Dynamically tunable multi-frequency modulator via triple plasmon-induced transparency in graphene metasurfaces

ZHANG Wenjie; ZHANG Xiaojiao; HU Shunan; ZHAN Jie; GAO Enduo; WANG Qi; NIE Guozheng

doi:10.7498/aps.74.20250488

Abstract

Plasmon-induced transparency (PIT) is a class of electromagnetically induced transparency phenomenon that enhances the interaction between light and matter, thereby improving the performance of nano-optical devices. However, traditional PITs usually rely on near-field coupling between bright modes and dark modes. In order to break through the limitation of this mechanism, in this study we propose a dual-polarized graphene hypersurface structure, which consists of four groups of symmetric L-shaped graphene surrounding cross-shaped hollow graphene, forming a triple PIT through the synergistic effect between two single PITs. The accuracy of the results is verified by simulating the transmission spectra using the finite-difference time-domain, which is highly similar to that of the coupled-mode theory results. It is found that by modulating the Fermi energy levels and carrier mobility, this structure exhibits a group refractive index of up to 500 as a slow-light device, demonstrating excellent slow-light control capability. As a polarizing device, this structure has dual polarization characteristics and can generate a triple PIT window under both x and y polarized light incidence. In particular, the resonant frequency f₆ is not affected by the direction of polarization of the incident light. This good stability and resistance to interference in various polarized light conditions are particularly important for designing polarization devices. Meanwhile, we adjust the length parameter of graphene L₂ and find that the resonance frequency f₆ is still highly stable, showing a better tolerance to structural changes. Therefore, in this study, a multifunctional integrated device with slow light modulation and polarization selection in one device is designed, providing new theoretical guidance and research directions for synergistic effects based on polarization insensitivity.

Keywords:

Authors and contacts

1.
Hunan Provincial Key Laboratory of Intelligent Sensors and New Sensor Materials, School of Physics and Electronic Science, Hunan University of Science and Technology, Xiangtan 411201, China
2.
School of Microelectronics and Physics, Hunan University of Technology and Business, Changsha 410205, China
3.
School of Physical and Electronic Science, Changsha University of Science and Technology, Changsha 410083, China
4.
Peking University Dongguan Institute of Opto-Electronics, Dongguan 523808, China

Corresponding author: ZHAN Jie, jiezhanwl@163.com ; GAO Enduo, 009004@csust.edu.cn ; NIE Guozheng, gzhnie@hnust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62175062, 62173135), the Natural Science Foundation of the Education Department of Hunan Province, China (Grant No. 23A0454), the Natural Science Foundation of Hunan Province, China (Grant No. 2025JJ50357), and the Open Fund for Hunan Provincial Key Laboratory of Intelligent Sensors and Novel Sensing Materials (Grant No. E22453).

