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Tri-band terahertz sensing and slow light based on graphene artificial microstructure

CHENG Yuxuan XU Hui YU Hongfei HUANG Linqin GU Zhichao CHEN Yufeng HE Longhui CHEN Zhiquan HOU Hailiang

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Tri-band terahertz sensing and slow light based on graphene artificial microstructure

CHENG Yuxuan, XU Hui, YU Hongfei, HUANG Linqin, GU Zhichao, CHEN Yufeng, HE Longhui, CHEN Zhiquan, HOU Hailiang
cstr: 32037.14.aps.74.20241576
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  • A monolayer graphene-based tunable triple-band terahertz plasmon device with superior sensing and slow light performance is proposed in this work. A very obvious dual PIT phenomenon is observed by adjusting the device structure. Then, the transmission curves and electric field distributions of the long- and short-graphene band at the three transmission windows are analyzed, to further investigate the mechanism of the bright mode and the dark mode of this structure. Afterward, the comparison between the theoretical data from the coupled-mode theory (CMT) and the simulation results of finite difference time domain (FDTD) shows that they are in excellent agreement with each other. In addition, the effective refractive indices of the real and imaginary parts at different Fermi energy levels are analyzed. The effective refractive indices are linearly related to the Fermi energy level. In this research, it is found that the phase of the electromagnetic wave fluctuates strongly at the transmission window. With the increase of the Fermi energy level, the peak frequency of the group refractive index peak value increases. When the Fermi energy level is at 1.1 eV, the peak value of the group refractive index reaches 327.1. In order to study the sensing effect of this device in more depth, various refractive indices of the medium are tested. Based on these results it can be seen that the device has excellent sensing performance. Its sensitivity and figure of merit (FOM) reach up to 1.442 THz/RIU and 39.6921, respectively. Compared with the traditional structure, this structure can regulate the Fermi energy levels very conveniently by applying a voltage, in order to modulate the resonant frequency of the dual PIT. The findings in this study are expected to lay a theoretical foundation and provide a design reference for potential applications in fields such as slow light technology and sensing.
      Corresponding author: XU Hui, 1067980351@qq.com ; HOU Hailiang, hhlcj1732@126.com
    • Funds: Project supported by the Key Project of Xiangjiang Laboratory, China (Grant No. 23XJ02001), the Natural Science Foundation of Hunan Province, China (Grant Nos. 2023JJ40218, 2022JJ30201), the Changsha Municipal Natural Science Foundation, China (Grant No. kq2202298), and the Scientific Research Foundation of Education Bureau of Hunan Province, China (Grant Nos. 21B0574, 21B0556).
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    Shalf J 2020 Phil. Trans. R. Soc. A 378 20190061Google Scholar

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    Yu Y F, Zhang Y, Zhong F, Bai L, Liu H, Lu J P, Ni Z H 2022 Chin. Phys. Lett. 39 058501Google Scholar

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    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

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    Li Y C, Pan Y Z, Chen F, Ke S L, Yang W X 2024 Opt. Quantum Electron. 56 1003Google Scholar

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    Yu Y S, Cui Z R, Wen K H, Lü H P, Liu W J, Zhang R L, Liu R M 2024 Phys. Scr. 99 075529Google Scholar

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    Wu X X, Chen J N, Wang S L, Ren Y, Yang Y N, He Z H 2024 Nanomaterials 14 997Google Scholar

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    Li Q, Wang T, Su Y K, Yan M, Qiu M 2010 Opt. Express 18 8367Google Scholar

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    Feng Y, Liu H, Chen C, Gao P, Luo H, Ren Z Y, Qiao Y J 2022 Acta Photonica Sin. 51 0923001Google Scholar

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    Liu J, Khan Z U, Wang C, Zhang H, Sarjoghian S 2020 J. Phys. D 53 233002Google Scholar

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    Efetov D K, Kim P 2010 Phys. Rev. Lett. 105 256805Google Scholar

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    Yang X J, Xu H, Xu H Y, Li M, He L H, Nie G Z, Chen Z Q 2023 J. Phys. D: Appl. Phys. 57 115101Google Scholar

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    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

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    Wang Y X, Cui W, Wang X J, Lei W L, Li L Q, Cao X L, He H, He Z H 2022 Vacuum 206 111515Google Scholar

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  • 图 1  (a)石墨烯结构侧视图; (b)石墨烯结构俯视图, 具体参数为a2 = 2.6 μm, a3 = 0.7 μm, a4 = 0.7 μm, a5 = 0.3 μm, a6 = 0.1 μm, h = 5 μm, h1 = 0.75 μm, h2 = 0.3 μm, l = 0.3 μm

    Figure 1.  (a) Side view of graphene structure; (b) top view of the graphene structure, the following parameters: a2 = 2.6 μm, a3 = 0.7 μm, a4 = 0.7 μm, a5 = 0.3 μm, a6 = 0.1 μm, h = 5 μm, h1 = 0.75 μm, h2 = 0.3 μm, l = 0.3 μm.

