Research ArticleAPPLIED PHYSICS

Structural dispersion–based reduction of loss in epsilon-near-zero and surface plasmon polariton waves

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Science Advances  11 Oct 2019:
Vol. 5, no. 10, eaav3764
DOI: 10.1126/sciadv.aav3764
  • Fig. 1 Generic representation of structural-based loss mitigation method.

    (A) Lossy plasmonic material with PPW outside; the middle mathematical plane perpendicular to the x axis is highlighted with a solid red line. (B) Relative effective permittivity spectra for a plasmonic material, with relative permittivity εact(ω)=1ωp2/ω(ω+iγ), γ = 0.03ωp, and placed within PPWs of different widths d. The operating angular frequency is normalized by the plasma angular frequency ωp.

  • Fig. 2 Complex wave number for a guided wave inside a lossy plasmonic medium.

    Phase constant β and attenuation constant α as a function of the distance between two parallel plates d and operating angular frequency ω for different collision frequencies γ. (A) β and (B) α for γ = 0.03ωp; (C) β and (D) α for γ = 0.01ωp. The ENZ frequency as a function of d is highlighted with a black dashed curve. Values of β and α at different ENZ frequencies for each width are extracted and plotted in the small figure of each panels.

  • Fig. 3 Field distributions of guided waves in structural-based ENZ medium.

    (A) Lossy plasmonic materials using the Drude model with γ = 0.03ωp, bounded by PEC PPW with the width of d. The overall length is 10λp along the z axis. Snapshots of Hx distributions in the middle mathematical plane at each ENZ frequency: (B) d = ∞ (i.e., with no parallel plates) at ωENZ ≈ ωp, (C) d = 0.5λp at ωENZ ≈ 1.41ωp, and (D) d = 0.3λp at ωENZ ≈ 1.93ωp. (E) Normalized magnitude of Hx along the z axis. (F) Practical scenario: SiC using the Lorentzian model in Eq. 9, bounded by Ag using the Drude model in Eq. 10, with the width of d and the thickness of λ0/5, λ0 = 10.3 μm at 29.13 THz. The overall length is 10λ0 along the z axis. Snapshots of Hx distributions in the middle mathematical plane at each ENZ frequency: (G) d = ∞ (i.e., with no parallel plates) at fENZ = 29.13 THz, (H) d = 0.5λ0 at fENZ = 29.93 THz, and (I) d = 0.3λ0 at fENZ = 31.65 THz. (J) Normalized magnitude of Hx along the z axis.

  • Fig. 4 Complex wave number for SPP propagation.

    Phase constant β and attenuation constant α as a function of the distance d between two parallel plates and operating angular frequency ω at different collision frequencies γ. (A) β and (B) α at γ = 0.03ωp; (C) β and (D) α at γ = 0.01ωp. The area between the black and white dashes is the SPP region. The detailed values of β and α at ω = 0.6ωp (expressed by the blue dashed curve) are shown in the middle figures of each panels as a function of d.

  • Fig. 5 Field distributions for structural-based SPP propagation.

    (A) Lossy plasmonic materials using the Drude model with γ = 0.03ωp, bounded by PEC PPW with the width of d. The overall length is 10λp along the z axis. Snapshots of Hx distributions in the middle mathematical plane at ω = 0.6ωp: (B) d = ∞ (i.e., with no parallel plates), (C) d = 2.5λp, (D) d = 2λp, and (E) d = 1.5λp. (F) Normalized magnitude of Hx along the z axis. (G) Practical scenario: SiC using the Lorentzian model in Eq. 9, bounded by Ag using the Drude model in Eq. 10, with the width of d and the thickness of λ0/5, λ0 = 10.7 μm at 28 THz. The overall length is 10λ0 in the z direction. Snapshots of Hx distributions in the middle mathematical plane at 28 THz: (H) d = ∞ (i.e., with no parallel plates), (I) d = 1.2λ0, (J) d = 1λ0, and (K) d = 0.8λ0. (L) Normalized magnitude of Hx along the z axis.

  • Fig. 6 Field distributions for structural dispersion–based SPP propagation when the SPP source is outside the waveguide.

    (A) Practical scenario: SiC using the Lorentzian model in Eq. 9, bounded by Ag using the Drude model in Eq. 10, with the width of d and the thickness of λ0/5, λ0 = 10.7μm at 28 THz. The overall length is 10λ0 in the z direction. (B) Side view of the structure with the input outside the Ag waveguide. Snapshots of Hx distributions in the middle mathematical plane at 28 THz: (C) d = ∞ (i.e., with no parallel plates), (D) d = 1.2λ0, (E) d = 1λ0, and (F) d = 0.8λ0. (G) Normalized magnitude of Hx along the z axis.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaav3764/DC1

    Fig. S1. Electric field distributions of the guided wave in structural dispersion–based ENZ medium.

    Fig. S2. Electric field distributions for the structural dispersion–based SPP propagation.

    Fig. S3. Magnetic field distributions for the structural dispersion–based SPP propagation, with Ag waveguide modeled following the material parameters given in (34).

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Electric field distributions of the guided wave in structural dispersion–based ENZ medium.
    • Fig. S2. Electric field distributions for the structural dispersion–based SPP propagation.
    • Fig. S3. Magnetic field distributions for the structural dispersion–based SPP propagation, with Ag waveguide modeled following the material parameters given in (34).

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