Topological surface plasmon polaritons

Geng Yi-Fei; Wang Zhu-Ning; Ma Yao-Guang; Gao Fei

doi:10.7498/aps.68.20191085

Abstract

The miniaturization of electromagnetic devices is a long-term theme for the development of modern technologies to achieve higher flexibilities, better performances, and higher density integration. Surface plasmon polaritons (SPPs) provide a powerful solution for reducing the size of integrated electromagnetic device due to its deep subwavelength confinement. However, materials or structures that support SPPs inevitably have impurities or structural defects, which leads to the loss of the propagating mode. In order to avoid scattering from impurities or defects, topological structures are introduced to address issues of discontinuities and have been proved to be an effective solution. In this paper, we first review the recent efforts devoted to SPPs based optical devices and those of artificial surface plasmon in terahertz/microwave band, and then summarize several important topological systems of SPPs. Finally, we present our perspectives on the future developments of this field.

Keywords:

Authors and contacts

1.
State Key Laboratory of Modern Optical Instruments, Zhejiang University, Hangzhou 310027, China
2.
College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding author: Ma Yao-Guang, mayaoguang@zju.edu.cn ; Gao Fei, gaofeizju@zju.edu.cn

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61801426)

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References

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Cited By

图 1 (a)杂质和结构缺陷对表面等离激元传输的影响; (b)拓扑表面等离激元的鲁棒传输特性

Figure 1. (a) Effect of impurity and structural defects on surface plasmon transport; (b) robust propagation characteristics of topological surface plasmons.

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图 2 二维拓扑表面等离激元晶体及其边界态^[30]　(a)石墨烯中圆孔三角点阵的示意图, 在外加磁场B作用下, 有限晶格支持拓扑保护的单向边缘等离子体; (b)在B ≠ 0的石墨烯中的等离激元色散能带, 当孔径d ≠ 0, 出现完全带隙; (c)不同磁感应强度下的边界态及其鲁棒性

Figure 2. Two-dimensional topological surface plasmon crystals and their boundary states ^[30]: (a) Schematic diagram of triangular circular hole lattices in graphene, under the action of an applied magnetic field B, finite lattices support a unidirectional edge plasma with topological protection; (b) energy band diagram of plasmon in graphene of B ≠ 0, when d ≠ 0, the complete band gap appears; (c) edge states under different magnetic induction and their robustness

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图 3 (a)基于石墨烯的能谷等离子激元晶体示意图: 由偏置电压V₀与相对于石墨烯晶格存在夹角的栅结构; (b)狄拉克点处的能带; (c) yz(x = 0)平面上的电场分布; (d)两种类型的边界; (e)不同夹角对应的谷陈数值; (f)图(d)所示一维结构能带^[32]

Figure 3. (a) Schematic diagram of graphene-based energy valley plasmon crystals: a gate structure with a biased voltage V₀ and an angle with respect to the graphene lattice; (b) energy band at the Dirac point; (c) electric field distribution on the yz (x = 0) plane; (d) two types of boundaries; (e) valley chern numbers corresponding to different angles; and (f) the one-dimensional structural energy band shown in Fig. (d).

DownLoad: Full-Size Img PowerPoint

图 4 人工表面等离激元QSH^[27,37]　(a)基于介质圆柱的光子QSH阵列; (b)图(a)中结构的能带; (c)单元胞收缩的SSPPs结构; (d)单元胞扩张的SSPPs结构; (e)SSPPs结构的能带仿真结果; (f)通过组合(c)和(d)中的结构构建边界; (g)边界态的模场分布

Figure 4. Spoof plasmonic QSH^[27,37]: (a) Photonic QSH with dielectric cylinders, the zoom in figure shows the hexagonal cluster; (b) edge states of photonic QSH; (c) spoof plasmonic structure whose unit cells of hexagonal clusters get shrunk, leading to zero spin Chern number; (d) spoof plasmonic structure whose unit cells of hexagonal clusters get expanded, which generates non vanishing spin Chern number; (e) simulated edge states at a domain wall between structures of (c) and (d); (f) constructed domain wall by combining structures in (c) and (d); (g) field patterns of edge states

DownLoad: Full-Size Img PowerPoint

图 5 人工表面等离激元VHE和QVH^[38,41,42]　(a)二维过渡金属二硫化物(TMDS)的示意图; (b)第一布里渊区TMDS的能带结构; (c)用于VHE的SSPPs结构; (d) SSPPs-VHE的模场扫描结果; (e)用于QVH的SSPPs结构; (f) SSPPs-QVH的模场测试结果

