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In practical applications, the performances of conventional metal-insulator-metal (MIM) waveguide structured optical devices cured during fabrication are not dynamically tunable. In order to address the problem that such devices are not dynamically tunable, based on the excellent optoelectronic properties of graphene materials, graphene nanotubes are induced into the metal-insulator-metal waveguide coupled circular resonant cavity structure, thus designing a dynamically tunable MIM-graphene nanotube hybrid structure refractive index sensor in this work. The finite element method (FEM) is used to numerically study the transmission characteristics, electric field distribution and magnetic field distribution of the system, and the theoretical analysis is performed by multimode interference coupled mode theory (MICMT) to verify its correctness. The results show that after adding graphene nanotube to the MIM waveguide coupled ring resonant cavity structure, a Fano resonance peak appears in this system, which originates from the coherent coupling between the TM10 cavity resonance mode and the graphene plasmonic electrical resonance mode. The sensor can dynamically tune the resonance wavelength and linewidth of Fano resonance in a wide wavelength range by changing the chemical potential of graphene, thus realizing the performance tuning of the refractive index sensor. Hence, the problem that the conventional plasma refractive index sensor is not dynamically tunable issolved. In addition, the influence of the geometrical parameters of the structure on the sensing performance of this system is also studied in detail. The sensor sensitivity increases up to 1250 nm/RIU and the quality factor rises up to 42.4 RIU–1 at the optimal structural parameters. Compared with the traditional metal-insulator-metal waveguide structure design, this device has many merits such as wide operating band range, easy processing and dynamic tunability, which is a guideline for designing the dynamically tunable high performance nano-photonic integrated devices.
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Keywords:
- surface plasmon polaritons /
- graphene nanotube /
- refractive index sensor /
- multimode interference coupled mode theory
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图 1 MIM-石墨烯纳米管混合结构示意图 (a) 三维模型; (b) 二维模型
Figure 1. The schematic of designed MIM-graphene nanotube: (a) 3D model; (b) 2D model.
图 2 (a) 加入石墨烯纳米管结构前后的透射光谱对比; (b)—(m) 不同波长对应波峰、波谷处的磁场图(上)和电场图(下)
Figure 2. (a) Comparison of transmission spectra with and without incorporated graphene nanotube structures; (b)–(m) magnetic field distribution (top) and electric field distribution (bottom) at the corresponding peaks and troughs at different wavelengths.
图 3 MIM-石墨烯纳米管混合结构的仿真计算和理论分析对比
Figure 3. Comparison of simulation calculation and theoretical analysis of MIM-graphene nanotube hybrid structure.
图 4 (a) 随石墨烯化学势
$ {\mu _{\text{c}}} $ 变化的透射光谱图; (b)—(e) 改变$ {\mu _{\text{c}}} $ 时仅峰II和峰III的透射光谱对比图;${\mu _{\text{c}}} = 0.65{\text{ eV}}$ , 峰II (b-l)和峰III (b-r) 的电场图;${\mu _{\text{c}}} = 0.75{\kern 1 pt} {\text{ }}{\kern 1 pt} {\text{eV}}$ , 峰II (c-l) 和峰III (c-r) 的电场图;${\mu _{\text{c}}} = 0.85{\kern 1 pt} {\kern 1 pt} {\text{ eV}}$ , 峰III (d-l) 和峰II (d-r) 的电场图;${\mu _{\text{c}}} = 0.95{\text{ }}{\kern 1 pt} {\kern 1 pt} {\text{eV}}$ , 峰III (e-l) 和峰 II (e-r) 的电场图; (f) 透射强度随入射波长及$ {\mu _{\text{c}}} $ 变化的光谱图Figure 4. (a) Transmission spectra when changing the chemical potential of graphene; (b)–(e) comparison of transmission spectra of Peak II and Peak III only when changing the chemical potential of graphene; the electric field diagram of Peak II (b-l) and Peak III (b-r) at
${\mu _{\text{c}}} = 0.65{\text{ eV}}$ ; the electric field diagram of Peak II (c-l) and Peak III (c-r) at${\mu _{\text{c}}} = 0.75{\kern 1 pt} {\text{ }}{\kern 1 pt} {\text{eV}}$ ; the electric field diagram of Peak III (d-l) and Peak II (d-r) at${\mu _{\text{c}}} = 0.85{\kern 1 pt} {\kern 1 pt} {\text{ eV}}$ ; the electric field diagram of Peak III (e-l) and Peak II (e-r) at${\mu _{\text{c}}} = 0.95{\text{ }}{\kern 1 pt} {\kern 1 pt} {\text{eV}}$ ; (f) spectra of the transmitted intensity with the variation incident wavelength and the chemical potential of graphene.
