旋转对称表面等离激元结构中极端局域光场的准正则模式分析

周强; 林树培; 张朴; 陈学文

doi:10.7498/aps.68.20190434

摘要

金属微纳结构中表面等离激元能够将自由空间光场局域到亚波长甚至纳米尺度, 增强光与物质相互作用等各种物理过程, 为等离激元光学在诸多领域带来诱人的应用. 然而, 目前对表面等离激元光学模场的局域性定量描述仍主要基于直观的空间几何尺寸确定的模式体积, 并常被用于刻画模场与物质相互作用的强度. 本文基于准正则模理论发展了表征表面等离激元结构中光场局域的理论描述方法, 并针对两类典型结构的表面等离激元共振进行了系统的模式分析. 结果显示表面等离激元共振可由多个本征模式构成, 观察到的光场局域是所有模式共同作用的结果, 只有当共振对应单一模式时可以用该本征模式的模式体积描述光场局域. 最后, 基于上述结果, 本文探讨了极端局域光场和近来出现的“皮米腔”的光场局域本质.

关键词:

Abstract

Surface plasmons in metallic nanostructures can confine the optical field within the region of subwavelength, even nanometer scale, and thus enhance the light-matter interaction and other physical processes, which will lead the plasmon optics to possess attractive applications in many areas. However, the " mode volume” often used to characterize field confinement in plasmonic structures is only defined phe-nomenologically and suffers ambiguity when applied to complex structures. In this work, we develop a theoretical method to characterize the field confinement based on quasi-normal mode analysis. We recognize the fact that a plasmonic resonance may result from many eigen-modes, which together contribute to the observed field confinement. An effective mode volume is introduced for quasi-normal modes and used to characterize the field confinement when the plasmonic resonance is dominated by a single quasi-normal mode. Two typical kinds of plasmonic structures are systematically examined, and the field confinement on the order of 10 nm³–100 nm³ is confirmed. In pursuit of the ultimate field confinement, we revisit the so-called " pico-cavity” formed by an atomistic protrusion in the nano gap of the particle-on-mirror configuration. The apparent hot spot is shown to have contributions from several quasi-normal modes. The dominant one exhibits a further squeezed mode volume compared with the scenario without the protrusion, but is still well above 10 nm³.

Keywords:

作者及机构信息

华中科技大学物理学院, 武汉　430074

通信作者: 张朴, puzhang0702@hust.edu.cn ; 陈学文, xuewen_chen@hust.edu.cn

基金项目: 国家自然科学基金(批准号: 11874166)和国家自然科学基金青年科学基金(批准号: 11604109)资助的课题.

Authors and contacts

School of Physics and Center for Quantum Optical Science, Huazhong University of Science and Technology, Wuhan 430074, China

Corresponding author: Zhang Pu, puzhang0702@hust.edu.cn ; Chen Xue-Wen, xuewen_chen@hust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874166) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11604109).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 半径40 nm金球的准正则模式分析　(a)旋转对称结构建模示意; (b)按指标l, m排列的归一化准正则模场分布, 中心线左右两侧分别为E_r和E_θ的实部; (c)准正则模式谱分布, 蓝色叉为模式聚点; (d)用全波仿真(full wave)、解析公式(analytical)和准正则模式重建(QNM)三种方法得到的距金纳米球表面10 nm处沿轴向的Purcell因子

Fig. 1. 2D axisymmetric quasinormal mode (QNM) analysis for a spherical gold nanoparticle with r_s = 40 nm: (a) Schematic of 2D axisymmetric modeling; (b) shows a table of normalized QNM profiles arranged according to indices l and m, where on the left and right side of the axis shows the real part of E_r and E_θ, respectively; (c) spectral distribution of QNMs with an accumulation point indicated by the blue cross; (d) at a position 10 nm away from the metal surface, Purcell factor in radial direction is calculated with full wave simulation, analytical methods and QNM reconstruction.

