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介绍了一种新型石墨烯太赫兹结构, 其周期单元包括一条长石墨烯单层带和两条短石墨烯单层带. 通过短石墨烯带所激发的明模式与长石墨烯带所激发的暗模式的相消干涉, 该结构产生了等离激元诱导透明效应. 利用耦合模理论推导了此效应的产生机理, 所得结果与时域有限差分方法的仿真值高度一致. 该结构除了具有外部动态可调性之外, 还具有十分出色的传感性能, 最大灵敏度和品质因子分别可达1.457 THz/RIU和30.5652. 此外, 提高结构中石墨烯的费米能级和载流子迁移率有助于增强慢光效应, 其中载流子迁移率的增强效果尤为明显. 当载流子迁移率从0.75 m2/(V⋅s)提高到2.0 m2/(V⋅s)时, 结构的群折射率从456增至1010. 本研究可为太赫兹波段传感器件和慢光器件的发展提供理论和概念框架.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.
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Keywords:
- graphene terahertz structure /
- plasmonic /
- sensing /
- slow light
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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
Fig. 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.
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
Fig. 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.
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(Ef = 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)
Fig. 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 Ef = 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).
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.
Ef/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 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 -
[1] Gosciniak J, Rasras M, Khurgin J B 2020 Acs Photonics 7 488Google Scholar
[2] He Z H, Li L Q, Ma H Q, Pu L H, Xu H, Yi Z, Cao X L, Cui W 2021 Results Phys. 21 103795Google Scholar
[3] Moon K, Park S 2019 Phys. Rev. Appl. 11 034074Google Scholar
[4] Yang H, Ou K, Wan H Y, Hu Y Q, Wei Z Y, Jia H H, Cheng X B, Liu N, Duan H G 2023 Mater. Today 67 424Google Scholar
[5] Yao B C, Liu Y, Huang S W, Choi C, Xie Z D, Flor Flores J, Wu Y, Yu M B, Kwong D L, Huang Y, Rao Y J, Duan X F, Wong C W 2018 Nat. Photonics 12 22Google Scholar
[6] Yang X J, Xu H, Xu H Y, Li M, Yu H F, Cheng Y X, Chen Z Q 2024 Phys. Scr. 99 055518Google Scholar
[7] Wang Y X, Chang B S, Xue J J, Cao X L, Xu H, He H, Cui W, He Z H 2022 Diam. Relat. Mater. 123 108881Google Scholar
[8] Li M, Xu H, Yang X J, Xu H Y, Liu P C, He L H, Nie G Z, Dong Y L, Chen Z Q 2023 Results Phys. 52 106798Google Scholar
[9] Sarker D, Nakti P P, Tahmid M I, Mamun M A Z, Zubair A 2021 Opt. Express 29 42713Google Scholar
[10] Xu H, Li M, Chen Z Q, He L H, Dong Y, Li X L, Wang X J, Nie G Z, He Z H, Zeng B 2023 Phys. Scr. 98 045511Google Scholar
[11] Yan H G, Low T, Zhu W J, Wu Y Q, Freitag M, Li X S, Guinea F, Avouris P, Xia F N 2013 Nat. Photonics 7 394Google Scholar
[12] Kim T T, Kim H D, Zhao R K, Oh S S, Ha T, Chung D S, Lee Y H, Min B, Zhang S 2018 Acs Photonics 5 1800Google Scholar
[13] Liu N, Langguth L, Weiss T, Kästel J, Fleischhauer M, Pfau T, Giessen H 2009 Nat. Mater. 8 758Google Scholar
[14] 宋瀚法, 胡小永 2019 北京大学学报(自然科学版) 55 871Google Scholar
Song H F, Hu X Y 2019 Acta Scientiarum Naturalium Universitatis Pekinensis 55 871Google Scholar
[15] Xia S X, Zhai X, Huang Y, Liu J Q, Wang L L, Wen S C 2017 J. Lightwave Technol. 35 4553Google Scholar
[16] Zhang S, Genov D A, Wang Y, Liu M, Zhang X 2008 Phys. Rev. Lett. 101 047401Google Scholar
[17] He X Y, Liu F, Lin F T, Shi W Z 2021 Opt. Lett. 46 472Google Scholar
[18] He Z H, Li Z X, Li C J, Xue W W, Cui W 2020 Opt. Express 28 17595Google Scholar
[19] 沈常宇, 隋文博, 周俊, 韩伟, 董洁, 方彬, 王兆坤 2023 激光与光电子学进展 60 1106004Google Scholar
Sheng C N, Sui W B, Zhou J, Han W, Dong J, Fang B, Wang Z K 2023 Laser Optoelectron. Prog. 60 1106004Google Scholar
[20] 鲁志琪, 董锐敏, 刘昌宁 2023 中国激光 50 0113020Google Scholar
Lu Z Q, Dong R M, Liu C N 2023 Chin. J. Lasers 50 0113020Google Scholar
[21] 向星诚, 马海贝, 王磊, 田达, 张伟, 张彩虹, 吴敬波, 范克彬, 金飚兵, 陈健 吴培亨 2023 物理学报 72 128701Google Scholar
Xiang X C, Ma H B, Wang L, Tian D, Zhang W, Zhang C H, Wu J B, Fan K B, Jin B B, Chen J, Wu P H 2023 Acta Phys. Sin. 72 128701Google Scholar