    图 2  双PIT耦合模理论模型

    Figure 2.  Theoretical coupling diagram between the resonant modes of the proposed structure.

    图 3  (a)双PIT耦合模理论模型的谐振示意图; (b)对应dip1, 3.49 THz共振频率下的电场分布图; (c)对应dip2, 4.85 THz共振频率下的电场分布图; (d)对应dip3, 6.12 THz共振频率下的电场分布图; 其中费米能级为1.0 eV、虚线表示石墨烯带

    Figure 3.  (a) Resonant schematic diagram of the dual-PIT coupled mode theory model; (b) for dip1, the electric field distribution at the resonance frequency of 3.49 THz; (c) for dip2, the electric field distribution at the resonance frequency of 4.85 THz; (d) for dip3, the electric field distribution at the resonance frequency of 6.12 THz. The Fermi energy level is 1.0 eV, and the dotted line represents the graphene band.

    图 4  (a)—(d)入射光偏振角θ = 0°, 30°, 60°, 90°时的透射谱图

    Figure 4.  (a)–(d) Transmission spectra at the incident light polarization angle θ = 0°, 30°, 60°, and 90°.

    图 5  (a)—(c)缺少部分石墨烯带后的透射谱图; (d)—(f)石墨烯带之间间隙不同时的透射谱图; (g)—(i)不同尺寸的石墨烯带的透射谱图

    Figure 5.  (a)–(c) Transmission spectra in the absence of different part of the graphene bands; (d)–(f) the transmission spectra of graphene bands with different gaps, respectively; (g)–(i) the transmission spectra of graphene bands with different sizes.

    图 6  双PIT的模拟与理论透射谱(黑色曲线表示FDTD模拟结果、红点曲线表示耦合理论数值) (a) EF = 0.8 eV; (b) EF = 0.9 eV; (c) EF = 1.0 eV; (d) EF = 1.1 eV

    Figure 6.  Simulated and theoretical transmission spectrum of the dual PIT: (a) EF = 0.8 eV; (b) EF = 0.9 eV; (c) EF = 1.0 eV; (d) EF = 1.1 eV. The black curve indicates the FDTD simulated results. The red-dotted curve indicates the coupled theoretical values.

    图 7  (a)有效折射率虚部大小; (b)有效折射率实部大小; (c)费米能级与共振频率的线性关系; (d)不同费米能级下的透射谱

    Figure 7.  (a) Imaginary part effective refractive index size; (b) real part effective refractive index size; (c) linear plot of Fermi energy levels versus resonance frequency; (d) transmission spectra with different Fermi energy levels.

    图 8  费米能级为0.8—1.1 eV时, 群折射率与相位的关系 (a) EF = 0.8 eV; (b) EF = 0.9 eV; (c) EF = 1.0 eV; (d) EF = 1.1 eV

    Figure 8.  Variation of group refractive index with phase for Fermi energy levels from 0.8 eV to 1.1 eV: (a) EF = 0.8 eV; (b) EF = 0.9 eV; (c) EF = 1.0 eV; (d) EF = 1.1 eV.

    图 9  不同待测介质下的透射谱图

    Figure 9.  Transmission spectra in different media.

    图 10  本结构在不同介质折射率下的双PIT现象与FOM值 (a) n = 1.1; (b) n = 1.2; (c) n = 1.3; (d) n = 1.4

    Figure 10.  Dual PIT phenomenon and FOM values of the structure for different media refractive indices: (a) n = 1.1; (b) n = 1.2; (c) n = 1.3; (d) n = 1.4.

    表 1  三个透射谷的频率差与灵敏度

    Table 1.  Frequency difference and sensitivity of three transmission valleys

    Δf1/
    THz
    Δf2/
    THz
    Δf3/
    THz
    S1/
    (THz·RIU–1)
    S2/
    (THz·RIU–1)
    S3/
    (THz·RIU–1)
    0.0421 0.0960 0.1441 0.421 0.961 1.442
    0.0541 0.0961 0.1382 0.541 0.960 1.381
    0.0481 0.1021 0.1381 0.480 1.021 1.381
    0.0541 0.0961 0.1383 0.541 0.961 1.381
    DownLoad: CSV

    表 2  与其他文献品质因子的比较

    Table 2.  Comparison of figure of merit with other literature.

