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In this work, we study the broadband manipulation of polarization states of terahertz (THz) waves with flexible metamaterial both theoretically and experimentally. Firstly, we construct a chiral THz metamaterial with asymmetric L-shaped metal-dielectric-metal structure, generating a series of electric dipoles via its interacting with terahertz waves. By changing the geometric parameters of the structure, the time responses of the electric dipoles in the two orthogonal directions are effectively modulated. Consequently, the chiral metamaterial efficiently converts linearly polarized terahertz wave into a circularly polarized one. The radiation of the metamaterial remains almost unaffected by the changing of the incident angle, which indicates that this chiral metamaterial can be used to realize a flexible terahertz circularly-polarized wave plate. Further, we present the working principle of this flexible terahertz circularly-polarized wave plate at the bending state based on the equivalent circuit model. Moreover, we fabricate a flexible metamaterial wave plate by using polymers as the dielectric layer. When the linearly polarized light is incident on the metamaterial, the circularly polarized output can be achieved in a wide frequency range of 0.46–0.62 THz. The polarization conversion remains quite stable even if the sample is bent. This flexible terahertz metamaterial wave plate is expected to be applied to 6G communication, molecular detection, etc.
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Keywords:
- metamaterials /
- broadband circular polarization /
- terahertz waves /
- flexible
[1] Yang P, Xiao Y, Xiao M, Li S 2019 IEEE Network 33 70
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图 1 柔性宽带太赫兹波片示意图 (a) 未弯曲情形; (b) 单元结构; (c) 弯曲情形
Figure 1. Schematic diagram of flexible broadband terahertz wave plate: (a) Wave plate without bending; (b) element structure; (c) wave plate under bending.
图 2 宽带偏振转换物理原理的计算验证 (a), (b) 入射光频率为0.55 THz时, 不同入射角下计算的结构上方0.5 μm 处Ez分量的(a)强度分布图和(b)相位分布图; (c) 计算的不同入射角度下的辐射场项
$|{{\boldsymbol{E}}_{{\text{rad}}}}|$ 和共轭关系项$\left| - {{\text{e}}^{{\text{i}}k\tfrac{d}{{\cos \theta }}}} + {{\text{e}}^{ - {\text{i}}k\tfrac{d}{{\cos \theta }}}}\right|$ 随频率的变化; (d) 计算的不同入射角度下 |Ey'|/|Ex'| 随频率的变化Figure 2. Theoretical verification of the physical principle of broadband polarization conversion: Calculated (a) intensity distribution maps and (b) phase distribution diagrams of Ez component at 0.5 μm above the structure at 0.55 THz with incident angles of 15°, 30°, 45°, 60°; (c) calculated radiation field term
$|{{\boldsymbol{E}}_{{\text{rad}}}}|$ and the conjugate term$\left| - {{\text{e}}^{{\text{i}}k\tfrac{d}{{\cos \theta }}}} + {{\rm e} ^{ - {\text{i}}k\tfrac{d}{{\cos \theta }}}}\right|$ at different incident angles and frequencies; (d) calculated |Ey'|/|Ex'| with different incident angles and frequencies.
图 3 弯曲情况下出射波偏振转换的稳定性 (a), (b) 计算的在不同入射角度下的(a) |Ey'|/|Ex'|和(b) φy' – φx'; (c), (d) 计算的(c) |Ey'|/|Ex'|和(d) φy' – φx'随入射角和频率的变化关系
Figure 3. Stability analysis on output polarization states of terahertz waves under bending: Calculated (a) |Ey'|/|Ex'| and (b) φy' – φx' at some different incident angles; calculated (c) |Ey'|/|Ex'| and (d) φy' – φx' at different incident angles and frequencies.
图 4 L型金属结构尺寸对偏振调控的影响 (a), (b) 计算的在不同L型结构臂长l下的(a) |Ey'|/|Ex'|和(b) φy' – φx'; (c), (d) 计算的在不同L型结构宽度w下的(c) |Ey'|/|Ex'|和(d) φy' – φx'
Figure 4. Effect of L-shaped structure size on polarization control: Calculated (a) |Ey'|/|Ex'| and (b) φy' – φx' with different l; calculated (c) |Ey'|/|Ex'| and (d) φy' – φx' with different w.
