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超表面由于具备独特的电磁响应特性, 在微波、太赫兹以及光学领域的应用十分广泛. 在电磁超表面中构建连续域束缚态(bound states in the continuum, BIC)模式谐振可以产生尖锐的谐振透射峰, 因此BIC被广泛用于设计具有高品质因子谐振的超表面. 本文实验研究了一种支持准 BIC (quasi-BIC, q-BIC)谐振的新型金属太赫兹超表面, 通过设计两组金属开口谐振环(split ring resonators, SRRs)的结构参数来调节各自主导的谐振的工作频率, 使不同模式谐振之间产生耦合, 形成q-BIC模式谐振. 并利用电磁场分布及其散射功率的多极分解的计算结果证明了不同模式的共振机制. 在入射电磁波分别沿x, y偏振时, 通过Jaynes-Cummings模型计算了两模式之间的归一化耦合强度比, 分别为0.54% (x偏振)与4.42% (y偏振), 解释了不同谐振模式的工作频率随SRRs器件结构参数改变而变化的规律.Metasurfaces have found extensive applications in microwave, terahertz, and optical range, serving different purposes such as filters, sensors, slow light devices, and nonlinear devices due to their distinctive electromagnetic response characteristics. Recent development requires metasurface devices to exhibit enhanced monochromaticity and stronger light interaction. Consequently, there is a growing interest in designing metasurfaces with high-quality factor (Q-factor) resonances, considering their crucial role in achieving sharp resonances through constructing bound states in the continuum (BIC) mode. The utilization of BIC has emerged as a prominent method of designing metasurfaces with high Q-factor resonances. Due to the fact that the changes in the structural parameters of metasurfaces can simultaneously affect the resonance of two components of q-BICs, it is difficult to achieve on-demand design of operating frequency, bandwidth, and Q-factor. In this work, we investigate a novel THz metasurfaces supporting q-BIC resonance. We optimize the geometric parameters of two split ring resonators (SRRs) to tailor the operating frequencies of intrinsic resonance, and tune the coupling between different resonance modes to form the q-BIC mode resonance. The dominant modes are demonstrated by the results of multipolar decomposition calculations of the electromagnetic field distributions and scattered power at different resonant operating frequencies. In x-polarized and y-polarized incident electromagnetic wave, the normalized coupling strength ratio between the two modes are calculated by Jaynes-Cummings model to be 0.54% (x-polarized) and 4.42% (y-polarized) respectively, which explains the law that the resonant frequency of different modes changes with the structural parameters of SRRs device. In order to analyze the refractive index sensing capabilities of our designed metasurfaces under the incident electromagnetic waves with different polarizations, we investigate the variations of the transmitted spectrum of the metasurface with refractive index of matters. The calculated results show that the sensitivity of the metasurface is 151 GHz/RIU when the incident wave is y-polarized and 108 GHz/RIU when the incident wave is x-polarized. We realize the effective control of the operating frequency, bandwidth, and Q-factor of the q-BIC mode resonance in the transmission spectrum of the metasurface, which provides a new idea for the practical designing of terahertz metasurfaces with high Q-factor.
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Keywords:
- metasurfaces /
- multipole decomposition /
- bound states in continuum /
- terahertz
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图 1 (a) 金属太赫兹超表面阵列单元几何结构示意图; (b) 超表面子单元; (c) 超表面样品光学照片; (d) 超表面显微照片
Fig. 1. (a) Geometry diagram of metal THz metasurface array cells; (b) metasurface subunits; (c) metasurface sample photographs; (d) metasurface micrographs.
图 2 入射电磁波沿y偏振 (a) q-BIC模式谐振时的透射谱(d = 10 μm), Mode 1的电场分布(c)和表面电流分布(f); Mode 2的电场分布(d)和表面电流分布(g); (b) BIC模式谐振时的透射谱(d = 30 μm), BIC的电场分布(e)和表面电流分布(h)
Fig. 2. y-polarized: (a) Transmission spectrum at q-BIC mode resonance (d = 10 μm), electric field distribution in Mode 1 (c) and surface current distribution (f); the electric field distribution (d) and surface current distribution (g) of Mode 2; (b) transmission spectrum at BIC mode resonance (d = 30 μm), electric field distribution (e) and surface current distribution (h) of BIC.
