2017
DOI: 10.1016/j.jcp.2017.03.014
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Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

Abstract: We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting … Show more

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Cited by 26 publications
(61 citation statements)
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“…For local refinement, the fit parameters we obtain are a local = 0.205333, b local = 1.25229×10 8 , c local = 1.57811, whereas for uniform refinement we get a unif = 0.206216, b unif = 85.8656, c unif = 0.612326. As expected [27], we obtain a much faster convergence rate (c ≈ 1.6) in the quantity of interest for local refinement as opposed to uniform refinement (c ≈ 0.6). We conclude that our computation of the energy transmission ratio with J (E) ≈ a local is reliable within 1%.…”
Section: Validation Of Local Refinement Strategysupporting
confidence: 84%
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“…For local refinement, the fit parameters we obtain are a local = 0.205333, b local = 1.25229×10 8 , c local = 1.57811, whereas for uniform refinement we get a unif = 0.206216, b unif = 85.8656, c unif = 0.612326. As expected [27], we obtain a much faster convergence rate (c ≈ 1.6) in the quantity of interest for local refinement as opposed to uniform refinement (c ≈ 0.6). We conclude that our computation of the energy transmission ratio with J (E) ≈ a local is reliable within 1%.…”
Section: Validation Of Local Refinement Strategysupporting
confidence: 84%
“…Next, we preform a parameter study of the energy transmition ratio for varying interlayer spacing d ranging from d min = 4 · 10 −12 to d max = 0.2, where d max corresponds to about 1/3 of the single-layer SPP wavelength, 2π/Re(k m,r ), or 1/30 of the free space wavelength [27]. The (interpolated) results are shown in Figure 5.…”
Section: Optimal Spacingmentioning
confidence: 99%
“…Equations (16) then entail ± (ξ ) → 0 as ξ → ∞ in C ± . Thus, by (18) we assert that E(ξ ) → 0 as ξ → ∞ in C. By Liouville's theorem, E(ξ ) must be a constant everywhere, which has to be zero; E(ξ ) ≡ 0. Consequently, formula (3) results from Fourier-inversion of (19) by use of (13) and (16).…”
Section: Derivation Of Exact Solutionmentioning
confidence: 99%
“…Next, we perform a finite element computation for the electric field in the presence of the semiinfinite sheet in 2D [18]. The computational domain is chosen to be large enough to account for distances, x, from the edge such that 0 ≤ k x ≤ 30.…”
Section: Numerically Computed Solution Umentioning
confidence: 99%
“…Building on computational methods that we developed for plasmonic problems [20,21], we propose the following computational approach for present purposes:…”
Section: Computational Frameworkmentioning
confidence: 99%