下载: 全尺寸图片幻灯片

图 2 二聚体结构准正则模式及场局域分析　二聚体由r_a = 40 nm和r_b = 5, 20, 40 nm的两个金纳米球组成, 间隙宽度d = 1, 5, 10 nm; 图中展示了: 准正则模式谱分布; 纳米间隙中心处轴向Purcell因子的准正则模式重建(黑色实线), 红色圆圈为全波仿真结果; 纳米间隙附近BDP模式的等效模体积分布

Fig. 2. QNM modal analysis for dimers and the field localization of the BDP modes. The dimers consist of two spherical gold nanoparticles with r_a = 40 nm and r_b = 5, 20, 40 nm. The gap size d = 1, 5, 10 nm. In the figure are illustrated: the spectral distributions of the QNMs; the QNM reconstruction (black solid lines) of the Purcell factor at the gap center and in the axial direction, the full wave simulation results are indicated by red circles; the mode volume profiles of the BDP modes in the gap region.

下载: 全尺寸图片幻灯片

图 3 PoM的准正则模式及场局域分析　PoM中金颗粒为半长轴a = 40 nm的旋转椭球, 镜面为相同材料无穷大半空间, 椭球半短轴b = 5, 20, 40 nm, 与镜面间距d = 1, 5, 10 nm; 图中展示了: 准正则模式谱分布; 纳米间隙中心处轴向Purcell因子的准正则模式重建(黑色实线), 红色圆圈为全波仿真结果; 纳米间隙附近BDP模式的等效模体积分布

Fig. 3. QNM modal analysis for particle-on-mirror (PoM) structures and the field localization of the BDP modes. The gold particles are ellipsoids of revolution with semi-axes a = 40 nm and b = 5, 20, 40 nm. The gap formed with gold mirrors has d = 1, 5, 10 nm. In the figure are illustrated: the spectral distributions of the QNMs; the QNM reconstruction (black solid lines) of the Purcell factor at the gap center and in the axial direction, the full wave simulation results are indicated by red circles; the mode volume profiles of the BDP modes in the gap region.

下载: 全尺寸图片幻灯片

图 4 PoM纳米间隙中原子凸起结构对光场局域的影响和准正则模式分析　(a) 存在与不存在原子凸起时的结构示意图; (b) 纳米间隙中心高度位置的局域场增强效应, 激励源为镜面上方716 nm处轴向偶极子; (c) BQP谐振波长处纳米间隙中心高度的局域场增强效应; (d) PoM结构的准正则模式谱分布以及纳米间隙中心处轴向Purcell因子的准正则模式重建; (e) BQP模式的归一化模场和等效模式体积

Fig. 4. The effects of the atomistic protrusion on the field localization in the nano-gap of the particle-on-mirror (PoM) structure and the QNM modal analysis: (a) Schematic diagrams of the PoM structures with and without the atomistic protrusion; (b) the local field enhancement at the half height in the gap when excited by an axially polarized dipole 716 nm above the mirror; (c) the cross section of the local field enhancement in (b) at the resonance wavelength of the BQP mode; (d) the spectral distributions of the QNMs and the QNM reconstruction of the Purcell factor at the gap center and in the axial direction; (e) the normalized modal profile of the BQP mode and its mode volume map in the gap region.