图 5 未弯曲时柔性太赫兹波片出射波偏振态的实验与计算结果 (a) 样品光学照片(白标尺为100 μm); (b) 太赫兹时域光谱仪测量原理图; 线偏振片透光轴相对y' 轴 (c) 45°和 (d) –45°时测得的电场时域谱; 实验测得的随频率变化的(e) |Ey'|/|Ex'|和(f) φy' – φx'; 计算的随频率变化的(g) |Ey'|/|Ex'|和(h) φy' – φx'
Figure 5. Measured and calculated polarization states of output waves of wave plate without bending: (a) Optical photograph of sample, white scale bar is 100 μm; (b) schematic diagram of terahertz time-domain spectrometer; the time-domain spectrum of electric field measured with transmission axis of linear polarizer relative to y' axis (c) 45° and (d) –45°; measured (e) |Ey'|/|Ex'| and (f) φy' – φx' as a function of frequency; calculated (g) |Ey'|/|Ex'| and (h) φy' – φx' as a function of frequency.
图 6 不同弯曲程度下的太赫兹波时域谱测量结果 (a) 不同弯曲程度下拍摄的样品照片; (b) 曲率半径与相关结构参数的关系式示意图; 不同曲率半径下测量的太赫兹时域谱, 其中(c) r = 0.71 m, (d) r = 0.36 m, (e) r = 0.24 m, (f) r = 0.18 m, (g) r = 0.14 m
Figure 6. Measured time domain results at different bending states: (a) Photographs at different bending states; (b) schematic diagram of the relationship between the radius of curvature and relevant structural parameters; the measured time-domain spectra under different curvature radius of (c) r = 0.71 m, (d) r = 0.36 m, (e) r = 0.24 m, (f) r = 0.18 m, (g) r = 0.14 m.
图 7 (a)—(e) 不同曲率半径下测量到的|Ey'|/|Ex'|, 其中(a) r = 0.71 m, (b) r = 0.36 m, (c) r = 0.24 m, (d) r = 0.18 m, (e) r = 0.14 m; (f) 在0.54 THz处|Ey'|/|Ex'| 随弯曲曲率半径的变化关系
Figure 7. Measured |Ey'|/|Ex'| under different curvature radius: (a) r = 0.71 m; (b) r = 0.36 m; (c) r = 0.24 m; (d) r = 0.18 m; (e) r = 0.14 m. (f) Relationship between |Ey'|/|Ex'| and curvature radius at 0.54 THz.
图 8 不同曲率半径下测量到的 φy' – φx', 其中(a) r = 0.71 m, (b) r = 0.36 m, (c) r = 0.24 m, (d) r = 0.18 m, (e) r = 0.14 m; (f) 在0.54 THz处 φy' – φx' 随弯曲曲率半径的变化关系
Figure 8. Measured φy' – φx' under different curvature radius: (a) r = 0.71 m; (b) r = 0.36 m; (c) r = 0.24 m; (d) r = 0.18 m; (e) r = 0.14 m. (f) Relationship between φy' – φx' and curvature radius at 0.54 THz.
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[1] Yang P, Xiao Y, Xiao M, Li S 2019 IEEE Network 33 70
[2] Giordani M, Polese M, Mezzavilla M, Rangan S, Zorzi M 2020 IEEE Commun. Mag. 58 55
Google Scholar
[3] Chowdhury M Z, Shahjalal M, Ahmed S, Jang Y M 2020 IEEE Open J. Commun. Soc. 1 957
Google Scholar
[4] Akyildiz I F, Kak A, Nie S 2020 IEEE Access 8 133995
Google Scholar
[5] Imoize A L, Adedeji O, Tandiya N, Shetty S 2021 Sensors 21 1709
Google Scholar
[6] Ferguson B, Zhang X C 2002 Nat. Mater. 1 26
Google Scholar
[7] Tonouchi M 2007 Nat. Photonics 1 97
Google Scholar
[8] Nagatsuma T, Ducournau G, Renaud C C 2016 Nat. Photonics 10 371
Google Scholar
[9] Yang Y, Yamagami Y, Yu X, Pitchappa P, Webber J, Zhang B, Fujita M, Nagatsuma T, Singh R 2020 Nat. Photonics 14 446
Google Scholar
[10] Yang F, Pitchappa P, Wang N 2022 Micromachines 13 285
Google Scholar
[11] Martinez-Lopez L, Rodriguez-Cuevas J, Martinez-Lopez J I, Martynyuk A E 2014 IEEE Antennas Wirel. Propag. Lett. 13 153
Google Scholar