Figure 5. Spoof plasmonic VHE and QVH^[38,41,42]: (a) Schematic of TMDS; (b) band structure of TMDS in the first Brillouin zone; (c) spoof-SPP platform for VHE; (d) experimental demonstration of spoof-SPP VHE; (e) spoof-SPP platform for QVH; (f) experimental demonstration of spoof-SPP QVH

DownLoad: Full-Size Img PowerPoint

图 6 基于SSPPs结构的反常Floquet拓扑相^[14]　(a)人工表面等离激元环的照片; (b)实验中5 × 5点阵; (c)随着环间耦合的增加产生的拓扑相变; (d)当激励源频率为11.3 GHz时在阵列内观察到的局域模场; (e)在11.3 GHz频率观察到的边界态; (f)边界态绕过缺陷晶格传播

Figure 6. Spoof plasmonic demonstration of the anomalous Floquet topological phase^[14]: (a) Photo of spoof plasmonic rings; (b) a 5 by 5 lattice inexperiment; (c) topological transition as the inter-ring coupling increases; (d) observed field pattern when the excitation is inside the bulk at frequency11.3 GHz; (e) observed edge state at frequency 11.3 GHz; (f) the edge state circumvents and tunnels through a defect lattice

DownLoad: Full-Size Img PowerPoint

map

[1]	Wood R W 1902 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (Abingdon: Taylor & Francis) pp4–396
[2]	Pines D 1956 Rev. Mod. Phys. 28 184 Google Scholar
[3]	Ritchie R H 1957 Phys. Rev. 106 874 Google Scholar
[4]	Ritchie R H, Arakawa E, Cowan J, Hamm R 1968 Phys. Rev. Lett. 21 1530 Google Scholar
[5]	Cunningham S, Maradudin A, Wallis R 1974 Phys. Rev. B 10 3342 Google Scholar
[6]	Pendry J B, Martin-Moreno L, Garcia-Vidal F J 2004 Science 305 847 Google Scholar
[7]	Garcia-Vidal F J, Martin-Moreno L, Pendry J B 2005 J. Opt. A: Pure Appl. Opt 7 S97 Google Scholar
[8]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 54
[9]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[10]	Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904 Google Scholar
[11]	Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772 Google Scholar
[12]	Lu L, Joannopoulos J D, Soljačić M 2014 Nat. Photonics 8 821 Google Scholar
[13]	Chen W J, Jiang S J, Chen X D, Zhu B C, Zhou L, Dong J W, Chan C T 2014 Nat. Commun. 5 5782 Google Scholar
[14]	Gao F, Gao Z, Shi X H, Yang Z J, Lin X, Xu H Y, Joannopoulos J D, Soljacic M, Chen H S, Lu L, Chong Y D, Zhang B L 2016 Nat. Commun. 7 11619 Google Scholar
[15]	Cheng X J, Jouvaud C, Ni X, Mousavi S H, Genack A Z, Khanikaev A B 2016 Nat. Mater. 15 542 Google Scholar
[16]	Dong J W, Chen X D, Zhu H Y, Wang Y, Zhang X 2017 Nat. Mater. 16 298 Google Scholar
[17]	Gao F, Xue H R, Yang Z J, Lai K F, Yu Y, Lin X, Chong Y D, Shvets G, Zhang B L 2018 Nat. Phys. 14 140 Google Scholar
[18]	Gao W L, Lawrence M, Yang B A, Liu F, Fang F Z, Beri B, Li J S, Zhang S 2015 Phys. Rev. Lett. 114 037402 Google Scholar
[19]	Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nat. Photonics 7 1001 Google Scholar
[20]	Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233 Google Scholar
[21]	Liang G, Chong Y 2013 Phys. Rev. Lett. 110 203904 Google Scholar
[22]	Ma T, Khanikaev A B, Mousavi S H, Shvets G 2015 Phys. Rev. Lett. 114 127401 Google Scholar
[23]	Ma T, Shvets G 2016 New J. Phys. 18 025012 Google Scholar
[24]	Noh J, Huang S, Chen K P, Rechtsman M C 2018 Phys. Rev. Lett. 120 063902 Google Scholar
[25]	Pasek M, Chong Y D 2014 Phys. Rev. B 89 075113 Google Scholar