    Our work Ref. [52] Ref. [53] Ref. [19] Ref. [54]
    FOM 39.69 31.09 28.72 23.61 17.28
    DownLoad: CSV
    Baidu
  • [1]

    Cavin R K, Lugli P, Zhirnov V V 2012 Proc. IEEE 100 1720Google Scholar

    [2]

    Lundstrom M 2003 Science 299 210Google Scholar

    [3]

    Lundstrom M S, Alam M A 2022 Science 378 722Google Scholar

    [4]

    Powell J R 2008 Proc. IEEE 96 1247Google Scholar

    [5]

    Shalf J 2020 Phil. Trans. R. Soc. A 378 20190061Google Scholar

    [6]

    杨肖杰, 许辉, 徐海烨, 李铭, 于鸿飞, 成昱轩, 侯海良, 陈智全 2024 73 157802Google Scholar

    Yang X J, Xu H, Xu H X, Li M, Yu H F, Cheng Y X, Hou H L, Chen Z Q 2024 Acta Phys. Sin. 73 157802Google Scholar

    [7]

    Yu Y F, Zhang Y, Zhong F, Bai L, Liu H, Lu J P, Ni Z H 2022 Chin. Phys. Lett. 39 058501Google Scholar

    [8]

    Bai Z Y, Zhang Q, Huang G X 2019 Chin. Opt. Lett. 17 012501Google Scholar

    [9]

    Pitarke J M, Silkin V M, Chulkov E V, Echenique P M 2006 Rep. Prog. Phys. 70 1Google Scholar

    [10]

    Liu K J, Li J, Li Q X, Zhu J J 2022 Chin. Phys. B 31 117303Google Scholar

    [11]

    徐倩, 陈科, 盛昌建, 王奇, 陈晓行, 刘頔威, 张开春 2019 中国科学: 物理学 力学 天文学 49 064201Google Scholar

    Xu Q, Chen K, Sheng C J, Wang Q, Chen X X, Liu D W, Zhang K C 2019 Sci. China-Phys. Mech. Astron. 49 064201Google Scholar

    [12]

    陈颖, 谢进朝, 周鑫德, 张灿, 杨惠, 李少华 2019 68 237301Google Scholar

    Chen Y, Xie J Z, Zhou X D, Zhang C, Yang H, Li S H 2019 Acta Phys. Sin. 68 237301Google Scholar

    [13]

    Artar A, Yanik A A, Altug H 2011 Nano Lett. 11 1685Google Scholar

    [14]

    Kekatpure R D, Barnard E S, Cai W S, Brongersma M L 2010 Phys. Rev. Lett. 104 243902Google Scholar

    [15]

    Zhu Y, Hu X Y, Yang H, Gong Q H 2014 Sci. Rep. 4 3752Google Scholar

    [16]

    Otsuji T, Tombet S B, Satou A, Fukidome H, Suemitsu M, Sano E, Popov V, Ryzhii M, Ryzhii V 2012 J. Phys. D: Appl. Phys. 45 303001Google Scholar

    [17]

    Rouhi N, Capdevila S, Jain D, Zand K, Wang Y Y, Brown E, Jofre L, Burke P 2012 Nano Res. 5 667Google Scholar

    [18]

    Zhou Q G, Qiu Q X, Huang Z M 2023 Opt. Laser Technol. 157 108558Google Scholar

    [19]

    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

    [20]

    Kumar S B, Guo J 2011 Appl. Phys. Lett. 98 222101Google Scholar

    [21]

    Santos E J, Kaxiras E 2013 Nano Lett. 13 898Google Scholar

    [22]

    Lukose V, Shankar R, Baskaran G 2007 Phys. Rev. Lett. 98 116802Google Scholar

    [23]

    Yan J, Zhang Y B, Kim P, Pinczuk A 2007 Phys. Rev. Lett. 98 166802Google Scholar

    [24]

    Glazov M, Ganichev S 2014 Phys. Rep. 535 101Google Scholar

    [25]

    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

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    Yan S Q, Zhu X L, Frandsen L H, Xiao S S, Mortensen N A, Dong J J, Ding Y H 2017 Nat. Commun. 8 14411Google Scholar

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    Zhang B H, Li H J, Xu H, Zhao M Z, Xiong C X, Liu C, Wu K 2019 Opt. Express 27 3598Google Scholar

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    Xu H Y, Xu H, Yang X J, Li M, Yu H F, Cheng Y X, Zhan S P, Chen Z Q 2024 Phys. Lett. A 504 129401Google Scholar

