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Unidirectional scattering of various plasmonic nanoantennas has been extensively studied, giving birth to applications such as in optical sensors, solar cells, spectroscopy and light-emitting devices. The directional scattering of magnetic nanoantenna is still unexplored, though it is beneficial to artificial magnetism applications including metamaterials, cloaking and nonlinear optical resonance. In this work, we numerically investigate the far-field scattering properties of the Si ring-Au split ring nanoantenna (Si R-Au SRN) excited by a tightly focused azimuthally polarized beam (APB) through using the finite-difference time-domain (FDTD) method. The results show that the magnetic resonant peaks with different widths can be deterministically excited in Si ring and Au split ring by tightly focusing APB. Owing to the plasmon hybridization effect, the two magnetic resonant modes form antibonding mode and bonding mode in the Si R-Au SRN. At a wavelength of λ=1064 nm, the destructive interference between the antibonding mode and bonding mode of nanostructure results in unidirectional far-field scattering in the transverse plane, which is affected dramatically by changes of geometrical parameters. Furthermore, the directional scattering of a dipole source is realized by the designed nanostructure, and its scattering directionality is superior to that excited with APB. Our work provides a flexible way to control the far-field scattering of nano-photon structures. We expect that this study can provide an avenue to the nano-light sources and optical sensors.
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Keywords:
- directional scattering /
- magnetic dipole mode /
- plasmon hybridization /
- split ring resonator nanostructure
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[4] Ahmed A, Pang Y, Hajisalem G, Gordon R 2012 Int. J. Opt. 2012 729138
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[6] Atwater H A, Polman A 2010 Nat. Mater. 9 205
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[8] Bharadwaj P, Deutsch B, Novotny L 2009 Adv. Opt. Photonics 1 438
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[11] Guo R, Decker M, Setzpfandt F, Staude I, Neshev D N, Kivshar Y S 2015 Nano Lett. 15 3324
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Google Scholar
[22] Bag A, Neugebauer M, Wozniak P, Leuchs G, Banzer P 2018 Phys. Rev. Lett. 121 193902
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[23] Bag A, Neugebauer M, Mick U, Christiansen S, Schulz S A, Banzer P 2020 Nat. Commun. 11 2915
Google Scholar
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Google Scholar
[25] 张富利, 赵晓鹏 2007 56 4661
Google Scholar
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Google Scholar
[26] Liu H, Genov D A, Wu D M, Liu Y M, Liu Z W, Sun C, Zhu S N, Zhang X 2007 Phys. Rev. B 76 073101
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Google Scholar
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Google Scholar
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[34] Youngworth K, Brown T 2000 Opt. Express 7 77
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 (a)三维和(b)二维直角坐标系中硅环-开口金环纳米天线结构及几何参数示意图
Figure 1. Schematic diagrams of Si R-Au SR nanoantenna with the geometrical parameters in (a) three-dimensional (3D) and (b) two-dimensional (2D) Cartesian coordinate systems.
图 2 紧聚焦角向矢量光在焦平面上(z = 0 nm)的电场和磁场分布 (a)电场(黑色箭头表示电场的偏振分布); (b)总磁场; (c)磁场面内分量(|Ht| = (|Hx|2+|Hy|2)1/2); (d)磁场纵向分量. 白色虚线区域给出焦场中纳米结构的所在位置
Figure 2. Distributions of electric and magnetic fields at focal plane for tightly focused APB: (a) Electric field; (b) magnetic field; (c) in-plane component of magnetic field; (d) longitudinal component of magnetic field. The black arrows represent the distribution of polarization and white dot line regions denote the nano-structure.
图 3 紧聚焦角向矢量光激发下的(a)硅纳米环和(d)开口金纳米环的散射光谱, (b)硅纳米环和(e)开口金纳米环上表面(z = 50 nm)的磁场纵向分量(Hz)分布(箭头表示电流密度分布), 以及(c)硅纳米环及(f)开口金纳米环的远场散射分布
Figure 3. Scattering spectra of (a) Si ring and (d) Au split ring excited by tightly focused APB, magnetic field distributions of the upper surface (z = 50 nm) for (b) Si ring and (e) Au split ring at their resonant peaks (the current density distributions denoted by the black arrows), and far-field scattering patterns of (c) Si ring and (f) Au split ring, respectively.
