Excitation of localized graphene plasmons by a metallic slit

Yu. V. Bludov, N. M. R. Peres, and M. I. Vasilevskiy

Phys. Rev. B 101, 075415 – Published 12 February 2020

Abstract

In this paper we show that graphene surface plasmons can be excited when an electromagnetic wave packet impinges on a single metal slit covered with graphene. The excitation of the plasmons localized over the slit is revealed by characteristic peaks in the absorption spectrum. It is shown that the position of the peaks can be tuned either by the graphene doping level or by the dielectric function of the material filling the slit. The whole system forms the basis for a plasmonic sensor when the slit is filled with an analyte.

Received 26 June 2019
Revised 24 January 2020
Accepted 24 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.075415

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Plasmonics Surface plasmons

Graphene

Electromagnetic wave theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yu. V. Bludov ^1,*, N. M. R. Peres ^1,2, and M. I. Vasilevskiy ^1,2

¹Department of Physics, Center of Physics, and QuantaLab, University of Minho, Campus of Gualtar, 4710-057 Braga, Portugal
²International Iberian Nanotechnology Laboratory (INL), Avenida Mestre José Veiga, 4715-330 Braga, Portugal

^*bludov@fisica.uminho.pt

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Vol. 101, Iss. 7 — 15 February 2020

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Images

Figure 1
Single slit (yellow) in the metal film (pink), covered with hBN-encapsulated graphene layer. Also shown are the coordinate axes and the proposed scheme for the obtaining of focused beam by means of diaphragm and cylindric lens.
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Figure 2
(a) Examples of spatial shape of the incident wave packet $H_{y}^{(i)} (x, 0)$ for $λ = 5 μ m$ and two values of the spectral width, $c k_{c} / ω = 1$ (solid line) and $c k_{c} / ω = 0.1$ (dashed line); (b),(c) reflectance $R$ (b) and transmittance $T$ (c) of graphene monolayer suspended over the slit for two values of the wave-packet spectral width: $c k_{c} / ω = 1$ (solid lines) and $c k_{c} / ω = 0.1$ (dashed lines). Other parameters of the structure are $d = 100$ nm, $W = 1.5 μ m, γ = 7.5 m eV, E_{F} = 0 eV$ (blue lines), $E_{F} = 0.3 eV$ (green lines).
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Figure 3
Absorbance $A$ vs wavelength $λ$ , and spectral width of the wave packet $k_{c}$ (left bottom panel) for doped graphene with $E_{F} = 0.3 eV$ suspended on top of the slit. The top panel shows the absorbance for two fixed values of the spectral width, $c k_{c} / ω = 0.1$ (dashed line, the dependence is taken along the corresponding dashed horizontal line in the left bottom panel) and $c k_{c} / ω = 1$ (solid line, the dependence is taken along the upper edge of the left bottom panel). Right bottom panel shows the absorbance (horizontal axis) vs spectral width (vertical axis) for two fixed values of wavelength $λ = 20 μ m$ (dashed-and-dotted line) and $λ = 25 μ m$ (dashed-and-double-dotted line). These dependencies are taken along the correspondent vertical dashed-and-dotted and dashed-and-double-dotted lines in the left bottom panel. The other parameters are the same as in Fig. 2.
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Figure 4
(a) Absorbance $A$ (depicted by color map) vs wavelength $λ$ and graphene's Fermi energy $E_{F}$ ; (b) amplitude of the electric field of the reflected wave harmonics $|c p^{(1)} (k_{x}) h_{r} (k_{x}) / ω|$ vs the wavelength and the wave vector $k_{x}$ for the fixed Fermi energy $E_{F} = 0.3 eV$ . In all panels $c k_{c} / ω = 0.5$ , while other parameters are the same as in Fig. 2. Solid white lines [superimposed on the color map in (a)] demonstrate the SPP eigenmodes with the wave vectors $k_{x}^{(n)} = 2 n π / W (n = 1, 2, 3$ , from right to left); the same wave vectors are depicted in (b) by white dashed horizontal lines.
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Figure 5
Reflectance (a), transmittance (b), and absorbance (c) of (i) suspended graphene layer (dashed green lines) and (ii) graphene layer cladded by two hBN layers with thicknesses $d_{BN} = 1 nm$ (solid red lines). In both cases $E_{F} = 0.3 eV$ and the incident wave packet is characterized by the spectral width $c k_{c} / ω = 0.5$ . Other parameters are the same as in Fig. 2.
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Figure 6
(a) Absorbance $A$ vs wavelength $λ$ and Fermi energy $E_{F}$ for the slit filled by a dielectric with $ε = 3.9$ ; (b) absorbance vs wavelength and refractive index $ε^{1 / 2}$ for the graphene Fermi energy $E_{F} = 0.3 eV$ . In both panels $c k_{c} / ω = 0.5$ and all other parameters are the same as in Fig. 2.
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