Sensing and slow light properties of dual-band terahertz metamaterials based on electromagnetically induced transparency-like

Sun Zhan-Shuo; Wang Xin; Wang Jun-Lin; Fan Bo; Zhang Yü; Feng Yao

doi:10.7498/aps.71.20212163

Abstract

Electromagnetically induced transparency (EIT) is a quantum interference phenomenon in a three-level atomic system. The generation of quantum interference effect significantly reduces the light absorptivity of the specific frequency that is strongly absorbed, and produces a sharp “transmission window” in the resonance absorption region. The EIT is usually accompanied by strong dispersion, which significantly reduces the group velocity of light and enhances the nonlinear interaction. The EIT phenomenon of atomic system usually needs to be observed at very low temperature or high intensity laser, which is a very serious challenge for the application of EIT technology. The simulation of electromagnetically induced transparency using metamaterials can effectively break through these limitations.In this work, an electromagnetically induced transparency-like terahertz metamaterial structure with three bright modes is proposed and investigated. Two weakly hybrid states are composed of two bright modes with similar resonant frequencies. The energy oscillates back and forth between the two modes, and a transparent window is generated between the two resonance points. The designed metamaterial is composed of three groups of bright modes with adjacent resonant frequencies, and the three groups of bright modes are coupled to produce two transparent windows. The electromagnetically induced transparency-like formation mechanism is analyzed based on the simulation curve and electric field distribution. In addition, the sensing properties of metamaterial are determined by simulation and calculation, and the refractive index sensitivities of the two windows can be as high as 451.92 GHz/RIU and 545.31 GHz/RIU under the optimal thickness of the measured substances. Through the sensing simulation of six petroleum products, it is verified that the dual-band has more excellent advantages in dielectric constant matching than the single frequency band. The characteristics of the designed metamaterial in the slow light effect are also studied. The maximum group delay times of the two windows can reach 9.98 ps and 6.23 ps. Therefore, the structure is considered to have an important application value in the field of high sensitivity sensors and slow light devices.

Keywords:

electromagnetically induced transparency-like /
terahertz metamaterials /
sensing characteristics /
slow light characteristics

Authors and contacts

College of Electronic Information Engineering, Inner Mongolia University, Hohhot 010021, China

Corresponding author: Wang Xin, wangxin219@imu.edu.cn ; Wang Jun-Lin, wangjunlin@imu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51965047), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2021MS06012), and the Science and Technology Planning Project of Inner Mongolia Autonomous Region, China (Grant No. 2020GG0185).

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References

[1]	Harris S E, Field J E, Imamoğlu A 1990 Phys. Rev. Lett. 64 1107 Google Scholar
[2]	Xiao M, Li Y Q, Jin S Z, Gea-Banacloche J 1995 Phys. Rev. Lett. 74 666 Google Scholar
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[37]	Zhang X, Wang Y, Cui Z, Zhang X, Chen S, Zhang K, Wang X 2021 Opt. Mater. Express 11 1470 Google Scholar
[38]	Liu T T, Zhou C B, Cheng L, Jiang X Y, Wang G Z, Xu C, Xiao S Y 2019 J. Opt. 21 035101 Google Scholar
[39]	Zhang Z, Yang J, Han Y, He X, Zhang J, Huang J, Chen D, Xu S, Xie W 2020 Appl. Phys. A 126 199 Google Scholar
[40]	Jiang J, Cui J, Fang R, Wu F, Yang Y 2020 Integr. Ferroelectr. 212 1 Google Scholar
[41]	Zeng F, Zhong M 2021 Opt. Mater. 111 110596 Google Scholar

Cited By

图 1 提出的超材料的几何结构和单元结构图

Figure 1. Geometry of the proposed metamaterial structure and the unit structure diagram.

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图 2 (a) 单波段超材料、DR和DT的透射幅值曲线; (b) 双波段超材料、DR、DT和FL的透射幅值曲线

Figure 2. (a) Transmission amplitude curves of the single-band metamaterial, DR and DT; (b) transmission amplitude curves of the dual-band metamaterial, DR, DT and FL.

DownLoad: Full-Size Img PowerPoint

图 3 EIT-like的等效原子能级示意图

Figure 3. Schematic diagram of EIT-like equivalent atomic energy level.

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图 4 (a) 三个波谷频率的电场分布; (b) 两个透射峰值频率的电场分布

Figure 4. (a) Electric field distribution of the three trough frequencies; (b) electric field distribution of two transmission peak frequencies.

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图 5 超材料覆盖厚度为4 µm且折射率不同的被测物的仿真曲线

Figure 5. Simulation curves of the metamaterial covered with the measured substances with thickness 4 µm and different refractive indices.