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References

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[8]	Landy N I, Sajuyigbe S, Mock J J, Smith D R, Padilla W J 2008 Phys. Rev. Lett. 100 207402 Google Scholar
[9]	Jablan M, Buljan H, Soljačić M 2009 Phys. Rev. B 80 245435 Google Scholar
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[11]	Chen Z Y, Liu N L, Nie G Z, Li Y Q, Su X, Tang X F, Zeng Y, Liu Y X 2024 Physica B. 686 416073 Google Scholar
[12]	Liu C B, Bai Y, Zhou J, Zhao Q, Qiao L J 2017 J. Korean Ceram. Soc. 54 349 Google Scholar
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[15]	Dhriti K M, Chowdhary A K, Chouhan B S, Sikdar D, Kumar G 2022 J. Phys. D: Appl. Phys. 55 285101 Google Scholar
[16]	Li Z L, Nie G Z, Chen Z Q, Zhan S P, Lan L F 2024 Opt. Lett. 49 3380 Google Scholar
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[21]	Zhang H Y, Cao Y Y, Liu Y Z, Li Y, Zhang Y P 2017 Opt. Commun. 391 9 Google Scholar
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[29]	胡树南, 李德琼, 詹杰, 高恩多, 王琦, 刘南柳, 聂国政 2025 物理学报 74 097801 Google Scholar Hu S N, Li D Q, Zhan J, Gao E D, Wang Q, Liu N L, Nie G Z 2025 Acta Phys. Sin. 74 097801 Google Scholar
[30]	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 106798 Google Scholar
[31]	Xu H, Zhao M Z, Xiong C X, Zhang B H, Zheng M F, Zeng J P, Xia H, Li H J 2018 Phys. Chem. Chem. Phys. 20 25959 Google Scholar
[32]	Zhou X W, Xu Y P, Li Y H, Cheng S B, Yi Z, Xiao G H, Wang Z Y, Chen Z Y 2022 Commun. Theor. Phys. 75 015501 Google Scholar
[33]	Liu Z M, Zhang X, Zhang Z B, Gao E D, Zhou F Q, Li H J, Luo X 2020 New J. Phys. 22 083006 Google Scholar
[34]	Zhang X, Zhou F Q, Liu Z M, Zhang Z B, Qin Y P, Zhou S S, Luo X, Gao E D, Li H J 2021 Opt. Express 29 29387 Google Scholar
[35]	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 405102 Google Scholar
[36]	Liu Z M, Yang G X, Luo X, Zhou F Q, Cheng Z Q, Yi Z 2024 Diam. Relat. Mater. 142 110786 Google Scholar
[37]	Zheng L, Cheng X H, Cao D, Wang G, Wang Z J, Xu D W, Xia C, Shen L Y, Yu Y H, Shen D S 2014 ACS Appl. Mater. Interfaces 6 7014 Google Scholar
[38]	Zheng L, Cheng X H, Cao D, Wang Z J, Xu D W, Xia C, Shen L Y, Yu Y H 2014 Mater. Lett. 137 200 Google Scholar
[39]	Jin R, Huang L J, Zhou C B, Guo J Y, Fu Z C, Chen J, Wang J, Li X, Yu F L, Chen J, Zhao Z Y, Chen X S, Lu W, Li G H 2023 Nano Lett. 23 9105 Google Scholar
[40]	Müller M, Bouša M, Hájková Z, Ledinský M, Fejar A, Drogowska-Horná K, Kalbáč M, Frank O 2020 Nanomaterials 10 589 Google Scholar
[41]	Wu D, Wang M, Feng H, Xu Z X, Liu Y P, Xia F, Zhang K, Kong W J, Dong L F, Yun M J 2019 Carbon 155 618 Google Scholar
[42]	Falkovsky L A, Varlamov A A 2007 Eur. Phys. J. B 56 281 Google Scholar
[43]	Rouhi N, Capdevila S, Jain D, Zand K, Wang Y Y, Brown E, Jofre L, Burke P 2012 Nano Res. 5 667 Google Scholar
[44]	Liang H W, Ruan S C, Zhang M, Su H, Li I L 2015 Appl. Phys. Lett. 107 091602 Google Scholar
[45]	Cheng H, Chen S Q, Yu P, Duan X Y, Xie B Y, Tian J G 2013 Appl. Phys. Lett. 103 203112 Google Scholar
[46]	Zentgraf T, Zhang S, Oulton R F, Zhang X 2009 Phys. Rev. B 80 195415 Google Scholar
[47]	Li M, Li H J, Xu H, Xiong C X, Zhao M Z, Liu C, Ruan B X, Zhang B H, Wu K 2020 New J. Phys. 22 103030 Google Scholar
[48]	Zhou X W, Xu Y P, Li Y H, Cheng S B, Yi Z, Xiao G H, Wang Z Y, Chen Z Y 2022 Commun. Theor. Phys. 74 115501 Google Scholar
[49]	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 129401 Google Scholar
[50]	Liu Z M, Qin Y P, Zhou F Q, Zhou S S, Ji C, Yang G X, Xie Y D, Yang R H, Luo X 2024 Mod. Phys. Lett. B 38 2350248 Google Scholar
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Cited By

图 1 (a) 所提出的超表面的三维结构透视图和侧视图; (b) 一个周期单元结构顶视图; (c) 石墨烯结构制备过程的示意图

Figure 1. (a) Perspective and side views of the three-dimensional structure of the proposed hypersurface; (b) top view of one cycle unit structure; (c) schematic diagram of the process of preparing graphene structures.