图 5 3个峰的灵敏度随
$ {\mu _{\text{c}}} $ 的变化Figure 5. Sensitivity trends of three peaks when changing
$ {\mu _{\text{c}}} $ .
图 6 (a), (b) 改变R和R1的透射光谱; (c) 改变R1时仅峰II和峰III的透射光谱(矩形框为Lorentz峰, 圆形框为Fano峰)
Figure 6. (a), (b) Transmission spectra with different parameters R and R1; (c) transmission spectra of Peak II and Peak III only with different parameters R1 (Rectangular frame is Lorentz peak, round frame is Fano peak).
图 7 3个峰的灵敏度随参数R和R1的变化
Figure 7. Sensitivity trends of the three peaks with different parameters R and R1.
图 8 改变折射率
$n$ 的透射光谱对比图Figure 8. Comparison of transmission spectra with different refractive indexes n.
表 1 拟合参数数值
Table 1. Fitting parameter values.
$\lambda $/nm ${\tau _m}$/fs ${\tau _{m0}}$/fs ${\varphi _m}$ 558 18.05855 176.34299 –0.73564π 1041 125.52873 260.88330 0.61392π 1095 5.92270 0.19382 –0.73322π 1114 447.50227 374.44485 0.60155π 
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[1] Zafar R, Salim M 2015 IEEE Sens. J. 15 11
Google Scholar
[2] Yuan M R, Lu Y C, Zhang Y, Zhang Z Y, Li Y F, Liu H C, Zhang X X, Han J G, Zhang W L 2020 Opt. Express 28 1987
Google Scholar
[3] Qi Y P, Ding J H, Zhang T, Liu W M, Wang L Y, Wang X X 2021 EPL 134 67001
Google Scholar
[4] Chen J, Nie H, Tang C J, Cui Y H, Yan B, Zhang Z Y, Kong Y R, Xu Z J, Cai P G 2019 Appl. Phys. Express 12 052015
Google Scholar
[5] Su W, Ding Y M, Luo Y L, Liu Y 2020 Results Phys. 16 102833
Google Scholar
[6] Wang M M, Zhang M, Wang Y F, Zhao R J, Yan S B 2019 Sensors 19 791
Google Scholar
[7] Chen H W, Qi Y P, Ding J H, Yuan Y J, Tian Z T, Wang X X 2022 Chin. Phys. B 31 034211
Google Scholar
[8] Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S 2017 Nat. Photon. 11 543
Google Scholar
[9] Fang Y H, Wen K H, Li Z F, Wu B Y, Guo Z C 2020 Mod. Phys. Lett. B 34 16
Google Scholar
[10] Yang X Y, Hua E, Su H, Guo J, Yan S B 2020 Sensors 20 4125
Google Scholar
[11] Xie Y Y, He C, Li J C, Song T T, Zhang Z D, Mao Q R 2016 IEEE Photon. J. 8 4802512
Google Scholar
[12] Cheng Q, Wang S T, Lv J T, Liu N, Pang B 2020 Opt. Commun. 464 125393
Google Scholar
[13] Morozov Y M, Lapchuk A S, Fu M L, Kryuchyn A A, Huang H R, Le Z C 2018 Photonics Res. 6 149
Google Scholar
[14] Li S L, Zhang Y Y, Song X K, Wang Y L, Yu L 2016 Opt. Express 24 15351
Google Scholar
[15] Zhang Z D, Luo L, Xue C Y, Zhang W D, Yan S B 2016 Sensors 16 642
Google Scholar
[16] Liu Z H, Ding L Z, Yi J P, Wei Z C, Guo J P 2018 Optoelectron. Lett. 14 421
Google Scholar
[17] Xiao G L, Xu Y P, Yang H Y, Ou Z T, Chen J Y, Li H O, Liu X P, Zeng L Z, Li J Q 2021 Sensors 21 1164