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图 6 (a) 超材料表面覆盖不同被测物厚度对应的第一个EIT-like窗口的拟合灵敏度; (b) 超材料表面覆盖不同被测物厚度对应的第二个EIT-like窗口的拟合灵敏度; (c) 被测物质的厚度对灵敏度的影响

Figure 6. (a) Fitting sensitivity of the first EIT-like window corresponding to different measured substances thickness covered on the surface of metamaterial; (b) fitting sensitivity of the second EIT-like window corresponding to different measured substances thickness covered on the surface of metamaterial; (c) influence of thickness of the measured substances on sensitivity.

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图 7 (a) 超材料的传输曲线和相移曲线; (b) 计算的超材料的群时延和群折射率

Figure 7. (a) Simulated transmission curve and phase shift curve of the metamaterial; (b) calculated group delay and group index of the metamaterial.

DownLoad: Full-Size Img PowerPoint

表 1 超材料覆盖待测物的仿真和计算结果

Table 1. Simulation and calculation results of metamaterial covering the measured substances.

The measured substance	ε	Frequency shift /GHz		Calculated ε		Calculated average ε
The measured substance	ε	First	Second	First	Second	Calculated average ε
JP-4	1.7	133.85	171.83	1.68	1.73	1.705
Petroleum ether	1.8	152.73	188.22	1.79	1.81	1.8
90#	2.01	188.82	227.67	2.01	2.01	2.01
93#	2.11	201.44	248.53	2.09	2.12	2.105
Transmission oil	2.2	218.42	265.2	2.2	2.21	2.205
97#	2.25	222.98	270.68	2.23	2.24	2.235

DownLoad: CSV

表 2 各种超材料在传感和慢光方面性能的比较

Table 2. Comparison of sensing and slow light properties of various metamaterials.

Performance index	Ref.[34]	Ref.[35]	Ref.[36]	Ref.[37]	Ref.[38]	Ref.[39]	Ref.[40]	Ref.[41]	This paper
Performance index	2018	2019	2020	2021	2019	2020	2020	2021	—
Q	58	22.05	30.5	—	—	—	11.88	—	26.63	19.46
S/(GHz·RIU^–1)	105	300	280	229.7	—	—	—	—	452	545
FOM	7.5	2.94	8.54	—	—	—	—	—	4.75	6.21
$ {\tau }_{\mathrm{g}} $/ps	—	—	—	—	6.74	7	7.28	5.5	9.98	6.23