图 4 (a) 硅环-开口金环纳米结构的模拟(红线)和拟合的散射谱(蓝色虚线); (b) 波长790, (c) 1200和(d) 1064 nm处, 结构上表面(z = 50 nm)的磁场纵向分量(Hz)分布(箭头表示电流密度分布)
Figure 4. (a) Calculated (red line) and fitted scattering spectra (blue dashed line) of the nanostructure. Magnetic field distributions of upper surface (z = 50 nm) for nano-structure at (b) 790, (c) 1200 and (d) 1064 nm, respectively (the white or black arrows represent the current density distributions).
图 5 紧聚焦角向光束激发下硅环-开口金环纳米结构在 (a)反键模式、(b)成键模式处, 以及(c)模式间的峰谷(λ = 1064 nm)的三维远场散射分布
Figure 5. 3D far-field scattering patterns of Si R-Au SRN at (a) the anti-bonding mode, (b) the bonding mode, and (c) λ = 1064 nm.
图 6 硅环-开口金环纳米结构反键与成键模式的(a)振幅比和(b)相位差随波长的变化
Figure 6. (a) Amplitude ratio and (b) phase difference of the two modes as a function of the wavelength for the Si R-Au SRN.
图 7 硅环-开口金环纳米结构在λ = 1064 nm的紧聚焦角向矢量光激发下, (a)硅环宽度w1和(b)两环心间距d取不同值时, xy平面上的二维远场散射分布. 纳米结构的反键和成键模式的振幅比|C1|/|C2|和相位差Δϕ随(c)硅环宽度w1和(d)两环心间距d的变化曲线
Figure 7. 2D far-field patterns on xy plane for Si R-Au SRN with different values of (a) the width of Si ring and (b) the distance between the centers of Si and Au rings. Changes of amplitude ratio and phase difference of the anti-bonging and bonding modes with respect to (c) the width of Si ring and (d) the distance between the centers of the two rings.
图 8 (a)电偶极子光源的激发配置图; (b)偶极光源及其激发下硅环-开口金环纳米结构在xy面上的二维远场发射(散射)分布; (c), (d)偶极光源和角向矢量光激发下纳米结构在xy和xz面的二维远场散射分布
Figure 8. (a) Schematic diagram of the Si R-Au SRN excited by an electric dipole; (b) 2D far-field patterns on xy plane of the dipole source and the Si R-Au SRN excited with the dipole source; (c), (d) 2D far-field patterns on xy and xz planes of the Si R-Au SRN excited by the dipole source and APB, respectively.
表 1 紧聚焦角向矢量光激发下硅环-开口金环纳米结构散射谱的耦合振子模型拟合参数
Table 1. Fitting coefficients of coupled-oscillator model for scattering spectrum of Si R-Au SRN excited by tightly focused APB
参数 ω1/eV ω2/eV γ1/eV γ2/eV η1/eV η2/eV g/eV E0/eV I0/arb.units 数值 1.5469 1.0445 0.0860 0.0651 0.0378 0.0103 0.0647 2.6384 0 
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[1] Engheta N 2011 Science 334 317
Google Scholar
[2] Taminiau T H, Stefani F D, Segerink F B, van Hulst N F 2008 Nat. Photonics 2 234
Google Scholar
[3] Ahmed A, Gordon R 2012 Nano Lett. 12 2625
Google Scholar
[4] Ahmed A, Pang Y, Hajisalem G, Gordon R 2012 Int. J. Opt. 2012 729138
[5] Ou Y C, Webb J A, Faley S, Shae D, Talbert E M, Lin S, Cutright C C, Wilson J T, Bellan L M, Bardhan R 2016 ACS Omega 1 234
Google Scholar
[6] Atwater H A, Polman A 2010 Nat. Mater. 9 205
Google Scholar
[7] Anker J N, Hall W P, Lyandres O, Shah N C, Zhao J, Van Duyne R P 2008 Nat. Mater. 7 442
Google Scholar
[8] Bharadwaj P, Deutsch B, Novotny L 2009 Adv. Opt. Photonics 1 438
Google Scholar
[9] 蒋双凤, 孔凡敏, 李康, 高辉 2011 60 045203
Google Scholar
Jiang S F, Kong F M, Li K, Gao H 2011 Acta Phys. Sin. 60 045203
Google Scholar
[10] Maksymov I S, Staude I, Miroshnichenko A E, Kivshar Y S 2012 Nanophotonics 1 65
Google Scholar
[11] Guo R, Decker M, Setzpfandt F, Staude I, Neshev D N, Kivshar Y S 2015 Nano Lett. 15 3324
Google Scholar
