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利用时域有限差分方法, 理论研究了由中间短棒和两侧长棒构成的对称金纳米棒三聚体结构的光学性质, 分析了结构参数和介电环境对其Fano共振特性的影响. 结果表明: 随着中间短棒长度、三棒整体尺寸或短棒两侧介质折射率的减小, Fano共振谷蓝移; 棒间距的增大同样导致Fano共振谷蓝移, 但边棒长度的变化对Fano共振谷位的影响较小; 同时, 随着纳米结构参数或介电环境的变化, Fano共振谷两侧共振峰强度发生改变, 共振对比度先增大后减小. 通过比较纳米结构截面的电磁场和电流密度矢量分布发现, 共振谷两侧光谱强度的变化源于结构参数或介电环境引起的等离激元共振模式的改变. 研究结果对基于Fano共振可控的纳米结构设计有一定的参考意义.A symmetrical gold nanorod trimer structure consisting of a short center nanorod and two long nanorods on both sides is proposed. The scattering spectra, electromagnetic field and current density vector distributions across the central cross section of the nanorod trimer are calculated by the finite difference time domain method, and the effects of structural parameters and dielectric environment on Fano resonance characteristics are theoretically investigated in detail. The results show that the Fano resonance can be generated mainly due to the interference between the bonding electric dipole mode in lower energy and the antibonding electric dipole mode or antiphase magnetic dipole mode in higher energy. The Fano dip is blue-shifted with the decrease in the short nanorod length, the size of whole trimer structure with constant displacement, or the refractive index of dielectric medium in the gaps between the central nanorod and two side nanorods; the resonance intensity on both sides of the Fano dip also changes. Meanwhile, the bonding mode on the red side of the Fano dip is gradually dominated by the electric dipole mode of two side nanorods, and the spectral intensity increases, while the antibonding mode on the blue side gradually evolves into the short nanorod-dominated antiphase magnetic dipole mode, and the spectral intensity becomes weaker. The increase in the inter-rod spacing also leads the Fano dip to be blue-shifted, and a similar change in the spectral intensity occurs on both sides of the Fano dip, due to the degeneration of bonding and antibonding modes caused by the decrease of near-field coupling between the short nanorod and two side nanorods, which finally degenerate into the electric dipole modes generated by the short nanorod or the two side nanorods, respectively. In addition, the Fano dip is insensitive to the change of the side nanorod length, but the relative resonance intensity on both sides of the Fano dip also changes. Furthermore, it is found that the spectral contrast ratio of the Fano resonance first increases and then decreases by varying the above-mentioned structural parameters or dielectric environment. These results are expected to be used for guiding the design of Fano controllable nanostructures and also for developing the applications of specific micro-nano photonics.
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Keywords:
- Fano resonance /
- surface plasmon polariton /
- nanorod /
- finite difference time domain
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图 1 对称金纳米棒三聚体结构的模型示意图
Fig. 1. Geometrical structure of the symmetric Au nanorod trimer structure.
图 2 金纳米棒三聚体的散射谱和吸收谱, 插图为在两个散射共振峰位971, 1319和共振谷1229 nm处的纳米结构截面电场和电流密度矢量分布
Fig. 2. Scattering and absorption spectra of a single gold nanorod trimer. Insets show the calculated electric field and current density vector distributions across the central cross section of the nanorod trimer at the indicated resonances.
图 3 金纳米棒三聚体的散射谱随中间短棒变化的关系, 插图为在指定频率处的纳米结构截面电磁场和电流密度矢量分布
Fig. 3. Scattering spectra of the nanorod trimer versus the length of center nanorod Li. Insets show the calculated electric field, magnetic field in the z-direction and current density vector distributions at the indicated resonances.
图 4 金纳米棒三聚体的散射谱随边棒变化的关系, 插图为在指定散射共振峰位处的纳米结构截面电磁场和电流密度矢量分布
Fig. 4. Scattering spectra of the nanorod trimer versus the length of side nanorod Lo. Insets show the calculated electric field, magnetic field in the z-direction and current density vector distributions at the indicated resonances.
图 5 金纳米棒三聚体的散射谱随三棒尺寸变化的关系, 插图为在指定散射共振峰位处的纳米结构截面电磁场和电流密度矢量分布
Fig. 5. Scattering spectra of the nanorod trimer versus the nanorod length with constant displacement ΔL = 100 nm. Insets show the calculated electric field, magnetic field in the z-direction and current density vector distributions at the indicated resonances.
图 6 金纳米棒三聚体的散射谱随棒间距变化的关系, 插图为在指定散射共振峰位处的纳米结构截面电场和电流密度矢量分布
Fig. 6. Scattering spectra of the nanorod trimer versus inter-rod spacing d. Insets show the calculated electric field and current density vector distributions at the indicated resonances.
图 7 当短棒与边棒的间隙内介电环境变化时, 金纳米棒三聚体的散射谱随介质折射率变化的关系, 插图为在两个散射共振峰位处的纳米结构截面电磁场和电流密度矢量分布
Fig. 7. Scattering spectra of the nanorod trimer with different media in the gaps between the center and side nanorods. Insets show the calculated electric field, magnetic field in the z-direction and current density vector distributions at the indicated resonances.
