Modulated Resonant Transmission of Graphene Plasmons Across a \ensuremath{\lambda}/50 Plasmonic Waveguide Gap

Modulated Resonant Transmission of Graphene Plasmons Across a λ/50 Plasmonic Waveguide Gap

Min Seok Jang, Seyoon Kim, Victor W. Brar, Sergey G. Menabde, and Harry A. Atwater

Phys. Rev. Applied 10, 054053 – Published 26 November 2018

Abstract

We theoretically demonstrate the nontrivial transmission properties of a graphene-insulator-metal waveguide segment of deeply subwavelength scale. We show that, at midinfrared frequencies, the graphene-covered segment allows for the resonant transmission through the graphene-plasmon modes as well as the nonresonant transmission through background modes, and that these two pathways can lead to a strong Fano interference effect. The Fano interference enables a strong modulation of the overall optical transmission with a very small change in graphene Fermi level. By engineering the waveguide junction, it is possible that the two transmission pathways perfectly cancel each other out, resulting in a zero transmittance. We theoretically demonstrate the transmission modulation from 0% to 25% at 7.5-µm wavelength by shifting the Fermi level of graphene by a mere 15 meV. In addition, the active region of the device is more than 50 times shorter than the free-space wavelength. Thus, the reported phenomenon is of great advantage to the development of on-chip plasmonic devices.

Received 7 June 2018
Revised 7 September 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.054053

Physics Subject Headings (PhySH)

Integrated optics Nanophotonics Optoelectronics Plasmonics

Graphene Optical microcavities Waveguides

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Min Seok Jang^1,*, Seyoon Kim^1,2, Victor W. Brar³, Sergey G. Menabde¹, and Harry A. Atwater^2,4

¹School of Electric Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
²Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
³Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
⁴Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA

^*jang.minseok@kaist.ac.kr

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Vol. 10, Iss. 5 — November 2018

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Figure 1
Two identical M-I-M waveguides are separated by a narrow gap covered by a sheet of graphene. The thicknesses of the $Si O_{2}$ (d) and the gold h layers are both 100 nm, and the width of the gap L is 140 nm.
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Figure 2
(a) The electric-field distribution at the M-I-M–G-I-M junction at E_F = 0.4 eV. (b),(c) The amplitude and phase of the reflection (r_MG, blue dashed) and transmission (t_MG, red solid) coefficients for incoming M-I-M TM₀ mode as a function of graphene Fermi level. (d),(e) Same as (b),(c), but for the opposite geometry with the graphene plasmons propagating from the G-I-M segment into the M-I-M waveguide. The geometric parameters are chosen as d = h = 100 nm.
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Figure 3
(a),(b) The transmittance (red solid), reflectance (blue dashed), absorption (purple solid), and radiation loss (orange dashed) of the plasmonic modulator. The geometrical parameters are chosen as d = h = 100 nm and L = 140 nm. (c–e) The amplitude of the electric field |E_x| at (c) E_F = 0.385 eV (the fundamental resonance mode), (d) at 0.3 eV (off resonance), and (e) at 0.22 eV (second-order resonance mode), all plotted in the same scale.
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Figure 4
(a) The amplitude of the transmission through the graphene-plasmon resonance (red solid), and through the background modes (blue dashed) vs E_F. (b) The phase difference between t_G and $t_{B}^{0}$ , $φ_{G} - φ_{B}^{0} = \arg (t_{G}) - \arg (t_{B}^{0})$ . (c),(d) The dependence of the amplitude and phase of the total transmission coefficient, t_total = t_G + t_B; the approximated analytic model (red) is in good accordance with the full simulation result (blue dashed) by capturing the distinctive asymmetric line shape.
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Figure 5
(a) The transmittance T vs E_F for the gap size L from 120 nm (red) up to 170 nm (blue) with a 10-nm step; here, the transmittances are obtained from full-wave simulations using the finite element method. (b) Dependence of E_res on L; the analytically obtained E_res (red dashed) perfectly agrees with the FEM simulation results (red circles). (c) The maximum transmittance T_max, and (d) the ratio of the maximum and minimum transmittance T_max/T_min plotted as a function of d and h. The T_max/T_min values over the 60 dB correspond to the total destructive interference between the resonant (graphene) and nonresonant (background) transmission. In (c) and (d), L is set to 140 nm as in the cases of Fig. 3.
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Figure 6
(a) The transmittance T vs E_F for different carrier mobility μ (as denoted). (b) Dependence of T_max (blue squares) and T_min (red circles) on μ.
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Physical Review Applied

Modulated Resonant Transmission of Graphene Plasmons Across a λ/50 Plasmonic Waveguide Gap

Min Seok Jang, Seyoon Kim, Victor W. Brar, Sergey G. Menabde, and Harry A. Atwater

Phys. Rev. Applied 10, 054053 – Published 26 November 2018

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