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图 2 耦合模理论示意图

Figure 2. Schematic diagram of coupled mode theory.

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图 3 (a)—(c) 不同石墨烯结构之间相互作用的透射光谱; (d) 三重PIT共振频率下的归一化电场分布图

Figure 3. (a)–(c) Transmission spectra illustrating interactions between different graphene structures; (d) normalized electric field distribution at triple PIT resonance frequencies.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 不同费米能级下FDTD模拟和CMT计算的透射光谱; (b) 三重PIT在不同费米能级的三维演化

Figure 4. (a) Transmission spectra from FDTD simulations and CMT calculations at Fermi levels; (b) three-dimensional evolution of the triple-PIT at different Fermi levels.

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图 5 不同结构参数下的透射光谱

Figure 5. Transmission spectra with different structural parameters.

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图 6 不同石墨烯载流子迁移率条件下, 群折射率和相移随频率的变化(E_F = 1.0 eV)　(a) 0.5 m²/(V·s); (b) 1.0 m²/(V·s); (c) 2.0 m²/(V·s); (d) 3.0 m²/(V·s)

Figure 6. Variation of group index and phase shift with frequency at graphene carrier mobilities of (a) 0.5 m²/(V·s), (b) 1.0 m²/(V·s), (c) 2.0 m²/(V·s), and (d) 3.0 m²/(V·s) (E_F = 1.0 eV).

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图 7 (a) 偏振光入射角从0°—90°变化的透射光谱; (b) 透射率随偏振光入射角和频率的三维演化; (c) 共振频率随角度变化的趋势图

Figure 7. (a) Transmission spectra under varying polarization angles of incident light from 0° to 90°; (b) three-dimensional mapping of transmittance versus frequency and polarization angle; (c) trend plot of resonance frequency versus angle.

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图 8 (a)—(c) SS, SZ和整个结构对于偏振光的透射光谱; (d) 不同偏振光下整体结构的电场分布图

Figure 8. (a)–(c) Transmission spectra of the SS, SZ, and the entire structure under polarized illumination; (d) plot of the electric field distribution of the overall structure under different polarized light.

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表 1 不同图案化石墨烯的性能比较

Table 1. Comparison of the properties of different patterned graphene.

Reference /year	Modulation mode	Material structure	Group index	Polarization direction or sensitive
2020^[47]	Dual-frequency	Single-layer continuous patterned graphene	358	x-polarization
2021^[34]	Multiple-frequency	Single-layer discrete patterned graphene	321	Polarization-insensitive
2022^[48]	Multiple-frequency	Double-layer patterned graphene	<500	x-polarization
2023^[49]	Dual-frequency	Monolayer patterned black phosphorus	219	x-polarization
2023^[50]	Multiple-frequency	Double-layer patterned graphene	424	Polarization-insensitive
2024^[51]	Multiple-frequency	Single-layer silicon nanostrip array	320	x or y-polarization
This work	Multiple-frequency	Single-layer discrete patterned graphene	500	x or y-polarization-insensitive