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    张银, 冯一军, 姜田, 曹杰, 赵俊明, 朱博 2017 66 204101Google Scholar

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    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

    [31]

    He H R, Peng M Y, Cao G T, Li Y B, Liu H, Yang H 2025 Opt. Laser Technol. 180 111555Google Scholar

    [32]

    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

    [33]

    Xia S X, Zhai X, Wang L L, Wen S C 2020 Opt. Express 28 7980Google Scholar

    [34]

    Xiao B G, Tong S J, Fyffe A, Shi Z M 2020 Opt. Express 28 4048Google Scholar

    [35]

    Xu H, He Z H, Chen Z Q, Nie G Z, Li H J 2020 Opt. Express 28 25767Google Scholar

    [36]

    Li Y C, Pan Y Z, Chen F, Ke S L, Yang W X 2024 Opt. Quantum Electron. 56 1003Google Scholar

    [37]

    Yu Y S, Cui Z R, Wen K H, Lü H P, Liu W J, Zhang R L, Liu R M 2024 Phys. Scr. 99 075529Google Scholar

    [38]

    Wu X X, Chen J N, Wang S L, Ren Y, Yang Y N, He Z H 2024 Nanomaterials 14 997Google Scholar

    [39]

    Nene P, Strait J H, Chan W M, Manolatou C, Tiwari S, McEuen P L, Rana F 2014 Appl. Phys. Lett. 105 143108Google Scholar

    [40]

    Li Q, Wang T, Su Y K, Yan M, Qiu M 2010 Opt. Express 18 8367Google Scholar

    [41]

    Lin H, Xu D, Yang H L, Pantoja M, Garcia S 2014 Chin. Phys. B 23 094203Google Scholar

    [42]

    冯越, 刘海, 陈聪, 高鹏, 罗灏, 任紫燕, 乔昱嘉 2022 光子学报 51 0923001Google Scholar

    Feng Y, Liu H, Chen C, Gao P, Luo H, Ren Z Y, Qiao Y J 2022 Acta Photonica Sin. 51 0923001Google Scholar

    [43]

    Liu J, Khan Z U, Wang C, Zhang H, Sarjoghian S 2020 J. Phys. D 53 233002Google Scholar

    [44]

    赵洪霞, 程培红, 丁志群, 王敬蕊, 鲍吉龙 2021 光学学报 41 0728001Google Scholar

    Zhao H X, Cheng P H, Ding Z Q, Wang J X, Bao J L 2021 Acta Opt. Sin. 41 0728001Google Scholar

    [45]

    Balci S, Balci O, Kakenov N, Atar F B, Kocabas C 2016 Opt. Lett. 41 1241Google Scholar

    [46]

    Efetov D K, Kim P 2010 Phys. Rev. Lett. 105 256805Google Scholar

    [47]

    Yang X J, Xu H, Xu H Y, Li M, He L H, Nie G Z, Chen Z Q 2023 J. Phys. D: Appl. Phys. 57 115101Google Scholar

    [48]

    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

    [49]

    Wang Y X, Cui W, Wang X J, Lei W L, Li L Q, Cao X L, He H, He Z H 2022 Vacuum 206 111515Google Scholar

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    樊元成, 杨振宁, 徐子艺, 张宏, 孙康瑶, 叶哲浩, 张富利, 娄菁 2024 激光与光电子学进展 61 0316003Google Scholar

    Fan Y C, Yang Z N, Xu Z Y, Zhang H, Sun K Y, Ye Z H, Zhang F L, Lou J 2024 Laser Optoelectron. Prog. 61 0316003Google Scholar

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    Li M, Xu H, Xu H Y, Yang X J, Yu H F, Cheng Y X, Chen Z Q 2024 Opt. Commun. 554 130175Google Scholar

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    Zhang H, Yao P J, Gao E D, Liu C, Li M, Ruan B X, Xu H, Zhang B H, Li H J 2022 J. Opt. Soc. Am. B 39 467Google Scholar

    [53]

    Xiao B G, Wang Y C, Cai W J, Xiao L H 2022 Opt. Express 30 14985Google Scholar

    [54]

    Jiang W J, Chen T 2021 Diamond Relat. Mater. 118 108531Google Scholar

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Metrics
  • Abstract views:  460
  • PDF Downloads:  17
  • Cited By: 0
Publishing process
  • Received Date:  10 November 2024
  • Accepted Date:  31 December 2024
  • Available Online:  09 February 2025
  • Published Online:  20 March 2025

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