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Periodic nanoparticle arrays with lower loss or high-quality (Q) factor resonances have made great advances in numerous applications. Such arrays can support narrow resonance modes by the hybridization of plasmonic-photonic modes, known as lattice plasmon modes (LPMs). The LPMs arise from the diffraction-induced coupling between localized surface plasmon resonances (LSPRs) of nanoparticles in symmetric or quasi-symmetric refractive index environment. To date, the great majority of researches have focused on the coupling of dipolar modes to in-plane orthogonal diffraction waves in nanoparticle arrays, resulting in dipolar lattice plasmon modes (DLPMs). However, there are few studies about quadrupolar lattice plasmon modes (QLPMs) for parallel coupling in symmetric environment, especially for high Q-factor QLPMs. In this work, we explore the sharp QLPMs of the silver nanodisk arrays by x-polarized light at normal incidence. In the first place, the scattering cross-section and near-field electric field distribution of single silver nanodisk indicate the existence of dipolar and quadrupolar LSPRs, thus, the optical responses of silver nanodisk arrays exhibit the peak-and-dip profiles of DLPMs and QLPMs at different wavelengths. Also, the electromagnetic field distributions confirm that the parallel propagating electric field introduces QLPM and results in electric field delocalization, while DLPM is existent in another way in periodic silver nanodisk arrays. Moreover, the position, linewidth and lineshape of the QLPM strongly depend on the role of lattice period. We enable these resonance modes to be selectively accessed and individually optimized by tuning lattice periods in the x- or y-direction. By changing the lattice period in the x-direction from 300 to 550 nm in steps of 50 nm, the dip of transmission intensity increases gradually, and when periods in the two directions are equal, the transmission dip exhibits a narrow-band QLPM resonance with a linewidth of 0.4 nm, corresponding quality factor is as high as Q = 1815 under the x-polarized light. In particular, by varying periods in the y-direction, the QLPM can also be manipulated in a range from an asymmetric Fano-like lineshape peak to a dip. The acquisition of these results may provide a design strategy for high-Q factor resonance in nanolaser, sensing, and nonlinear optics.
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Keywords:
- finite difference time domain method /
- quadrupolar lattice plasmon modes /
- quality factors /
- nanoparticles
[1] Wang D Q, Bourgeois M R, Guan J, Fumani A K, Schatz G C, Odom T W 2020 ACS Photonics 7 630
Google Scholar
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[4] Chowdhury M H, Ray K, Gray S K, Pond J, Lacowicz J R 2009 Anal. Chem. 81 1397
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[5] Castellanos G W, Bai P, Gómez Rivas J 2019 J. Appl. Phys. 125 213105
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[6] Humphrey A D, Barnes W L 2016 J. Opt. 18 035005
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[7] Khlopin D, Laux F, Wardley W P, Martin J, Wurtz G A, Plain J, Bonod N, Zayats A V, Dickson W, Gérard D 2017 J. Opt. Soc. Am. B: Opt. Phys. 34 691
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[8] Le-Van Q, Zoethout E, Geluk E J, Ramezani M, Berghuis M, Gómez Rivas J 2019 Adv. Opt. Mater. 7 1801451
Google Scholar
[9] Humphrey A D, Barnes W L 2014 Phys. Rev. B 90 075404
Google Scholar
[10] Zundel L, May A, Manjavacas A 2021 ACS Photonics 8 360
Google Scholar
[11] Bin-Alam M S, Reshef O, Mamchur Y, Alam M Z, Carlow G, Upham J, Sullivan B T, Ménard J-M, Huttunen M J, Boyd R W, Dolgaleva K 2021 Nat. Commun. 12 947
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[12] Hakala T K, Antti J M, Aaro I V, Guo R, Martikainen J P, Daskalakis K S, Rekola H T, Julku A, Törmä P 2018 Nat. Phys. 14 739
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[14] 张萌徕, 覃赵福, 陈卓 2021 70 054206
Google Scholar
Zhang M L, Qin Z F, Chen Z 2021 Acta Phys. Sin. 70 054206
Google Scholar
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Google Scholar
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Google Scholar
[18] Li R, Wang D Q, Guan J, Wang W J, Ao X Y, Schatz G C, Schaller R, Odom T W 2019 J. Opt. Soc. Am. B: Opt. Phys. 36 E104
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Google Scholar
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Google Scholar
[21] Liu S D, Yue P, Zhang S, Wang M S, Dai H W, Chen Y Q, Nie Z Q, Cui Y X, Han J B, Duan H G 2020 Adv. Opt. Mater. 8 1901109
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图 1 (a) 银纳米圆柱在均匀介电环境下的阵列结构示意图, 电场沿x方向的光场垂直入射到阵列表面; (b) 单个单元的结构示意图, 其中阵列在x与y方向的周期用
$ {P_x} $ 与$ {P_y} $ 表示, 圆柱高度、直径分别用h, d表示Figure 1. (a) A schematic diagram of silver nanodisk arrays in a symmetric medium environment under x-polarized light incidence; (b) oblique view of a unit cell of the proposed array structure.