DownLoad: CSV

[1]	Harris S E, Field J E, Imamoğlu A 1990 Phys. Rev. Lett. 64 1107 Google Scholar
[2]	Xiao M, Li Y Q, Jin S Z, Gea-Banacloche J 1995 Phys. Rev. Lett. 74 666 Google Scholar
[3]	Hau L V, Harris S E, Dutton Z, Behroozi C H 1999 Nature 397 594 Google Scholar
[4]	Boller K J, Imamoğlu A, Harris S E 1991 Phys. Rev. Lett. 66 2593 Google Scholar
[5]	Lin X Q, Chen Z, Yu J W, Liu P Q, Li P F, Chen Z Z 2016 IEEE Sens. J. 16 293 Google Scholar
[6]	Lin X Q, Peng J, Chen Z, Yu J W, Yang X F 2018 IEEE Sens. J. 18 9251 Google Scholar
[7]	Li H M, Liu S B, Liu S Y, Zhang H F 2014 Appl. Phys. Lett. 105 133514 Google Scholar
[8]	Zhang F L, He X, Zhou X, Zhou Y L, An S, Yu G Y, Pang L N 2013 Appl. Phys. Lett. 103 221904 Google Scholar
[9]	Longdell J J, Fraval E, Sellars M J, Manson N B 2005 Phys. Rev. Lett. 95 063601 Google Scholar
[10]	Ma J Y, Qin J Y, Campbell G T, Lecamwasam R, Sripathy K, Hope J, Buchler B, Lam P K 2020 Sci. Adv. 6 eaax8256 Google Scholar
[11]	Liu N, Weiss T, Mesch M, Langguth L, Eigenthaler U, Hirscher M, Sonnichsen C, Giessen H 2010 Nano Lett. 10 1103 Google Scholar
[12]	Waks E, Vuckovic J 2006 Phys. Rev. Lett. 96 153601 Google Scholar
[13]	Tassin P, Zhang L, Koschny T, Economou E N, Soukoulis C M 2009 Opt. Express 17 5595 Google Scholar
[14]	Sun Y R, Chen H, Li X J, Hong Z 2017 Opt. Commun. 392 142 Google Scholar
[15]	Xiao S Y, Wang T, Liu T T, Yan X C, Li Z, Xu C 2018 Carbon 126 271 Google Scholar
[16]	Zhang S, Genov D A, Wang Y, Liu M, Zhang X 2008 Phys. Rev. Lett. 101 047401 Google Scholar
[17]	Hokmabadi M P, Kim J H, Rivera E, Kung P, Kim S M 2015 Sci. Rep. 5 14373 Google Scholar
[18]	Zheng S Q, Zhao Q X, Peng L, Jiang X 2021 Results Phys. 23 104040 Google Scholar
[19]	Zhang J J, Xiao S S, Jeppesen C, Kristensen A, Mortensen N A 2010 Opt. Express 18 17187 Google Scholar
[20]	Hu S, Yang H L, Han S, Huang X J, Xiao B X 2015 J. Appl. Phys. 117 043107 Google Scholar
[21]	Tang B, Jia Z P, Huang L, Su J B, Jiang C 2021 IEEE J. Sel. Top. Quantum Electron. 27 4700406 Google Scholar
[22]	Gu J Q, Singh R, Liu X J, Zhang X Q, Ma Y F, Zhang S, Maier S A, Tian Z, Azad A K, Chen H T, Taylor A J, Han J G, Zhang W L 2012 Nat. Commun. 3 1151 Google Scholar
[23]	Sarkar R, Devi K M, Ghindani D, Prabhu S S, Chowdhury D R, Kumar G 2020 J. Opt. 22 035105 Google Scholar
[24]	Li H M, Liu S B, Liu S Y, Wang S Y, Zhang H F, Bian B R, Kong X K 2015 Appl. Phys. Lett. 106 114101 Google Scholar
[25]	Li H M, Liu S B, Liu S Y, Wang S Y, Ding G W, Yang H, Yu Z Y, Zhang H F 2015 Appl. Phys. Lett. 106 083511 Google Scholar
[26]	Zhang K, Wang C, Qin L, Peng R W, Xu D H, Xiong X, Wang M 2014 Opt. Lett. 39 3539 Google Scholar
[27]	Liu T T, Wang H X, Liu Y, Xiao L S, Zhou C B, Liu Y B, Xu C, Xiao S Y 2018 J. Phys. D:Appl. Phys. 51 415105 Google Scholar
[28]	Devi K M, Chowdhury D R, Kumar G, Sarma A K 2018 J. Appl. Phys. 124 063106 Google Scholar
[29]	Zhu L, Meng F Y, Fu J H, Wu Q, Hua J 2012 Opt. Express 20 4494 Google Scholar
[30]	Hu J, Lang T T, Hong Z, Shen C Y, Shi G H 2018 J. Lightwave Technol. 36 2083 Google Scholar
[31]	Kang M, Li Y N, Chen J, Chen J, Bai Q, Wang H T, Wu P H 2010 Appl. Phys. B 100 699 Google Scholar
[32]	Wu X J, Quan B G, Pan X C, Xu X L, Lu X C, Gu C Z, Wang L 2013 Biosens. Bioelectron. 42 626 Google Scholar
[33]	Zhang C, Liang L, Ding L, Jin B, Hou Y, Li C, Jiang L, Liu W, Hu W, Lu Y, Kang L, Xu W, Chen J, Wu P 2016 Appl. Phys. Lett. 108 241105 Google Scholar
[34]	Xie Q, Dong G X, Wang B X, Huang W Q 2018 Nanoscale Res. Lett. 13 2947 Google Scholar
[35]	Saadeldin A S, Hameed M F O, Elkaramany E M A, Obayya S S A 2019 IEEE Sens. J. 19 7993 Google Scholar
[36]	Chen T, Zhang D P, Huang F Y, Li Z, Hu F R 2020 Mater. Res. Express 7 095802 Google Scholar
[37]	Zhang X, Wang Y, Cui Z, Zhang X, Chen S, Zhang K, Wang X 2021 Opt. Mater. Express 11 1470 Google Scholar
[38]	Liu T T, Zhou C B, Cheng L, Jiang X Y, Wang G Z, Xu C, Xiao S Y 2019 J. Opt. 21 035101 Google Scholar
[39]	Zhang Z, Yang J, Han Y, He X, Zhang J, Huang J, Chen D, Xu S, Xie W 2020 Appl. Phys. A 126 199 Google Scholar
[40]	Jiang J, Cui J, Fang R, Wu F, Yang Y 2020 Integr. Ferroelectr. 212 1 Google Scholar
[41]	Zeng F, Zhong M 2021 Opt. Mater. 111 110596 Google Scholar

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