DownLoad: CSV

[1]	Barnes W L, Dereux A, Ebbesen T W 2003 Nature 424 824 Google Scholar
[2]	Ebbesen T W, Genet C, Bozhevolnyi S I 2008 Phys. Today 61 44 Google Scholar
[3]	Zhang S, Genov D A, Wang Y, Liu M, Zhang X 2008 Phys. Rev. Lett. 101 047401 Google Scholar
[4]	Hutter E, Fendler J H 2004 Adv. Mater. 16 1685 Google Scholar
[5]	Gramotnev D K, Bozhevolnyi S I 2010 Nat. Photon. 4 83 Google Scholar
[6]	Farmani A, Mir A, Sharifpour Z 2018 Appl. Surf. Sci. 453 358 Google Scholar
[7]	Creighton J A, Blatchford C G, Albrecht M G 1979 J. Chem. Soc. , Faraday Trans. 75 790 Google Scholar
[8]	Landy N I, Sajuyigbe S, Mock J J, Smith D R, Padilla W J 2008 Phys. Rev. Lett. 100 207402 Google Scholar
[9]	Jablan M, Buljan H, Soljačić M 2009 Phys. Rev. B 80 245435 Google Scholar
[10]	Chen P Y, Argyropoulos C, Farhat M, Gomez-Diaz J S 2017 Nanophotonics 6 1239 Google Scholar
[11]	Chen Z Y, Liu N L, Nie G Z, Li Y Q, Su X, Tang X F, Zeng Y, Liu Y X 2024 Physica B. 686 416073 Google Scholar
[12]	Liu C B, Bai Y, Zhou J, Zhao Q, Qiao L J 2017 J. Korean Ceram. Soc. 54 349 Google Scholar
[13]	Han M Y, Özyilmaz B, Zhang Y, Kim P 2007 Phys. Rev. Lett. 98 206805 Google Scholar
[14]	Zhang B H, Huang X T, Chen G, Wang Z, Qian W, Zhang Z X, Cai W Q, Du K, Zhou C, Wang T T, Zhu W, He D P, Wang S X 2023 Opt. Laser Technol. 164 109431 Google Scholar
[15]	Dhriti K M, Chowdhary A K, Chouhan B S, Sikdar D, Kumar G 2022 J. Phys. D: Appl. Phys. 55 285101 Google Scholar
[16]	Li Z L, Nie G Z, Chen Z Q, Zhan S P, Lan L F 2024 Opt. Lett. 49 3380 Google Scholar
[17]	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 128701 Google 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 128701 Google Scholar
[18]	Li Z L, Nie G Z, Wang J H, Zhong F, Zhan S P 2024 Phys. Rev. Appl. 21 034039 Google Scholar
[19]	Zhan Y, Fan C Z 2023 Mater. Res. Express 10 055802 Google Scholar
[20]	Zayats A V, Smolyaninov I I, Maradudin A A 2005 Phys. Rep. 408 131 Google Scholar
[21]	Zhang H Y, Cao Y Y, Liu Y Z, Li Y, Zhang Y P 2017 Opt. Commun. 391 9 Google Scholar
[22]	Scott Z, Muhammad S, Shahbazyan T V 2022 J. Chem. Phys. 156 194702 Google Scholar
[23]	Kurter C, Tassin P, Zhang L, Koschny T, Zhuravel A P, Ustinov A V, Anlage S M, Soukoulis C M 2011 Phys. Rev. Lett. 107 043901 Google Scholar
[24]	成昱轩, 许辉, 于鸿飞, 黄林琴, 谷志超, 陈玉峰, 贺龙辉, 陈智全, 侯海良 2025 物理学报 74 067801 Google Scholar Cheng Y X, Xu H, Yu H F, Huang L Q, Gu Z C, Chen Y F, He L H, Chen Z Q, Hou H L 2025 Acta Phys. Sin. 74 067801 Google Scholar
[25]	Yang H, Li G H, Cao G T, Zhao Z Y, Chen J, Ou K, Chen X S, Lu W 2018 Opt. Express 26 5632 Google Scholar
[26]	Tsakmakidis K L, Shen L, Schulz S A, Zheng X, Upham J, Deng X, Altug H, Vakakis A F, Boyd R 2017 Science 356 1260 Google Scholar
[27]	He Z H, Li L Q, Cui W, Wang Y X, Xue W W, Xu H, Yi Z, Li C J, Li Z X 2021 New J. Phys. 23 053015 Google Scholar
