Sensing and slow light applications of graphene plasmonic terahertz structure

Yang Xiao-Jie; Xu Hui; Xu Hai-Ye; Li Ming; Yu Hong-Fei; Cheng Yu-Xuan; Hou Hai-Liang; Chen Zhi-Quan

doi:10.7498/aps.73.20240668

Abstract

In this work, Ansys FDTD is used to design and simulate a terahertz metamaterial structure based on periodic continuous pattern graphene monolayer, and the high-quality PIT phenomena are obtained by continuously adjusting structural parameters. To validate the designed structure, the simulated transmission curve (reflection curve) obtained is compared with the theoretical transmission curve (reflection curve) derived from coupled-mode theory. It is observed that these two results exhibit a remarkably high degree of overlap. The resonant frequency and Fermi energy reveals a perfect linear correlation between them with the resonant frequency increasing proportionally with Fermi energy increasing. Dynamic tuning of PIT can be realized by adjusting the Fermi energy of graphene. For a more in-depth study of its sensing characteristics, the structure is placed in different environments. As the refractive index of the detection medium increases, the resonant frequency gradually decreases, demonstrating a redshift phenomenon. By manipulating the resonant frequency of the PIT sensor, the selective detection of specific target can berealized. After analyzing the sensitivity and FOM values of the structure, it is found that the maximum sensitivity is 1.457 THz/RIU. At a resonant frequency of 6.8174 THz, FOM reaches 30.5652. In summary, the sensor structure designed in this work has dual frequency sensing characteristics and can be used for dual frequency detection. Moreover, compared with other sensor structures, it demonstrates superior sensing performance. Additionally, in studying the slow light effect of the structure, it is found that as the Fermi energy increases, the group index and phase shift at the transparency window continue to increase. At the Fermi energy of 1.2 eV, the group index reaches a high value of 584. This is because in the PIT phenomenon, transparent peaks are formed due to multimodal coupling. This coupling will significantly improve the dispersion characteristics near the transparent peak, resulting in a large group index near the transparent peak. Furthermore, with the increase of carrier mobility, the group index and phase shift of the structure also gradually increase. At a carrier mobility of 0.75 m²/(V·s), the group refractive index is 456, and reaches 1010 at 2.0 m²/(V·s). In this study, the slow-light performance of graphene structure can be optimized through jointly adjusting the Fermi energy and carrier mobility. This research provides theoretical support and methods for designing advanced graphene-based sensors and devices for slow-light applications.

Keywords:

Authors and contacts

1.
School of Microelectronics and Physics, Hunan University of Technology and Business, Changsha 410205, China
2.
Xiangjiang Laboratory, Changsha 410205, China
3.
School of Intelligent Engineering and Intelligent Manufacturing, Hunan University of Technology and Business, Changsha 410205, China

Corresponding author: Xu Hui, 1067980351@qq.com ; Chen Zhi-Quan, zqchen0106@qq.com

Funds: Project supported by the Key Project of Xiangjiang Laboratory, China (Grant No. 23XJ02001), the Natural Science Foundation of Hunan Province, China (Grant No. 2023JJ40218, 2022JJ30201), the Changsha Municipal Natural Science Foundation, China (Grant No. kq2202298), and the Scientific Research Foundation of Hunan Provincial Education Department, China (Grant No. 21B0574, 21B0556).

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Cited By

图 1 石墨烯结构图　(a)石墨烯结构侧视图; (b)周期单元俯视图, 其中a₁ = 0.8 μm, a₂ = 1.6 μm, h₂ = 0.8 μm, h₃ = 0.9 μm, h₄ = 2.3 μm

Figure 1. Graphene structure diagram: (a) Side view of graphene structure; (b) unit structure top view, where a₁ = 0.8 μm, a₂ = 1.6 μm, h₂ = 0.8 μm, h₃ = 0.9 μm, h₄ = 2.3 μm.

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图 2 耦合模理论模型.

Figure 2. Coupled mode theoretical model.

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图 3 石墨烯等离激元诱导透明效应　(a)石墨烯外加电压与费米能级的关系图; (b)石墨烯等离激元透射谱; (c)—(e) G1, G2和G3电场分布图, 频率是5.13 THz; (f) dip1电场分布图, 共振频率是2.81 THz; (g) dip2电场分布图, 共振频率是6.47 THz

Figure 3. Graphene plasmon induced transparency effect: (a) Relationship between the applied voltage and Fermi energy of graphene; (b) graphene plasmon transmission spectrum; (c)–(e) electric field distribution map of G1, G2 and G3, where the frequency is 5.13 THz; (f) electric field distribution map of dip1, where the resonant frequency is 2.81 THz; (g) electric field distribution map of dip2, where the resonant frequency is 6.47 THz.