图 3 入射电磁波沿x偏振 (a) q-BIC 模式谐振时的透射谱 (n=20 μm), Mode 3 处的电场分布(c)和表面电流分布(f), Mode 4处的电场分布(d)和表面电流分布(g); (b) BIC模式谐振时的透射谱(n=14.6 μm); Mode BIC处的电场分布(e)和表面电流分布(h)
Fig. 3. x-polarized: (a) Transmission spectrum at q-BIC mode resonance (n=20 μm), electric field distribution (c) and surface current distribution (f) at Mode 3, electric field distribution (d) and surface current distribution (g) at Mode 4; (b) transmission spectrum at BIC mode resonance (n = 14.6 μm); electric field distribution (e) and surface current distribution (h) at Mode BIC.
图 4 当入射电磁波沿y (a), x (b)偏振时的多极分解结果. MQ, EQ, TD, MD和ED分别表示磁四极子、电四极子、环偶极子、磁偶极子和电偶极子
Fig. 4. Multipole decomposition results during irradiation of y-polarized (a) and x-polarized (b) waves: MQ, EQ, TD, MD and ED represent magnetic quadrupole, electric quadrupole, ring dipole, magnetic dipole, and electric dipole, respectively.
图 5 y-偏振: 透射谱 (a)和q-BIC谐振透射峰的Q-因子(b)与参数d的关系; x-偏振: 透射谱(c)和q-BIC谐振透射峰的Q-因子(d)随着参数n的关系
Fig. 5. y-polarization: Relationship of the transmission spectrum (a) and the Q-factorof the q-BIC resonant transmission peak (b) to parameter d; x-polarization: relationship of the transmission spectrum (c) and the Q-factor of and the q-BIC resonant transmission peak (d) to the parameter n.
图 6 设待测物介电常数ε=2, 待测物厚度对超表面透射光谱的影响 (a)入射电磁波沿y方向偏振; (b)入射电磁波沿x方向偏振
Fig. 6. The influence of the thickness of the measured object on the transmission spectrum of the metasurface with the dielectric constant of the object to be measured ε = 2: (a) The incident electromagnetic wave is polarized along the y direction; (b) the incident electromagnetic wave is polarized along the x direction.
图 7 y-偏振 (a) q-BIC谐振透射峰与待测物介电常数ε的关系(损耗角正切tanδ = 0); (b) q-BIC谐振透射峰与待测物tanδ的关系 (介电常数ε = 1). x-偏振 (c) q-BIC谐振透射峰与待测物介电常数ε的关系(损耗角正切tanδ = 0); (d) q-BIC谐振透射峰与待测物tanδ的关系(介电常数ε = 1)
Fig. 7. y-polarization: (a) Relationship between transmission peak of the q-BIC resonance and the dielectric constant of the subject to be measured ε (loss angle tanδ = 0); (b) relationship between q-BIC resonance transmission peak and tan δ to be measured (dielectric constant ε = 1). x-polarization: (c) Relationship between transmission peak of the q-BIC resonance and the dielectric constant of the subject to be measured ε (loss angle tanδ = 0); (d) relationship between q-BIC resonance transmission peak and tan δ to be measured (dielectric constant ε = 1).