[28]	Yan Y, Jiang Y F, Li B X, Deng C S 2023 J. Lightwave Technol. 42 732 Google Scholar
[29]	胡树南, 李德琼, 詹杰, 高恩多, 王琦, 刘南柳, 聂国政 2025 物理学报 74 097801 Google Scholar Hu S N, Li D Q, Zhan J, Gao E D, Wang Q, Liu N L, Nie G Z 2025 Acta Phys. Sin. 74 097801 Google Scholar
[30]	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 106798 Google Scholar
[31]	Xu H, Zhao M Z, Xiong C X, Zhang B H, Zheng M F, Zeng J P, Xia H, Li H J 2018 Phys. Chem. Chem. Phys. 20 25959 Google Scholar
[32]	Zhou X W, Xu Y P, Li Y H, Cheng S B, Yi Z, Xiao G H, Wang Z Y, Chen Z Y 2022 Commun. Theor. Phys. 75 015501 Google Scholar
[33]	Liu Z M, Zhang X, Zhang Z B, Gao E D, Zhou F Q, Li H J, Luo X 2020 New J. Phys. 22 083006 Google Scholar
[34]	Zhang X, Zhou F Q, Liu Z M, Zhang Z B, Qin Y P, Zhou S S, Luo X, Gao E D, Li H J 2021 Opt. Express 29 29387 Google Scholar
[35]	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 405102 Google Scholar
[36]	Liu Z M, Yang G X, Luo X, Zhou F Q, Cheng Z Q, Yi Z 2024 Diam. Relat. Mater. 142 110786 Google Scholar
[37]	Zheng L, Cheng X H, Cao D, Wang G, Wang Z J, Xu D W, Xia C, Shen L Y, Yu Y H, Shen D S 2014 ACS Appl. Mater. Interfaces 6 7014 Google Scholar
[38]	Zheng L, Cheng X H, Cao D, Wang Z J, Xu D W, Xia C, Shen L Y, Yu Y H 2014 Mater. Lett. 137 200 Google Scholar
[39]	Jin R, Huang L J, Zhou C B, Guo J Y, Fu Z C, Chen J, Wang J, Li X, Yu F L, Chen J, Zhao Z Y, Chen X S, Lu W, Li G H 2023 Nano Lett. 23 9105 Google Scholar
[40]	Müller M, Bouša M, Hájková Z, Ledinský M, Fejar A, Drogowska-Horná K, Kalbáč M, Frank O 2020 Nanomaterials 10 589 Google Scholar
[41]	Wu D, Wang M, Feng H, Xu Z X, Liu Y P, Xia F, Zhang K, Kong W J, Dong L F, Yun M J 2019 Carbon 155 618 Google Scholar
[42]	Falkovsky L A, Varlamov A A 2007 Eur. Phys. J. B 56 281 Google Scholar
[43]	Rouhi N, Capdevila S, Jain D, Zand K, Wang Y Y, Brown E, Jofre L, Burke P 2012 Nano Res. 5 667 Google Scholar
[44]	Liang H W, Ruan S C, Zhang M, Su H, Li I L 2015 Appl. Phys. Lett. 107 091602 Google Scholar
[45]	Cheng H, Chen S Q, Yu P, Duan X Y, Xie B Y, Tian J G 2013 Appl. Phys. Lett. 103 203112 Google Scholar
[46]	Zentgraf T, Zhang S, Oulton R F, Zhang X 2009 Phys. Rev. B 80 195415 Google Scholar
[47]	Li M, Li H J, Xu H, Xiong C X, Zhao M Z, Liu C, Ruan B X, Zhang B H, Wu K 2020 New J. Phys. 22 103030 Google Scholar
[48]	Zhou X W, Xu Y P, Li Y H, Cheng S B, Yi Z, Xiao G H, Wang Z Y, Chen Z Y 2022 Commun. Theor. Phys. 74 115501 Google Scholar
[49]	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 129401 Google Scholar
[50]	Liu Z M, Qin Y P, Zhou F Q, Zhou S S, Ji C, Yang G X, Xie Y D, Yang R H, Luo X 2024 Mod. Phys. Lett. B 38 2350248 Google Scholar
[51]	Wang Y J, Luo G L, Yan Z D, Wang J P, Tang C J, Liu F X, Zhu M W 2024 J. Lightwave Technol. 42 406 Google Scholar

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Vol. 74, Issue 15 - 2025-08-05

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