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[1] Zhang S P, Xu H X 2016 Nanoscale 8 13722
Google Scholar
[2] Biswas S, Duan J, Nepal D, Park K, Pachter R, Vaia R A 2013 Nano Lett. 13 6287
Google Scholar
[3] Artar A, Yanik A A, Altug H 2011 Nano Lett. 11 3694
Google Scholar
[4] Wu D, Liu C, Liu Y, Yu L, Yu Z, Chen L, Ma R, Ye H 2017 Opt. Lett. 42 450
Google Scholar
[5] Zhang J, Chen S, Wang J,Mu K, Fan C, Liang E, Ding P 2018 Sci. Rep. 8 740
Google Scholar
[6] Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S 2017 Nat. Photon. 11 543
Google Scholar
[7] Chen J, Gan F, Wang Y, Li G 2018 Adv. Opt. Mater. 6 1701152
Google Scholar
[8] Huang C Y, Chang H C 2019 IEEE Photon. J. 11 4800208
Google Scholar
[9] Li G Z, Hu H J, Wu L 2019 Phys. Chem. Chem. Phys. 21 7654
Google Scholar
[10] Wu C, Khanikaev A B, Shvets G 2011 Phys. Rev. Lett. 106 107403
Google Scholar
[11] Chang W S, Lassiter J B, Swanglap P, Sobhani H, Khatua S, Nordlander P, Halas N J, Link S 2012 Nano Lett. 12 4977
Google Scholar
[12] Yu Y, Xue W, Semenova E, Yvind K, Mork J 2017 Nat. Photon. 11 81
Google Scholar
[13] Hu H J, Zhang F W, Li G Z, Chen J Y, Li Q, Wu L J 2018 Photon. Res. 6 204
Google Scholar
[14] Yang Z J, Hao Z H, Lin H Q, Wang Q Q 2014 Nanoscale 6 4985
Google Scholar
[15] 黄运欢, 李璞 2015 物理学报 64 207301
Google Scholar
Huang Y H, Li P 2015 Acta Phys. Sin. 64 207301
Google Scholar
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Google Scholar
[17] Fu Y H, Zhang J B, Yu Y F, Lukyanchuk B 2012 ACS Nano 6 5130
Google Scholar
[18] Zhao W, Jiang Y 2015 Opt. Lett. 40 93
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[19] Yang Z J, Wang Q Q, Lin H Q 2013 Appl. Phys. Lett. 103 111115
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[20] Zhang S, Genov D A, Wang Y, Liu M, Zhang X 2008 Phys. Rev. Lett. 101 047401
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[21] Wang J, Liu X, Li L, He J, Fan C, Tian Y, Ding P, Chen D, Xue Q, Liang E 2013 J. Opt. 15 105003
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[22] Dong Z G, Liu H, Xu M X, Li Tao, Wang S M, Zhu S N, Zhang X 2010 Opt. Express 18 18229
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[23] Jin X R, Park J, Zheng H, Lee S, Lee Y, Rhee J Y, Kim K W, Cheong H S, Jang W H 2011 Opt. Express 19 21652
Google Scholar
[24] Bozhevolnyi S I, Evlyukhin A B, Pors A, Nielsen M G, Willatzen M, Albrektsen O 2011 New J. Phys. 13 023034
Google Scholar
[25] Yang Z J, Zhang Z S, Zhang L H, Li Q Q, Hao Z H, Wang Q Q 2011 Opt. Lett. 36 1542
Google Scholar
[26] Kai G, Zhang Y L, Qian C, Fung K H 2018 Opt. Express 26 11984
Google Scholar
[27] Liu G D, Zhai X, Wang L L, Wang B X, Lin Q, Shang X J 2016 Plasmonics 11 381
Google Scholar
[28] Liu S D, Leong E S P, Li G C, Hou Y, Deng J, Teng J H, Ong H C, Lei D Y 2016 ACS Nano 10 1442
Google Scholar
[29] Wang J, Fan C, He J, Ding P, Liang E, Xue Q 2013 Opt. Express 21 2236
Google Scholar
[30] Li G, Li Q, Xu L, Wu L 2015 Plasmonics 10 1401
Google Scholar
[31] 丛超, 吴大建, 刘晓峻 2011 物理学报 60 046102
Google Scholar
Cong C, Wu D J, Liu X J 2011 Acta Phys. Sin. 60 046102
Google Scholar
[32] Taflove A, Hagness S 2000 Computational Electrodynamics: the Finite-Difference Time-Domain Method (Vol. 2) (Boston: Artech House) pp75−85
[33] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
Google Scholar
[34] Halas N J, Lal S, Chang W S, Nordlander P 2011 Chem. Rev. 111 3913
Google Scholar
[35] Feng R, Qiu J, Liu L, Ding W, Chen L 2014 Opt. Express 22 A1713
Google Scholar
[36] Hu X, Huang Y, Yuan S, Liu Y, Jiao Z, Wang Y, Huang Q, Yu J, Xia J 2015 Plasmonics 10 1817
Google Scholar
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