·αthd2kthΔT.(13)

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    κLsinh(iγL)=±γL;γ=i[(g2+iΔ)2+κ2]1/2,(14)

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    [2iβ0kz(i)+(ky(i))2]ai=4χTC/SCm,n=0N1Δimnaiamanλm¯,n¯;Δimn1dydz0dy0dzeik(i)·rφm,n(r)dr,(15)

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    2iβ0Az+2Ay2V(0)(r)A=0;V(0)(r)Δεd=χTC/SCdrGl(r,r)|A(0)(r)|2.(16)

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    V(0)(r)=V0[cos(2n¯βx)+2cos(n¯βx)cos(m¯βy)];V0q¯bM/(λn¯,0τth)=bηmax/3,(17)

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    Shimon Rubin, Yeshaiahu Fainman. Nonlinear, tunable, and active optical metasurface with liquid film[J]. Advanced Photonics, 2019, 1(6): 066003
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