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[1] Hsu C W, Zhen B, Stone A D, Joannopoulos J D, Soljačić M 2016 Nat. Rev. Mater. 1 16048
Google Scholar
[2] von Neumann J, Wigner E P 1929 Physics Z 30 467
[3] Kaelberer T, Fedotov V A, Papasimakis N, Tsai D P, Zheludev N I 2010 Science 330 1510
Google Scholar
[4] Plotnik Y, Peleg O, Dreisow F, Heinrich M, Nolte S, Szameit A, Segev M 2011 Phys. Rev. Lett. 107 183901
Google Scholar
[5] Hsu C W, Zhen B, Lee J, Chua S L, Johnson S G, Joannopoulos J D, Soljacic M 2013 Nature 499 188
Google Scholar
[6] Urseel F 1997 Phys. Eng. Sci. 435 575
[7] Porter R, Evans D V 2005 Wave Motion 43 29
Google Scholar
[8] Xiao Y X, Ma G, Zhang Z Q, Chan C T 2017 Phys. Rev. Lett. 118 166803
Google Scholar
[9] Retzler C H 2001 Appl. Ocean Res. 23 249
Google Scholar
[10] Cobelli P J, Pagneux V, Maurel A, Petitjeans P 2009 Europhys. Lett. 88 20006
Google Scholar
[11] Cobelli P J, Pagneux V, Maurel A, Petitjeans P 2011 J. Fluid Mech. 666 445
Google Scholar
[12] Fang C, Yang Q, Yuan Q, Gan X, Zhao J, Shao Y, Liu Y, Han G, Hao Y 2021 Opto-Electron. Adv. 4 200030
Google Scholar
[13] Friedrich H, Wintgen D 1985 Phys. Rev. A 32 3231
Google Scholar
[14] Feshbach H 1958 Ann. Phys. 5 357
Google Scholar
[15] Tittl A, Leitis A, Liu M, Yesilkoy F, Choi D Y, Neshev D N, Kivshar Y S, Altug H 2018 Science 360 1105
Google Scholar
[16] Jahani Y, Arvelo E R, Yesilkoy F, Koshelev K, Cianciaruso C, De Palma M, Kivshar Y, Altug H 2021 Nat. Commun. 12 3246
Google Scholar
[17] Chen X, Fan W 2019 Opt. Lett. 44 5876
Google Scholar
[18] Srivastava Y K, Ako T R, Gupta M, Bhaskaran M, Sriram S, Singh R, T 2019 Appl. Phys. Lett. 115 151105
Google Scholar
[19] Wang Y L, Han Z H, Du Y, Qin J Y 2021 Nanophotonics 10 1295
Google Scholar
[20] Yue L S, Wang Y, Cui Z J, Zhang X J, Zhu Y Q, Zhang X, Chen S G, Wang X M, Zhang K 2021 Opt. Express 29 13563
Google Scholar
[21] Zhang Y B, Liu W W, Li Z C, Li Z, Cheng H, Chen S, Tian J G 2018 Opt. Lett. 43 1842
Google Scholar
[22] Huo Y Y, Zhang X, Yan M, Sun K, Jiang S Z, Ning T Y, Zhao L N 2022 Opt. Express 30 19030
Google Scholar
[23] Foley J M, Young S M, Phillips J D 2014 Phys. Rev. B 89 165111
Google Scholar
[24] Chen S S, Zhang W X, Yang B, Wu T, Zhang X D 2019 Sci. Rep. 9 5551
Google Scholar
[25] 杜芊, 陈溢杭 2021 物理学报 70 154206
Google Scholar
Du Q, Chen Y H 2021 Acta Phys. Sin. 70 154206
Google Scholar
[26] Zhou C B, Huang L J, Jin R, Xu L, Li G H, Mohsen R, Chan X S, Lu W 2023 Laser Photonics Rev. 17 2200564
Google Scholar
[27] Qin H Y, Su Z P, Liu M Q, Zeng Y X, Tang M C, Li M Y, Shi Y Z, Huang W, Qiu C W, Song Q H 2023 Light Sci. Appl. 12 66
Google Scholar
[28] Li H J, Zhou H M, Wei G G, Xu H S, Qin M, Liu J Q, Wu F 2023 Nanoscale 15 6636
Google Scholar
[29] Romano S, Zito G, Torino S 2018 Photonics Res. 6 726
Google Scholar
[30] Zhou Y, Zheng H Y, Kravchenko I I, Valentine J 2020 Nat. Photonics 14 316
Google Scholar
[31] Azzam S I, Shalaev V M, Boltasseva A, Kildishev A V 2018 Phys. Rev. Lett. 121 253901
Google Scholar
[32] Savinov V, Fedotov V A, Zheludev N I 2014 Phys. Rev. B 89 205112
Google Scholar
[33] Forn-Díaz P, Lamata L, Rico E, Kono J, Solano E 2019 Rev. Mod. Phys. 91 025005
Google Scholar
[34] Singh R, Cao W, Al-Naib I, Cong L, Withayachumnankul W, Zhang W 2014 Appl. Phys. Lett. 105 171101
Google Scholar
[35] Ho L, Pepper M, Taday P 2008 Nat. Photonics 2 541
Google Scholar
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