[12] Hossain T M, Mirza H, Soh P J, Jamlos M F, Sheikh R A, Al-Hadi A A, Akkaraekthalin P 2019 IEEE Access 7 149262
Google Scholar
[13] Lokman A H, Soh P J, Azemi S N, et al. 2017 Int. J. Antennas Propag. 2017 4940656
[14] Paracha K N, Rahim S K A, Soh P J, Khalily M 2019 IEEE Access 7 56694
Google Scholar
[15] Li J, Zhang L, Zhang M, Su H, Li I L, Ruan S, Liang H 2020 Adv. Opt. Mater. 8 2000068
Google Scholar
[16] Sayem A S M, Simorangkir R B V B, Esselle K P, Lalbakhsh A, Gawade D R, O'Flynn B, Buckley J L 2022 Sensors 22 1276
Google Scholar
[17] Wen D D, Yue F Y, Liu W W, Chen S Q, Chen X Z 2018 Adv. Opt. Mater. 6 1800348
Google Scholar
[18] Niu X X, Hu X Y, Chu S S, Gong Q H 2018 Adv. Opt. Mater. 6 1701292
Google Scholar
[19] Che Y H, Wang X T, Song Q H, Zhu Y B, Xiao S M 2020 Nanophotonics 9 4407
Google Scholar
[20] Fan R H, Xiong B, Peng R W, Wang M 2020 Adv. Mater. 32 1904646
[21] Grady N K, Heyes J E, Chowdhury D R, Zeng Y, Reiten M T, Azad A K, Taylor A J, Dalvit D A R, Chen H T 2013 Science 340 1304
Google Scholar
[22] Fan R H, Zhou Y, Ren X P, Peng R W, Jiang S C, Xu D H, Xiong X, Huang X R, Wang M 2015 Adv. Mater. 27 1201
Google Scholar
[23] 杨磊, 范飞, 陈猛, 张选洲, 常胜江 2016 65 080702
Google Scholar
Yang L, Fan F, Chen M, Zhang X Z, Chang S J 2016 Acta Phys. Sin. 65 080702
Google Scholar
[24] 付亚男, 张新群, 赵国忠, 李永花, 于佳怡 2017 66 180701
Google Scholar
Fu Y N, Zhang X Q, Zhao G Z, Li Y H, Yu J Y 2017 Acta Phys. Sin. 66 180701
Google Scholar
[25] Cheng Y, Zhu X, Li J, Chen F, Luo H, Wu L 2021 Physica E 134 114893
Google Scholar
[26] Li S X, Yang Z Y, Wang J, Zhao M 2011 J. Opt. Soc. Am. A 28 19
Google Scholar
[27] Yu Y, Yang Z Y, Zhao M, Lu P X 2011 J. Opt. 13 055104
Google Scholar
[28] Pan W, Ren X, Chen Q, Wang X 2019 Optoelectron. Lett. 15 352
Google Scholar
[29] Li Z, Pan J, Hu H, Zhu H 2022 Adv. Electron. Mater. 8 2100978
Google Scholar
[30] Zhang S, Zhou J, Park Y S, Rho J, Singh R, Nam S, Azad A K, Chen H T, Yin X, Taylor A J, Zhang X 2012 Nat. Commun. 3 942
Google Scholar
[31] Wang D, Zhang L, Gu Y, Mehmood M Q, Gong Y, Srivastava A, Jian L, Venkatesan T, Qiu C W, Hong M 2015 Sci. Rep. 5 15020
Google Scholar
[32] Vasić B, Zografopoulos D C, Isić G, Beccherelli R, Gajić R 2017 Nanotechnology 28 124002
Google Scholar
[33] Fu Y, Wang Y, Yang G, Qiao Q, Liu Y 2021 Opt. Express 29 13373
Google Scholar
[34] Cong L Q, Xu N N, Gu J Q, Singh R, Han J G, Zhang W L 2014 Laser Photonics Rev. 8 626
Google Scholar
[35] Sonsilphong A, Gutruf P, Withayachumnankul W, Abbott D, Bhaskaran M, Sriram S, Wongkasem N 2015 J. Opt. 17 085101
Google Scholar
[36] Baena J D, Bonache J, Martín F, Sillero R M, Falcone F, Lopetegi T, Laso M A G, García-García J, Gil I, Portillo M F, Sorolla M 2005 IEEE Trans. Microwave Theory Tech. 53 1451
Google Scholar
[37] Jiang S C, Xiong X, Sarriugarte P, Jiang S W, Yin X B, Wang Y, Peng R W, Wu D, Hillenbrand R, Zhang X, Wang M 2013 Phys. Rev. B 88 161104
Google Scholar
[38] Jiang S C, Xiong X, Hu Y S, Hu Y H, Ma G B, Peng R W, Sun C, Wang M 2014 Phys. Rev. X 4 021026
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