下载: 全尺寸图片幻灯片

[1]	Alvarez Puebla R, Liz Marzán L M, García de Abajo F J 2010 J. Phys. Chem. Lett. 1 2428 Google Scholar
[2]	Kuznetsov A I, Miroshnichenko A E, Brongersma M L, Kivshar Y S, Luk’yanchuk B 2016 Science 354 aag2472 Google Scholar
[3]	Schuller J A, Barnard E S, Cai W, Jun Y C, White J S, Brongersma M L 2010 Nat. Mater. 9 193 Google Scholar
[4]	Polman A 2008 Science 322 868 Google Scholar
[5]	Benz F, Schmidt M K, Dreismann A, Chikkaraddy R, Zhang Y, Demetriadou A, Carnegie C, Ohadi H, de Nijs B, Esteban R, Aizpurua J, Baumberg J J 2016 Science 354 726 Google Scholar
[6]	Kern J, Großmann S, Tarakina N V, Hackel T, Emmerling M, Kamp M, Huang J S, Biagioni P, Prangsma J C, Hecht B 2012 Nano Lett. 12 5504 Google Scholar
[7]	Ciracì C, Hill R, Mock J, Urzhumov Y, Fernández Domínguez A, Maier S, Pendry J, Chilkoti A, Smith D 2012 Science 337 1072 Google Scholar
[8]	Wei H, Xu H 2013 Nanoscale 5 10794 Google Scholar
[9]	Oulton R F, Sorger V J, Genov D, Pile D, Zhang X 2008 Nat. Photon. 2 496 Google Scholar
[10]	Kleinman S L, Frontiera R R, Henry A I, Dieringer J A, van Duyne R P 2013 Phys. Chem. Chem. Phys. 15 21 Google Scholar
[11]	Kneipp K, Wang Y, Kneipp H, Perelman L T, Itzkan I, Dasari R R, Feld M S 1997 Phys. Rev. Lett. 78 1667 Google Scholar
[12]	Stranahan S M, Willets K A 2010 Nano Lett. 10 3777 Google Scholar
[13]	Willets K A, Wilson A J, Sundaresan V, Joshi P B 2017 Chem. Rev. 117 7538 Google Scholar
[14]	Chen W, Zhang S, Deng Q, Xu H 2018 Nat. Commun. 9 801 Google Scholar
[15]	Loo C, Lowery A, Halas N, West J, Drezek R 2005 Nano Lett. 5 709 Google Scholar
[16]	Huang X, Jain P K, Sayed I H E, Sayed M A E 2007 Nanomedicine 2 681 Google Scholar
[17]	Juan M L, Righini M, Quidant R 2011 Nat. Photon. 5 349 Google Scholar
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[19]	Pelton M 2015 Nat. Photon. 9 427 Google Scholar
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[21]	Reiserer A, Rempe G 2015 Rev. Mod. Phys. 87 1379 Google Scholar
[22]	Wen J, Wang H, Chen H, Deng S, Xu N 2018 Chin. Phys. B 27 096101 Google Scholar
[23]	Maier S A 2006 Opt. Express 14 1957 Google Scholar
[24]	Koenderink A F 2010 Opt. Lett. 35 4208 Google Scholar
[25]	Esteban R, Aizpurua J, Bryant G W 2014 New J. Phys. 16 013052 Google Scholar
[26]	Muljarov E, Langbein W 2016 Phys. Rev. B 94 235438 Google Scholar
[27]	Sauvan C, Hugonin J P, Maksymov I S, Lalanne P 2013 Phys. Rev. Lett. 110 237401 Google Scholar
[28]	Leung P, Liu S, Young K 1994 Phys. Rev. A 49 3057 Google Scholar
[29]	Lalanne P, Yan W, Vynck K, Sauvan C, Hugonin J P 2018 Laser Photon. Rev. 12 1700113 Google Scholar
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[31]	Muljarov E, Weiss T 2018 Opt. Lett. 43 1978 Google Scholar
[32]	Franke S, Hughes S, Dezfouli M K, Kristensen P T, Busch K, Knorr A, Richter M 2018 arXiv: 1808.06392
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[35]	Dung H T, Knöll L, Welsch D G 1998 Phys. Rev. A 57 3931 Google Scholar