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图 4 不同入射光方向下G1, G2, G3的光谱响应　(a)—(d) G1偏振角分别为0°, 30°, 60°, 90°的场图分布; (e)—(h) G2偏振角分别为0°, 30°, 60°, 90°的场图分布; (i)—(l)是G3偏振角分别为0°, 30°, 60°, 90°的场图分布

Figure 4. Spectral responses of G1, G2, and G3 under different incident light directions: (a)–(d) Field plot distribution of G1 polarization angles of 0°, 30°, 60°, 90°, respectively; (e)–(h) field plot distribution of G2 polarization angles of 0°, 30°, 60°, 90°, respectively; (i)–(l) field plot distribution of G2 polarization angles of 0°, 30°, 60°, 90°, respectively.

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图 5 石墨烯太赫兹结构的FDTD和CMT透射曲线和反射曲线　(a)透射率; (b)反射率

Figure 5. Comparison of transmission curve and reflection curve fitting between FDTD and CMT of graphene terahertz structure: (a) Transmission curve; (b) reflection curve.

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图 6 共振频率与费米能级关系图　(a)费米能级和共振频率的线性拟合图; (b)随费米能级连续变化的透射谱图

Figure 6. Relationship diagram between resonant frequency and Fermi energy: (a) Linear fitting graph of Fermi energy and resonance frequency; (b) transmission spectrum with continuous variation of Fermi energy.

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图 7 不同检测介质下结构的透射谱

Figure 7. Transmission spectra of structure under different detection media.

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图 8 石墨烯结构的FOM值　(a) n = 1.2; (b) n = 1.3; (c) n = 1.4; (d) n = 1.5; (e) n = 1.6; (f) n = 1.7

Figure 8. FOM of graphene structure: (a) n = 1.2; (b) n = 1.3; (c) n = 1.4; (d) n = 1.5; (e) n = 1.6; (f) n = 1.7.

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图 9 不同费米能级下石墨烯结构的群折射率与相移　(a) E_f = 0.9 eV; (b) E_f = 1.0 eV; (c) E_f = 1.1 eV; (d) E_f = 1.2 eV

Figure 9. Group index and phase shift of graphene structure under different Fermi energy: (a) E_f = 0.9 eV; (b) E_f = 1.0 eV; (c) E_f = 1.1 eV; (d) E_f = 1.2 eV.

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图 10 当载流子迁移率从0.75 m²/(V·s)增至2.0 m²/(V·s)时, 群折射率与相移的演变(E_f = 1.2 eV)　(a) κ = 0.75 m²/(V·s); (b) κ = 1.0 m²/(V·s); (c) κ = 1.25 m²/(V·s); (d) κ = 1.5 m²/(V·s); (e) κ = 1.75 m²/(V·s); (f) κ = 2.0 m²/(V·s)

Figure 10. Evolution of group index and phase shift when carrier mobility increases from 0.75 m²/(V·s) to 2.0 m²/(V·s) when E_f = 1.2 eV: (a) κ = 0.75 m²/(V·s); (b) κ = 1.0 m²/(V·s); (c) κ = 1.25 m²/(V·s); (d) κ = 1.5 m²/(V·s); (e) κ = 1.75 m²/(V·s); (f) κ = 2.0 m²/(V·s).

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表 1 不同费米能级下的耦合强度与本征损耗

Table 1. Coupling strength and intrinsic loss at different Fermi energy.

E_f/eV	γ₁/(10¹² rad·s^–1)	γ₂/(10¹² rad·s^–1)	$\frac{\gamma_1- \gamma_2}{2}$/(10¹¹ rad·s^–1)	μ/(10¹¹ rad·s^–1)
0.8	2.0899	1.2955	3.972	2.6
0.9	2.1826	1.2772	4.527	2.6
1.0	2.2656	1.2670	4.993	2.6
1.1	2.3394	1.26	5.397	2.6
1.2	2.4304	1.2496	5.904	2.6

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表 2 两个透射谷的频率差与灵敏度

Table 2. Frequency difference and sensitivity of two transmission dips.

Δf₁/THz	Δf₂/THz	S₁/(THz·RIU^–1)	S₂/(THz·RIU^–1)
0.0689	0.1444	0.689	1.444
0.0689	0.1456	0.689	1.456
0.0663	0.1456	0.663	1.456
0.0663	0.1457	0.663	1.457
0.0677	0.1430	0.677	1.430
0.0637	0.1404	0.637	1.404

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表 3 与其他文献报道传感器的FOM比较

Table 3. Comparison of FOM with other sensors.

	Our work	Ref. [48]	Ref. [49]	Ref. [50]	Ref. [2]
FOM	30.5652	21.92	6.111	24	23.61

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