[12] Curto A G, Volpe G, Taminiau T H, Kreuzer M P, Quidant R, van Hulst N F 2010 Science 329 930
Google Scholar
[13] Vercruysse D, Sonnefraud Y, Verellen N, Fuchs F B, Di Martino G, Lagae L, Moshchalkov V V, Maier S A, Van Dorpe P 2013 Nano Lett. 13 3843
Google Scholar
[14] Hancu I M, Curto A G, Castro-Lopez M, Kuttge M, van Hulst N F 2014 Nano Lett. 14 166
Google Scholar
[15] Kerker M, Wang D S, Giles C L 1983 J. Opt. Soc. Am. 73 765
Google Scholar
[16] Geffrin J M, Garcia-Camara B, Gomez-Medina R, Albella P, Froufe-Perez L S, Eyraud C, Litman A, Vaillon R, Gonzalez F, Nieto-Vesperinas M, Saenz J J, Moreno F 2012 Nat. Commun. 3 1171
Google Scholar
[17] Fu Y H, Kuznetsov A I, Miroshnichenko A E, Yu Y F, Luk'yanchuk B 2013 Nat. Commun. 4 1527
Google Scholar
[18] Person S, Jain M, Lapin Z, Saenz J J, Wicks G, Novotny L 2013 Nano Lett. 13 1806
Google Scholar
[19] Ma C, Yan J, Huang Y, Yang G 2017 Adv. Opt. Mater. 5 1700761
Google Scholar
[20] Neugebauer M, Woźniak P, Bag A, Leuchs G, Banzer P 2016 Nat. Commun. 7 11286
Google Scholar
[21] Nechayev S, Eismann J S, Neugebauer M, Woźniak P, Bag A, Leuchs G, Banzer P 2019 Phys. Rev. A 99 041801
Google Scholar
[22] Bag A, Neugebauer M, Wozniak P, Leuchs G, Banzer P 2018 Phys. Rev. Lett. 121 193902
Google Scholar
[23] Bag A, Neugebauer M, Mick U, Christiansen S, Schulz S A, Banzer P 2020 Nat. Commun. 11 2915
Google Scholar
[24] Linden S, Enkrich C, Wegener M, Zhou J F, Koschny T, Soukoulis C M 2004 Science 306 1351
Google Scholar
[25] 张富利, 赵晓鹏 2007 56 4661
Google Scholar
Zhang F L, Zhao X P 2007 Acta Phys. Sin. 56 4661
Google Scholar
[26] Liu H, Genov D A, Wu D M, Liu Y M, Liu Z W, Sun C, Zhu S N, Zhang X 2007 Phys. Rev. B 76 073101
Google Scholar
[27] Guo H C, Liu N, Fu L W, Meyrath T P, Zentgraf T, Schweizer H, Giessen H 2007 Opt. Express 15 12095
Google Scholar
[28] Liu N, Kaiser S, Giessen H 2008 Adv. Mater. 20 4521
Google Scholar
[29] Yang Z J, Zhang Z S, Hao Z H, Wang Q Q 2012 Opt. Lett. 37 3675
Google Scholar
[30] Ye J, Kong Y, Liu C 2016 J. Phys. D:Appl. Phys. 49 205106
Google Scholar
[31] Zhang D, Xiang J, Liu H F, Deng F, Liu H Y, Ouyang M, Fan H H, Dai Q F 2017 Opt. Express 25 26704
Google Scholar
[32] Bao Y J, Hu Z J, Li Z W, Zhu X, Fang Z Y 2015 Small 11 2177
Google Scholar
[33] Shegai T, Chen S, Miljkovic V D, Zengin G, Johansson P, Kall M 2011 Nat. Commun. 2 481
Google Scholar
[34] Youngworth K, Brown T 2000 Opt. Express 7 77
Google Scholar
[35] Palik E D 1991 Handbook of Optical Constants of Solids (Boston: Academic Press)
[36] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
Google Scholar
[37] Woźniak P, Banzer P, Leuchs G 2015 Laser Photonics Rev. 9 231
Google Scholar
[38] Prodan E, Radloff C, Halas N J, Nordlander P 2003 Science 302 419
Google Scholar
[39] Lovera A, Gallinet B, Nordlander P, Martin O J 2013 ACS Nano 7 4527
Google Scholar
[40] Shang W Y, Xiao F J, Zhu W R, He H S, Premaratne M, Mei T, Zhao J L 2017 Sci. Rep. 7 1049
Google Scholar
[41] Yang Z J, Zhao Q, He J 2017 Opt. Express 25 15927
Google Scholar
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