[36]	Lalanne P, Yan W, Gras A, Sauvan C, Hugonin J P, Besbes M, Demésy G, Truong M, Gralak B, Zolla F 2018 arXiv: 1811.11751
[37]	Muljarov E, Langbein W 2016 Phys. Rev. B 93 075417 Google Scholar
[38]	Bai Q, Perrin M, Sauvan C, Hugonin J P, Lalanne P 2013 Opt. Express 21 27371 Google Scholar
[39]	Dezfouli M K, Hughes S 2018 Phys. Rev. B 97 115302 Google Scholar
[40]	Dezfouli M K, Tserkezis C, Mortensen N A, Hughes S 2017 Optica 4 1503 Google Scholar
[41]	Raman A, Fan S 2010 Phys. Rev. Lett. 104 087401 Google Scholar
[42]	Demésy G, Nicolet A, Gralak B, Geuzaine C, Campos C, Roman J E 2018 arXiv: 1802.02363
[43]	Tisseur F, Meerbergen K 2001 SIAM Rev. 43 235 Google Scholar
[44]	Taflove A, Hagness S C 2005 Computational Electrodynamics: the Fnite-Difference Time-Domain Method (Norwood: Artech House) pp517–552
[45]	Oxborrow M 2007 IEEE Trans. Microw. Theory Tech. 55 1209 Google Scholar
[46]	Chinellato O, Arbenz P, Streiff M, Witzig A 2005 Future Gener. Comput. Syst. 21 1263 Google Scholar
[47]	Jin J 2014 The Finite Element Method in Electromagnetics (Hoboken: Wiley-IEEE Press) pp315–371
[48]	Ho K, Leung P, van Den Brink A M, Young K 1998 Phys. Rev. E 58 2965 Google Scholar
[49]	Ge R C, Kristensen P T, Young J F, Hughes S 2014 New J. Phys. 16 113048 Google Scholar
[50]	Kristensen P T, Hughes S 2013 ACS Photon. 1 2
[51]	Iranzo D A, Nanot S, Dias E J, Epstein I, Peng C, Efetov D K, Lundeberg M B, Parret R, Osmond J, Hong J Y 2018 Science 360 291 Google Scholar
[52]	Amendola V, Pilot R, Frasconi M, Marago O M, Iati M A 2017 J. Phys. Condens. Matter 29 203002 Google Scholar
[53]	Baranov D G, Wersall M, Cuadra J, Antosiewicz T J, Shegai T 2017 ACS Photon. 5 24
[54]	Prodan E, Radloff C, Halas N J, Nordlander P 2003 Science 302 419 Google Scholar
[55]	Urbieta M, Barbry M, Zhang Y, Koval P, Sánchez Portal D, Zabala N, Aizpurua J 2018 ACS Nano 12 585 Google Scholar
[56]	Ciracì C 2017 Phys. Rev. B 95 245434 Google Scholar
[57]	Savage K J, Hawkeye M M, Esteban R, Borisov A G, Aizpurua J, Baumberg J J 2012 Nature 491 574 Google Scholar
[58]	Esteban R, Borisov A G, Nordlander P, Aizpurua J 2012 Nat. Commun. 3 825 Google Scholar
[59]	Chikkaraddy R, de Nijs B, Benz F, Barrow S J, Scherman O A, Rosta E, Demetriadou A, Fox P, Hess O, Baumberg J J 2016 Nature 535 127 Google Scholar
[60]	Barbry M, Koval P, Marchesin F, Esteban R, Borisov A G, Aizpurua J, Sánchez Portal D 2015 Nano Lett. 15 3410 Google Scholar
[61]	Trautmann S, Aizpurua J, Götz I, Undisz A, Dellith J, Schneidewind H, Rettenmayr M, Deckert V 2017 Nanoscale 9 391 Google Scholar
[62]	Weaver J, Frederikse H 1977 CRC Handbook of Chemistry and Physics (Boca Raton: CRC Press) pp12–156
[63]	Bohren C F, Huffman D R 2008 Absorption and Scattering of Light by Small Particles (Hoboken: John Wiley & Sons) pp82–129

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