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In this paper, we have proposed a multiband plasmon-induced transparency (PIT) hybrid model based on silver nanorods, silver nanodisk and graphene. The electromagnetic properties are numerically and theoretically studied in this paper. The research results show that using the bright-bright mode coupling between silver nanorods and silver nanodisk, based on the weak hybridization effect induced by the detuning of each bright mode unit, the single-band, dual-band and triple-band PIT effects can be achieved. By changing the chemical potential of graphene, the tunability of the resonant frequencies and transmission amplitude can be achieved simultaneously in each PIT model. When the chemical potential of graphene is 0 in each of the three PIT models, that is, without graphene, the resonant frequencies of its transparent window is the smallest. As the chemical potential of graphene increases from 0 to 0.5 eV, the resonant notches of the transparent peak in all three PIT models are both enhanced and blue shifted. Especially, when the chemical potential is 0.5 eV, the absolute increment of resonance notch generated by the sing-band PIT transparent window is $\Delta f = 1.01$ THz and the relative increment is 2.91% while the largest absolute increment of resonance notch generated by the dual-band PIT transparent window is$\Delta f = 1.77$ THz and the largest relative increment is 5.97%. In the next place, when the chemical potential is 0.3 eV, the absolute increment of resonance notch generated by the triple-band PIT transparent window is$\Delta f = 1.26$ THz and the relative increment of the window is 4.02%.On the other hand, when graphene is existent in none of the three models, the resonance between silver nanodisk and silver nanorods, and the resonance between silver nanorods and silver nanorods are the weakest and the transmission amplitude of transparent window is the strongest in each of the three PIT models. Thereafter, with the increase of chemical potential, the number of surface charges on the silver nanodisk and silver nanorods increases and the intensity of electric field is enhanced. At the same time, the coupling strength between silver nanodisk and silver nanorods, and the coupling strength between silver nanorods and silver nanorods are also gradually enhanced. As a result, the transmission amplitude of each PIT model will gradually decrease. Especially, when the chemical potential is 0.5 eV, the amplitude modulation depth of the single-band PIT transparent peak is 20.2% and the amplitude modulation depth of the two transparent windows in dual-band PIT model are 31.2% and 24.2% respectively. In addition, when the chemical potential is 0.3 eV, the amplitude modulation depths of the three transparent windows in triple-band PIT model are 29.8%, 33.8%, and 20.5%. Finally, the sensing properties of the single-band PIT model are further investigated. The results show that the sensitivities of the model with refractive index of different background materials reach 3906.6 nm/RIU all, which provides a theoretical reference for the design of multiband filtering and ultrasensitive sensors. [1] Tassin P, Zhang L, Koschny T 2009 Phys. Rev. Lett. 102 4
[2] Li H J, Wang L L, Liu J Q 2013 Appl. Phys. Lett. 103 211104
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[3] Liu N, Langguth L, Weiss T 2009 Nat. Mater. 8 9
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[4] Papasimakis N, Fu Y H, Fedotov V A 2009 Appl. Phys. Lett. 94 211902
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[5] 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 69
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[6] Qin M, Wang L L, Zhai X 2018 IEEE Photonic. Tech. L. 30 11
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[7] Ding J, Arigong B, Ren H 2014 Sci. Rep. 4 1
[8] Xiao S Y, Wang T, Liu T T 2018 Carbon 126 271
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[9] Shi C Y, He X Y, Peng J 2019 Opt. Laser Technol. 114 28
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[10] Ma Q C, Zhan Y W, Hong W Y 2018 Nanomaterials 9 7
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[11] Wei B Z, Jian S S 2018 Plasmonics 13 6
[12] Liu T T, Zhou C B, Cheng L 2019 J. Opt. 21 3
[13] Sun C, Dong Z W, Si J N 2017 Opt. Express 25 1242
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[14] Dong Z W, Sun C, Si J N 2017 Opt. Express 25 12251
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[15] 王越, 冷雁冰, 王丽 2018 物理学报 67 097801
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Wang Y, Leng Y B, Wang L 2018 Acta Phys. Sin. 67 097801
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[16] Lao C D, Liang Y Y, Wang X J 2019 Nanomaterials 9 171
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[17] Wang X J, Meng H Y, Deng S Y 2019 Nanomaterials 9 385
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[18] Zhang X B, Wang G Q, Zhang L 2019 Crystals 9 146
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[19] Cen H F, Wang F Q, Liang R S 2018 Opt. Commun. 420 78
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[20] Hu X G, Yuan S, Armghan A 2017 J. Phys. D: Appl. Phys. 50 025301
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[21] Zhang S, Genov D A, Wang Y 2008 Phys. Rev. Lett. 101 047401
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[22] Berardi S Z, Rusen Y M, Kelly M 2012 Nat. Commun. 3 780
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[23] Habib M, Rashed A R, Ozbay E 2018 Opt. Mater. Express 8 1069
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[25] Zhang Z J, Yang J B, He X 2018 RSC Adv. 8 27746
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Google Scholar
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图 1 单频段PIT模型结构图 (a) 三维空间结构图; (b) 二维平面结构图
Figure 1. Schematic diagrams of single-band PIT model: (a) Three-dimensional space schematic; (b) two-dimensional plane schematic.
图 2 单银盘谐振器、单银棒谐振器、单频段PIT模型的透射曲线
Figure 2. Transmission spectra of the sole disks array, the sole rods array, and the single-band PIT model.
图 3 单频段PIT模型在 (a) dip A, (b) dip B和(c) peak的电场分布
Figure 3. Distributions of electric field of single-band PIT model at (a) dip A, (b) dip B, and (c) peak.
图 4 单频段PIT模型改变石墨烯化学势时, 谐振频率和透射振幅随频率的变化情况
Figure 4. Variations of resonant frequency and amplitude in transmission with frequency under different chemical potential of graphene in single-band PIT model.