Google Scholar
[18] Wang W, Meng Z, Liang R S, Chen S J, Ding L, Wang F Q, Liu H Z, Meng H Y, Wei Z C 2018 Opt. Commun. 415 130
Google Scholar
[19] Chen X, Fan W H, Song C 2018 Carbon 133 416
Google Scholar
[20] 肖功利, 杨秀华, 杨宏艳, 窦婉滢, 徐俊林, 韦清臣, 李海鸥, 张法碧, 李琦, 陈永和, 傅涛, 孙堂友 2019 光学学报 39 0728011
Google Scholar
Xiao G L, Yang X H, Yang H Y, Dou W Y, Xu J L, Wei Q C, Li H O, Zhang F B, Li Q, Chen Y H, Fu T, Sun T Y 2019 Acta Opt. Sin. 39 0728011
Google Scholar
[21] Dai X Y, Ruan B X, Xiang Y J 2021 Biosensors 11 400
Google Scholar
[22] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
Google Scholar
[23] García de Abajo F J 2014 ACS Photonics 1 135
Google Scholar
[24] Yan X C, Wang T, Han X, Xiao S Y, Zhu Y J, Wang Y B 2016 Plasmonics 12 1449
Google Scholar
[25] Yuan Y J, Qi Y P, Zhang B H, Ding J H, Liu W M, Chen H W, Wang X X 2022 Phys. Scr. 97 025507
Google Scholar
[26] Liu Q, Liu M W, Zhan S P, Wu L X, Xie S X, Chen Z H, Zhang Y C 2019 Plasmonics 14 1005
Google Scholar
[27] Wang P F, Ding M, Murugan G S, Bo L, Guan C Y, Semenova Y, Wu Q, Farrell G, Brambilla G 2014 Opt. Lett. 39 5208
Google Scholar
[28] 孟令俊, 王梦宇, 沈远, 杨煜, 徐文斌, 张磊, 王克逸 2020 物理学报 69 014203
Google Scholar
Meng L J, Wang M Y, Shen Y, Yang Y, Xu W B, Zhang L, Wang K Y 2020 Acta Phys. Sin. 69 014203
Google Scholar
[29] 祁云平, 张婷, 郭嘉, 张宝和, 王向贤 2020 物理学报 69 167301
Google Scholar
Qi Y P, Zhang T, Guo J, Zhang B H, Wang X X 2020 Acta Phys. Sin. 69 167301
Google Scholar
[30] Lu H, Zeng C, Zhang Q M, Liu X M, Hossain M M, Reineck P, Gu M 2015 Sci. Rep. 5 8443
Google Scholar
[31] Falkovsky L A 2008 J. Phys. :Conf. Ser. 129 012004
Google Scholar
[32] Kuzmenko A B, van Heumen E, Carbone F, van der Marel D 2008 Phys. Rev. Lett. 100 117401
Google Scholar
[33] Wang C L, Wang Y Q, Hu H, Liu D J, Gao D L, Gao L 2019 Opt. Express 27 35925
Google Scholar
[34] Yan X, Fu R, Cheng T L, Li S G 2021 Sensors 21 3782
Google Scholar
[35] Cen C L, Chen Z Q, Xu D Y, Jiang L Y, Chen X F, Yi Z, Wu P H, Li G F, Yi Y G 2020 Nanomaterials 10 95
Google Scholar
[36] Zhang Y J, Kuang Y Q, Zhang Z D, Tang Y, Han J Q, Wang R B, Cui J G, Hou Y L, Liu W Y 2018 Appl. Phys. A 125 13
Google Scholar
[37] Chen Y Q, Bi K X, Wang Q J, Zheng M J, Liu Q, Han Y X, Yang J B, Chang S L, Zhang G H, Duan H G 2016 ACS Nano 10 11228
Google Scholar
[38] 王文雨, 张帅国, 冯宇, 米杰 2020 天然气化工(C1化学与化工) 45 123
Google Scholar
Wang W Y, Zhang S G, Feng Y, Mi J 2020 Natural Gas Chemical Industry 45 123
Google Scholar
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