[26]	Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M, Szameit A 2013 Nature 496 196 Google Scholar
[27]	Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901 Google Scholar
[28]	Xiao M, Lin Q, Fan S H 2016 Phys. Rev. Lett. 117 057401 Google Scholar
[29]	Lu L, Joannopoulos J D, Soljacic M 2016 Nat. Phys. 12 626 Google Scholar
[30]	Jin D, Christensen T, Soljačić M, Fang N X, Lu L, Zhang X 2017 Phys. Rev. Lett. 118 245301 Google Scholar
[31]	Pan D, Yu R, Xu H, de Abajo F J G 2017 Nat. Commun. 8 1243 Google Scholar
[32]	Jung M, Fan Z, Shvets G 2018 Phys. Rev. Lett. 121 086807 Google Scholar
[33]	Gao Z, Gao F, Zhang Y M, Xu H Y, Luo Y, Zhang B L 2017 Adv. Mater. 29 1700018 Google Scholar
[34]	Murakami S, Nagaosa N, Zhang S C 2003 Science 301 1348 Google Scholar
[35]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[36]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[37]	Yves S, Fleury R, Berthelot T, Fink M, Lemoult F, Lerosey G 2017 Nat. Commun. 8 16023 Google Scholar
[38]	Xu X D, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[39]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489 Google Scholar
[40]	Ju L, Shi Z W, Nair N, Lv Y C, Jin C H, Velasco J, Ojeda-Aristizabal C, Bechtel H A, Martin M C, Zettl A, Analytis J, Wang F 2015 Nature 520 650 Google Scholar
[41]	Gao Z, Yang Z J, Gao F, Xue H R, Yang Y H, Dong J W, Zhang B L 2017 Phys. Rev. B 96 201402 Google Scholar
[42]	Wu X X, Meng Y, Tian J X, Huang Y Z, Xiang H, Han D Z, Wen W J 2017 Nat. Commun. 8 1304 Google Scholar
[43]	Yin X B, Ye Z L, Rho J, Wang Y, Zhang X 2013 Science 339 1405 Google Scholar
[44]	Kitagawa T, Berg E, Rudner M, Demler E 2010 Phys. Rev. B 82 235114 Google Scholar
[45]	Kitagawa T, Rudner M S, Berg E, Demler E 2010 Phys. Rev. A 82 033429 Google Scholar
[46]	Rudner M S, Lindner N H, Berg E, Levin M 2013 Phys. Rev. X 3 031005
[47]	Lohse M, Schweizer C, Price H M, Zilberberg O, Bloch I 2018 Nature 553 55 Google Scholar
[48]	Zilberberg O, Huang S, Guglielmon J, Wang M H, Chen K P, Kraus Y E, Rechtsman M C 2018 Nature 553 59 Google Scholar
[49]	Benalcazar W A, Bernevig B A, Hughes T L 2017 Science 357 61 Google Scholar
[50]	Khanikaev A B, Mousavi S H, Shvets G, Kivshar Y S 2010 Phys. Rev. Lett. 105 126804 Google Scholar
[51]	Leykam D, Chong Y D 2016 Phys. Rev. Lett. 117 143901 Google Scholar
[52]	Ni X, Purtseladze D, Smirnova D A, Slobozhanyuk A, Alù A, Khanikaev A B 2018 Sci. Adv. 4 eaap8802 Google Scholar
[53]	Yu N F, Wang Q J, Kats M A, Fan J A, Khanna S P, Li L H, Davies A G, Linfield E H, Capasso F 2010 Nat. Mater. 9 730 Google Scholar
[54]	Karl N J, McKinney R W, Monnai Y, Mendis R, Mittleman D M 2015 Nat. Photonics 9 717 Google Scholar
[55]	Ma J J, Karl N J, Bretin S, Ducournau G, Mittleman D M 2017 Nat. Commun. 8 729 Google Scholar
[56]	Grady N K, Heyes J E, Chowdhury D R, Zeng Y, Reiten M T, Azad A K, Taylor A J, Dalvit D A, Chen H T 2013 Science 340 1304 Google Scholar
[57]	Chen H T, O'hara J F, Azad A K, Taylor A J, Averitt R D, Shrekenhamer D B, Padilla W J 2008 Nat. Photonics 2 295 Google Scholar

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