图 5 化学势为0和0.3 eV时, FDTD仿真结果与RTO拟合结果比较
Figure 5. Comparisons of the PIT calculated by FDTD method and fitted by RTO model when chemical potential is 0 and 0.3 eV.
图 6 化学势为0.1 和0.5 eV时, FDTD仿真结果与RTO拟合结果比较
Figure 6. Comparison of the PIT calculated by FDTD method and fitted by RTO model when chemical potential is 0.1 and 0.5 eV.
图 7 (a) 当化学势由0 变化到0.5 eV时, RTO模型中各拟合参数随化学势的变化关系; (b) 引入修正因子后新的拟合结果
Figure 7. (a) The fitting values of parameters in RTO model with the chemical potential of graphene varying from 0 to 0.5 eV; (b) new fitting result after introducing correction factor.
图 8 单频段PIT模型不同背景材料下的透射窗对比
Figure 8. Variations of transmission windows with different background materials in single-band PIT model.
图 9 单频段PIT模型 dip A, dip B和peak随背景材料折射率的变化规律
Figure 9. Variations of dip A, dip B, and peak with the different background materials in single-band PIT model.
图 10 双频段PIT模型二维平面图
Figure 10. Two-dimensional plane schematic of dual-band PIT model.
图 11 双频段PIT模型的透射曲线
Figure 11. Transmission spectra of dual-band PIT model.
图 12 双频段PIT模型在 (a) dip A, (b) dip B, (c) dip C, (d) peak I和(e) peak II的电场分布
Figure 12. Distributions of electric field of dual-band PIT model at (a) dip A, (b) dip B, (c) dip C, (d) peak I and (e) peak II.
图 13 双频段PIT模型改变石墨烯化学势时, 谐振频率和透射振幅随频率的变化情况
Figure 13. Variations of resonant frequency and amplitude in transmission with frequency under different chemical potential of graphene in dual-band PIT model.
图 14 三频段PIT模型二维平面图
Figure 14. Two-dimensional plane schematic diagram of triple-band PIT model.
图 15 三频段PIT模型的透射曲线
Figure 15. Transmission spectra of triple-band PIT model.
图 16 三频段PIT模型在 (a) dip A, (b) dip B, (c) dip C, (d) dip D, (e) peak I, (f) peak II和(g) peak III 的电场分布
Figure 16. Distribution of electric field of triple-band PIT model at (a) dip A, (b) dip B, (c) dip C, (d) dip D, (e) peak I, (f) peak II and (g) peak III.
图 17 三频段PIT模型改变石墨烯化学势时, 谐振频率和透射振幅随频率的变化情况
Figure 17. Variations of resonant frequency and amplitude in transmission with frequency under different chemical potential of graphene in triple-band PIT model.
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[1] Tassin P, Zhang L, Koschny T 2009 Phys. Rev. Lett. 102 4
[2] Li H J, Wang L L, Liu J Q 2013 Appl. Phys. Lett. 103 211104
Google Scholar
[3] Liu N, Langguth L, Weiss T 2009 Nat. Mater. 8 9
Google Scholar
[4] Papasimakis N, Fu Y H, Fedotov V A 2009 Appl. Phys. Lett. 94 211902
Google Scholar
[5] 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 69
Google Scholar
[6] Qin M, Wang L L, Zhai X 2018 IEEE Photonic. Tech. L. 30 11
Google Scholar
[7] Ding J, Arigong B, Ren H 2014 Sci. Rep. 4 1
[8] Xiao S Y, Wang T, Liu T T 2018 Carbon 126 271
Google Scholar
[9] Shi C Y, He X Y, Peng J 2019 Opt. Laser Technol. 114 28
Google Scholar
[10] Ma Q C, Zhan Y W, Hong W Y 2018 Nanomaterials 9 7
Google Scholar
[11] Wei B Z, Jian S S 2018 Plasmonics 13 6
[12] Liu T T, Zhou C B, Cheng L 2019 J. Opt. 21 3
[13] Sun C, Dong Z W, Si J N 2017 Opt. Express 25 1242
Google Scholar
[14] Dong Z W, Sun C, Si J N 2017 Opt. Express 25 12251
Google Scholar
[15] 王越, 冷雁冰, 王丽 2018 物理学报 67 097801
Google Scholar
Wang Y, Leng Y B, Wang L 2018 Acta Phys. Sin. 67 097801
Google Scholar
[16] Lao C D, Liang Y Y, Wang X J 2019 Nanomaterials 9 171
Google Scholar
[17] Wang X J, Meng H Y, Deng S Y 2019 Nanomaterials 9 385
Google Scholar
[18] Zhang X B, Wang G Q, Zhang L 2019 Crystals 9 146
Google Scholar
[19] Cen H F, Wang F Q, Liang R S 2018 Opt. Commun. 420 78
Google Scholar
[20] Hu X G, Yuan S, Armghan A 2017 J. Phys. D: Appl. Phys. 50 025301
Google Scholar
[21] Zhang S, Genov D A, Wang Y 2008 Phys. Rev. Lett. 101 047401
Google Scholar
[22] Berardi S Z, Rusen Y M, Kelly M 2012 Nat. Commun. 3 780
Google Scholar
[23] Habib M, Rashed A R, Ozbay E 2018 Opt. Mater. Express 8 1069
Google Scholar
[24] Shu C, Chen Q, Mei J 2019 Mater. Res. Express 6 055808
Google Scholar
[25] Zhang Z J, Yang J B, He X 2018 RSC Adv. 8 27746
Google Scholar
[26] Liu Y, Zhong R B, Lian Z 2018 Sci. Rep. 8 2828
Google Scholar
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