Tunable terahertz radiation from graphene induced by moving electrons

Tianrong Zhan, Dezhuan Han, Xinhua Hu, Xiaohan Liu, Siu-Tat Chui, and Jian Zi

Phys. Rev. B 89, 245434 – Published 20 June 2014

Abstract

Based on a structure consisting of a single graphene layer situated on periodic dielectric gratings, we show theoretically that terahertz radiation can be generated by low-energy electron bunches moving atop the graphene layer. The THz emission arises from graphene plasmons excited efficiently by the moving electrons. We find that the radiation intensity can be strongly enhanced due to the local field enhancement of graphene plasmons arising from their low losses and high confinement. Importantly, the radiation frequency can be tuned over a wide spectral range by varying the Fermi level of the graphene layer. Our results could find applications in developing tunable and miniature free-electron terahertz radiation sources.

Received 4 September 2013
Revised 27 May 2014

DOI:https://doi.org/10.1103/PhysRevB.89.245434

Authors & Affiliations

Tianrong Zhan^1,2,*, Dezhuan Han^1,3, Xinhua Hu⁴, Xiaohan Liu¹, Siu-Tat Chui², and Jian Zi^1,†

¹Department of Physics, Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), and Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, People's Republic of China
²Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA
³Department of Applied Physics, College of Physics, Chongqing University, Chongqing 400044, People's Republic of China
⁴Department of Materials Science and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, People's Republic of China

^*phystrzhan@gmail.com
^†jzi@fudan.edu.cn

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Vol. 89, Iss. 24 — 15 June 2014

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Images

Figure 1
Excitation of GPs in a graphene layer at $z = 0$ on a dielectric substrate with $ɛ_{d} = 4$ by an electron bunch moving with constant velocity $v$ in the $x$ direction and at $z = b$ . The graphene has an intrinsic relaxation time of $τ = 0.6$ ps throughout this work. (a) Dispersion curves of GPs at different $E_{F}$ (black lines). The red solid line shows the electron beam line $ω / k_{x} = v$ with $v = 0.057 c$ , and the blue dashed line represents the light line $ω / k_{x} = c$ , where $c$ is the light speed in air. (b) Distribution of field Re( $E_{x}$ ) for two GP modes [dots in (a)]. (c) $| E_{x} (z = 0) |$ vs frequency for $v = 0.057 c$ and $b = 0.1$ $μ m$ at different $E_{F}$ .
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Figure 2
(a) Three-dimensional (3D) view (upper panel) and side view (lower panel) of an electron bunch moving atop a graphene layer on an 1D dielectric grating. (b) Dispersion curves (black solid lines) of GPs for the structure in (a). Red solid, dashed, and dashed-dotted lines show folded electron beam lines $ω / (k_{x} + 2 π / a) = v$ with $v =$ $0.034 c$ , $0.04 c$ , and $0.0436 c$ , respectively. Blue dashed and solid lines represent light lines $ω / k_{x} =$ $c$ (air) and $ω / k_{x} = c / \sqrt{ɛ_{g}}$ (substrate), respectively. (c) Distribution of field Re $(E_{x})$ at frequencies of modes A, B, and C excited by the electron bunch with corresponding $v$ in (b) and $b = 0.1$ $μ m$ . The black solid lines in (c) depict the profile of the grating.
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Figure 3
Radiation intensity $| R_{+} |^{2}$ toward the air side (red dashed lines) and $| R_{-} |^{2}$ toward the substrate side (black solid lines) vs frequency (left panels) and observation angle $θ$ (right panels) for the setup shown in Fig. 2. The velocity of electron bunch is $v = 0.034 c$ in (a) and (d), $0.04 c$ in (b) and (e), and $0.0436 c$ in (c) and (f). The modes B and C in (b) and (c) are related to those in Fig. 2, respectively.
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Figure 4
(a)–(c) Numerical results of radiation intensity $| R_{-} |^{2}$ toward the substrate side (black solid lines) and their fitting to the theory of Eq. (6) (red dashed lines). The results are obtained for the setup shown in Fig. 2 with (a) $v = 0.04 c$ , (b) $v = 0.0436 c$ , and (c) $v = 0.0473 c$ . (d) Fitted value of $Q$ , $λ / V$ , and $Q / Q_{r, -}$ for different $v$ .
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Figure 5
(a) Spectral density of radiated energy $d W_{-} / d ω$ toward the substrate vs $v$ and frequency for a setup with $b = 0$ as shown in Fig. 2. $d W_{-} / d ω$ is of units of $ρ^{2} / ε_{0} c$ and plotted in a color scale form. Green dashed lines are obtained from Eq. (1). Blue dashed (blue solid) lines are obtained from intersection points of the red lines with blue dashed (blue solid) lines in Fig. 2. (b) Frequency of the excited GP at $k_{x} = 0$ [see Fig. 2] vs $E_{F}$ . The corresponding $v$ can be calculated from $ω / (k_{x} + 2 π / a) = v$ .
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Figure 6
(a) Spectral density of radiated energy $d W_{-} / d ω$ toward the substrate vs frequency, and (b) radiated energy $W_{-}$ toward the substrate vs $v$ for a setup with $b = 0.1$ $μ m$ as shown in Fig. 2. The inset to (b) plots the radiated energy $W_{-}$ vs $b$ for different $v$ studied in (a). $v_{1}$ and $v_{2}$ in (b) correspond to those in Fig. 5, respectively.
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