[22] Gao E D, Liu Z M, Li H J, Xu H, Zhang Z B, Luo X, Xiong C X, Liu C, Zhang B H, Zhou F Q 2019 Opt. Express 27 13884Google Scholar
[23] 许辉, 李铭, 杨肖杰, 徐海烨 陈智全 2024 中国科学: 物理学 力学 天文学 54 234211Google Scholar
Xu H, Li M, Yang X J, Xu H Y, Chen Z Q 2024 Sci. China Phys. Mech. Astron. 54 234211Google Scholar
[24] Safavi-Naeini A H, Alegre T P M, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E, Painter O 2011 Nature 472 69Google Scholar
[25] Zhao X Q, Huang R X, Du X, Zhang Z R, Li G Y 2024 Nano Lett. 24 1238Google Scholar
[26] Yang H, He P, Ou K, Hu Y Q, Jiang Y T, Ou X N, Jia H H, Xie Z W, Yuan X C, Duan H G 2023 Light Sci. Appl. 12 79Google Scholar
[27] Ji C, Liu Z M, Zhou F Q, Luo X, Yang G X, Xie Y D, Yang R H 2023 J. Phys. D Appl. Phys. 56 405102Google Scholar
[28] Zhuo S S, Liu Z M, Zhou F Q, Qin Y P, Luo X, Ji C, Yang G X, Yang R H, Xie Y 2022 Opt. Express 30 47647Google Scholar
[29] Jiang L Y, Yuan C, Li Z Y, Su J, Yi Z, Yao W T, Wu P H, Liu Z M, Cheng S B, Pan M 2021 Diam. Relat. Mater. 111 108227Google Scholar
[30] Gao E D, Jin R, Fu Z C, Cao G T, Deng Y, Chen J, Li G H, Chen X S, Li H J 2023 Photonics Res. 11 456Google Scholar
[31] Xu H, Chen Z Q, He Z H, Nie G Z, Li D Q 2020 New J. Phys. 22 123009Google Scholar
[32] Yang H, Jiang Y T, Hu Y Q, Ou K, Duan H G 2022 Laser Photonics Rev. 16 2200351Google Scholar
[33] Zhang X, Liu Z M, Zhang Z B, Gao E D, Luo X, Zhou F Q, Li H J, Yi Z 2020 Opt. Express 28 36771Google Scholar
[34] Tang P R, Li J, Du L H, Liu Q, Peng Q X, Zhao J H, Zhu B, Li Z R, Zhu L G 2018 Opt. Express 26 30655Google Scholar
[35] Xu H, Wang X J, Chen Z Q, Li X L, He L H, Dong Y L, Nie G Z, He Z H 2021 New J. Phys. 23 123025Google Scholar
[36] Ren Y, Cui W, Yang Z M, Xiong B W, Zhang L, Li Z X, Lu S J, Huo Y S, Wu X X, Li G, Bai L, He Z H 2024 Opt. Mater. 149 115073Google Scholar
[37] Yang X J, Xu H, Xu H Y, Li M, He L H, Nie G Z, Chen Z Q 2024 J. Phys. D Appl. Phys. 57 115101Google Scholar
[38] Cui W, Wang Y X, Ma H Q, Xu H, Yi Z, Li L Q, Cao X L, Ren X C, He Z H 2021 Phys. Status Solidi 15 2100036Google Scholar
[39] Xu H, He Z H, Chen Z Q, Nie G Z, Li H 2020 Opt. Express 28 25767Google Scholar
[40] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183Google Scholar
[41] Grigorenko A N, Polini M, Novoselov K S 2012 Nat. Photonics 6 749Google Scholar
[42] Gao E D, Liu Z M, Li H J, Xu H, Zhang Z B, Zhang X, Luo X, Zhou F Q 2019 Appl. Phys. Express 12 126001Google Scholar
[43] Efetov D K, Kim P 2010 Phys. Rev. Lett. 105 256805Google Scholar
[44] Balci S, Balci O, Kakenov N, Atar F B, Kocabas C 2016 Opt. Lett. 41 1241Google Scholar
[45] Li M, Xu H, Xu H Y, Yang X J, Dong Y L, He L H, Nie G Z, Wang X J, Chen Z Q 2024 Opt. Commun. 554 130175Google Scholar
[46] Wang Y X, Cui W, Ma H Q, Xu H, Yi Z, Cao X L, Ren X C, He Z H 2021 Results Phys. 23 104002Google Scholar
[47] Peng B, Ozdemir Ş K, Chen W J, Nori F, Yang L 2014 Nat. Commun. 5 5082Google Scholar
[48] Li Z X, Yang N X, Liu Y T, Li L, Zhong Z Y, Song C, He Z H, Cui W, Xue W W, Li L Q, Li C J, Xu H, Chen Z Q, He H 2022 Diam. Relat. Mater. 126 109071Google Scholar
[49] Jie X, Zhao T, Ran W Y, Feng Z H 2023 Phys. Chem. Chem. Phys. 524 128775Google Scholar
[50] Askari M, Bahadoran M 2022 Optik 253 168589Google Scholar
[51] Zhang T, Zhou J Z, Dai J, Dai Y T, Han X, Li J Q, Yin F F, Zhou Y, Xu K 2018 J. Phys. D Appl. Phys. 51 055103Google Scholar
[52] Liu Y, Zhong R B, Lian Z, Bu C, Liu S G 2018 Sci. Rep. 8 2828Google Scholar
[53] Xiao B G, Tong S J, Fyffe A, Shi Z M 2020 Opt. Express 28 4048Google Scholar
[54] Gao E D, Cao G T, Deng Y, Li H J, Chen X S, Li G H 2024 Opt. Laser Technol. 168 109840Google Scholar
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