${P_{ {x}}}$ ,$ {P_y} $ , h and d represent period in x and y directions, height and diameter of silver nanodisk arrays, respectively.
图 2 (a) 高度h = 100 nm, 直径d = 160 nm的单个银纳米粒子散射截面光谱; 插图为偶极与四偶极LSPRs在x-z平面对应的电场强度与方向(箭头)分布, 纳米圆柱的侧面轮廓用白色框表示, “+”与“–”符号表示正负电荷; (b) 银纳米圆柱阵列在x偏振光照射下的透射谱, 插图为QLPM的放大图; (c) 银纳米圆柱阵列极化率倒数(
$ 1/\alpha $ )与格点和(S), 黑色虚线表示瑞利异常衍射, 粉色虚线表示DLPM共振波长Figure 2. (a) Scattering cross section for single silver nanoparticle with h = 100 nm and d = 160 nm. The inset shows the electric field intensity and direction (in arrow) distribution corresponding to the dipolar and the quadrupolar LSPR modes. The outline of the nanoparticle is represented by a white box, and the sign “+” and “–” indicate positive and negative charges; (b) the transmission spectra of DLPM and QLPM of the silver nanodisks array under the x-polarized light. Inset: zoom-in of the transmission dip for the QLPM; (c) the real part of the reciprocal polarizability (
$ 1/\alpha $ ) and the lattice sum (S) for the silver nanodisk arrays. The black and pink dashed lines represent the (0, ± 1) RAs and resonance wavelength, respectively.
图 3 波长在(a), (c) 725.9 nm与(b), (d) 801 nm处QLPM与DLPM电场强度分布
Figure 3. The electric field intensity distribution of QLPM for (a), (c) corresponding to resonance wavelength at 725.9 nm and DLPM for (b), (d) corresponding to resonance wavelength at 801 nm.
图 4 当其他所有参数保持不变时 (a), (b) 分别是x与y方向上不同周期的阵列透射谱; (c), (d)分别是相对应的FWHMs与品质因子
Figure 4. (a), (b) Transmission spectra, and (c), (d) FWHMs and quality factors for different lattice periods while all others parameters are fixed.
图 5 周期
$ {P_x} $ =$ {P_{\text{y}}} $ = 500 nm保持不变, 对于银纳米圆柱高度(a) h = 50, (b) 100 与 (c) 150 nm下直径d从50 nm变化到200 nm时阵列的透射谱. 高度h = 100 nm保持不变, 对于圆柱直径(d) d = 80, (e) 100 与(f) 120 nm下, 银纳米圆柱阵列周期P从350 nm变化到550 nm时的透射谱. 粉色虚线表示瑞利异常衍射阶次, 颜色条代表透射强度Figure 5. Transmission spectra of silver nanodisk arrays with (a) h = 50, (b) 100, and (c) 150 nm for different diameters (from 50 to 200 nm with a 5 nm step) under the normal incidence, while
$ {P_{\text{x}}} $ =$ {P_y} $ = 500 nm is fixed. Transmission spectra of silver nanodisk arrays with (d) d = 80, (e) 100 and (f) 120 nm for different lattice periods (from 350 to 550 nm with a 5 nm step) under the normal incidence, when h = 100 nm is fixed. The pink dashed lines represent the diffraction orders, and the color bar represents the transmission intensity.表 1 数值仿真获得的高Q值LPMs总结
Table 1. Summary of numerically obtained high-Q factors of LPMs.
