Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial

Hui Xu; Cuixiu Xiong; Zhiquan Chen; Mingfei Zheng; Mingzhuo Zhao; Baihui Zhang; Hongjian Li

doi:10.1364/JOSAB.35.001463

Journal of the Optical Society of America B
Vol. 35,
Issue 6,
pp. 1463-1468
(2018)
•https://doi.org/10.1364/JOSAB.35.001463

Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial

Hui Xu, Cuixiu Xiong, Zhiquan Chen, Mingfei Zheng, Mingzhuo Zhao, Baihui Zhang, and Hongjian Li

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Hui Xu, Cuixiu Xiong, Zhiquan Chen, Mingfei Zheng, Mingzhuo Zhao, Baihui Zhang, and Hongjian Li, "Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial," J. Opt. Soc. Am. B 35, 1463-1468 (2018)

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Abstract

We have investigated an obvious plasmon-induced transparency (PIT) that results from the destructive interference between the bright and dark modes in a novel planar metamaterial structure. Two different kinds of graphene, respectively, play the parts of optical bright and dark modes. We have investigated the spectral location and line shape and find that they can be successfully tuned by shifting the Fermi energy. We have theoretically studied its resonance mechanism, and the numerical simulation data are well verified by the theoretical analytical results. Furthermore, the absorption rate is up to 50%. Thus, the narrow PIT phenomena render our nano plasmonic system ideal for an excellent modulator and novel absorber.

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Fig. 1. (a) Schematic illustration of our terahertz graphene planar metamaterial device. (b) Enlarged top view of the unit cell in our designed graphene-based PIT planar metamaterial structure with geometric parameters:

L = 5 μm

l = 4 μm

w = 0.25 μm

. (c) Theoretical equivalent coupled damped resonance model for this hypothetical graphene-based plasmonic resonator.

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Fig. 2. (a) Transmission spectra of graphene planar metamaterial device composed of the bright graphene element only (black), the dark graphene element only (red), and the combination of them (blue). The Fermi energy of the dark and bright graphene elements are, respectively, set to 0.7 eV and 0.5 eV. (b)–(d) Simulated electric field distributions in the

x y

plane at the corresponding resonance frequency locations 3.09 THz, 4.56 THz, and 3.96 THz, indicated by the arrows of (a), respectively.

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Fig. 3. (a) Numerical simulation transmittance results marked with blue solid lines and theoretical fitting transmittance data marked with red dotted lines as

E_{F} = 0.9 eV

, 0.8 eV, 0.7 eV, 0.6 eV, and 0.5 eV in the planar metamaterial structure, respectively. (b) Resonance frequency values of dip and peak versus Fermi energy

E_{F}

. (c) Evolutional relation of the transmission spectra as a function of Fermi energy

E_{F}

and frequency.

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Fig. 4. (a) Numerical simulation absorbance results marked with blue solid lines and theoretical fitting absorbance data marked with red dotted lines as

E_{F} = 0.9 eV

, 0.8 eV, 0.7 eV, 0.6 eV, and 0.5 eV in the planar metamaterial structure, respectively. (b) Frequency values of dip and peak versus Fermi energy

E_{F}

. (c) Evolutional relation of the absorption spectra as a function of Fermi energy

E_{F}

and frequency.

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Equations (8)

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σ = \frac{i e^{2} E_{F}}{π ℏ^{2} (ω + i τ^{- 1})},

\frac{ϵ_{1}}{\sqrt{β^{2} - ϵ_{1} k_{0}^{2}}} + \frac{ϵ_{2}}{\sqrt{β^{2} - ϵ_{2} k_{0}^{2}}} = - \frac{i σ}{ω ϵ_{0}},

(\begin{matrix} γ_{1} & - i μ_{12} \\ - i μ_{21} & γ_{2} \end{matrix}) \cdot (\begin{matrix} a_{1} \\ a_{2} \end{matrix}) = (\begin{matrix} - τ_{e 1}^{- 1 / 2} & 0 \\ 0 & - τ_{e 2}^{- 1 / 2} \end{matrix}) \cdot (\begin{matrix} B_{+}^{in} + B_{-}^{in} \\ D_{+}^{in} + D_{-}^{in} \end{matrix}),

D_{+}^{in} = B_{+}^{out} e^{i ϕ}, B_{-}^{in} = D_{-}^{out} e^{i ϕ},

B_{\pm}^{out} = B_{\pm}^{in} - τ_{e 1}^{- 1 / 2} a_{1}, D_{\pm}^{out} = D_{\pm}^{in} - τ_{e 2}^{- 1 / 2} a_{2},

t = \frac{D_{+}^{out}}{B_{+}^{in}} = e^{i ϕ} + (τ_{e 1}^{- 1} γ_{2} e^{i ϕ} + τ_{e 2}^{- 1} e^{i ϕ} γ_{1} + {(τ_{e 1} τ_{e 2})}^{- 1 / 2} e^{2 i ϕ} χ_{1} + {(τ_{e 1} τ_{e 2})}^{- 1 / 2} χ_{2}) {(γ_{1} γ_{2} - χ_{1} χ_{2})}^{- 1},

r = \frac{B_{-}^{out}}{B_{+}^{in}} = (τ_{e 1}^{- 1} γ_{2} + τ_{e 2}^{- 1} e^{2 i ϕ} γ_{1} + {(τ_{e 1} τ_{e 2})}^{- 1 / 2} e^{i ϕ} χ_{1} + {(τ_{e 1} τ_{e 2})}^{- 1 / 2} e^{i ϕ} χ_{2}) {(γ_{1} γ_{2} - χ_{1} χ_{2})}^{- 1},

E_{F} = ℏ v_{F} {(\frac{π ϵ_{0} ϵ_{d} V_{g}}{d_{sub} e})}^{1 / 2},

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Figures (4)

Equations (8)

Journal of the Optical Society of America B