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[1] Wang D Q, Bourgeois M R, Guan J, Fumani A K, Schatz G C, Odom T W 2020 ACS Photonics 7 630
Google Scholar
[2] Polavarapu L, Liz-Marzán L M 2013 Phys. Chem. Chem. Phys. 15 5288
Google Scholar
[3] Nie S M, Emory S R 1997 Science 275 1102
Google Scholar
[4] Chowdhury M H, Ray K, Gray S K, Pond J, Lacowicz J R 2009 Anal. Chem. 81 1397
Google Scholar
[5] Castellanos G W, Bai P, Gómez Rivas J 2019 J. Appl. Phys. 125 213105
Google Scholar
[6] Humphrey A D, Barnes W L 2016 J. Opt. 18 035005
Google Scholar
[7] Khlopin D, Laux F, Wardley W P, Martin J, Wurtz G A, Plain J, Bonod N, Zayats A V, Dickson W, Gérard D 2017 J. Opt. Soc. Am. B: Opt. Phys. 34 691
Google Scholar
[8] Le-Van Q, Zoethout E, Geluk E J, Ramezani M, Berghuis M, Gómez Rivas J 2019 Adv. Opt. Mater. 7 1801451
Google Scholar
[9] Humphrey A D, Barnes W L 2014 Phys. Rev. B 90 075404
Google Scholar
[10] Zundel L, May A, Manjavacas A 2021 ACS Photonics 8 360
Google Scholar
[11] Bin-Alam M S, Reshef O, Mamchur Y, Alam M Z, Carlow G, Upham J, Sullivan B T, Ménard J-M, Huttunen M J, Boyd R W, Dolgaleva K 2021 Nat. Commun. 12 947
Google Scholar
[12] Hakala T K, Antti J M, Aaro I V, Guo R, Martikainen J P, Daskalakis K S, Rekola H T, Julku A, Törmä P 2018 Nat. Phys. 14 739
Google Scholar
[13] Han A X, Dineen C, Babicheva V E, Moloney J V 2020 Nanophotonics 9 3545
Google Scholar
[14] 张萌徕, 覃赵福, 陈卓 2021 70 054206
Google Scholar
Zhang M L, Qin Z F, Chen Z 2021 Acta Phys. Sin. 70 054206
Google Scholar
[15] Lozano G, Louwers D J, Rodríguez S R K, Murai S, Jansen O T A, Verschuuren M A, Gómez Rivas J 2013 Light-Sci. Appl. 2 e66
Google Scholar
[16] Vitrey A, Aigouy L, Prieto P, García-Martín J M, González M U 2014 Nano Lett. 14 2079
Google Scholar
[17] Wang D Q, Bourgeois M R, Lee W K, Li R, Trivedi D, Knudson M P, Wang W J, Schatz G C, Odom T W 2018 Nano Lett. 18 4549
Google Scholar
[18] Li R, Wang D Q, Guan J, Wang W J, Ao X Y, Schatz G C, Schaller R, Odom T W 2019 J. Opt. Soc. Am. B: Opt. Phys. 36 E104
Google Scholar
[19] Lin L H, Zheng Y B 2015 Nanoscale 7 12205
Google Scholar
[20] Muravitskaya A, Movsesyan A, Kostcheev S, Adam P M 2019 J. Opt. Soc. Am. B: Opt. Phys. 36 E65
Google Scholar
[21] Liu S D, Yue P, Zhang S, Wang M S, Dai H W, Chen Y Q, Nie Z Q, Cui Y X, Han J B, Duan H G 2020 Adv. Opt. Mater. 8 1901109
Google Scholar
[22] Nikitin A G 2014 Appl. Phys. Lett. 104 061107
Google Scholar
[23] Lin L H, Yi Y S 2015 Opt. Express 23 130
Google Scholar
[24] Meier M, Wokaun A, Liao P F 1985 J. Opt. Soc. Am. B: Opt. Phys. 2 931
Google Scholar
[25] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
Google Scholar
[26] Kravets V G, Kabashin A V, Barnes W L, Grigorenko A N 2018 Chem. Rev. 118 5912
Google Scholar
[27] Teperik T V, Degiron A 2012 Phys. Rev. B 86 245425
Google Scholar
[28] Yang A, Hryn A J, Bourgeois M R, Lee W K, Hu J, Schatz G C, Odom T W 2016 Proc. Natl. Acad. Sci. U. S. A. 113 14201
Google Scholar
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