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表面等离激元共振激发的亚波长金属孔透射较Bethe理论有大幅度的提高, 然而, 由于共振对频率的敏感性以及金属在光频的高损耗特性, 表面等离激元共振难以实现亚波长金属孔的宽带高透射传输. 本文采用放置在金属孔两边的硅纳米颗粒的Mie谐振耦合取代表面等离激元共振, 实现亚波长金属孔的宽带高透射传输. 全波仿真结果表明, 采用Mie谐振耦合的亚波长金属孔(r/λ = 0.1)光传输, 透射系数超过90%的带宽达到65 nm, 与表面等离激元共振诱导的透射增强相比, 峰值增高了1.5倍, 3 dB带宽拓宽了17倍. 根据耦合模理论, 建立了Mie谐振耦合亚波长金属孔透射的等效电路模型, 并在临界耦合状态下反演出电路模型中的元件参数值. 进一步研究发现, 仅通过改变等效电路模型中的耦合系数, 就可全面揭示Mie谐振耦合亚波长金属孔透射的传输规律, 并得到与全波电磁仿真完全一致的结果, 从而找到光与放置硅纳米颗粒的亚波长金属孔相互作用的数学表达, 也给予人们在光学领域按照电路设计方法构建相应功能模块的启示.Transmission of the subwavelength metal aperture excited by the surface plasmon resonance is much higher than that from the Bethe theory. However, due to the sensitivity of resonant frequency and the loss of metal in optical band, it is difficult to achieve broadband and high transmission of the subwavelength metal aperture through surface plasmon resonance. In this article, the broadband and high transmission of the subwavelength metal aperture is realized when Mie-resonant-coupled silicon nanoparticles placed on both sides of the metal aperture are used to replace the surface plasmon resonance. The full wave simulation results show that bandwidth of the transmission coefficient more than 90% of the subwavelength aperture (
$ {r \mathord{\left/ {\vphantom {r {\lambda = 0.1}}} \right. } {\lambda = 0.1}}$ ) reaches 65 nm by using Mie-resonance-coupled silicon nanoparticles. Compared with the transmission induced by surface plasmon resonance, the peak value is improved by 1.5 times and the 3 dB bandwidth is widened by 17 times. According to the coupled mode theory, the equivalent circuit model of transmission of the subwavelength metal aperture added with Mie-resonance-coupled silicon nanoparticles is established, and the element parameters in the circuit model are inversed under the critical coupling state. Further research shows that transmission rule of the subwavelength metal aperture added with Mie-resonance coupled silicon nanoparticles can be accurately revealed by changing the coupling coefficient in the equivalent circuit model, and the results are consistent with the full wave electromagnetic simulation results. The mathematical expression of the interaction between light and Mie-resonance-coupled subwavelength metal aperture is found, therefore it can inspire us to construct certain functional modules in optical field according to circuit design method.-
Keywords:
- subwavelength metal aperture /
- broadband /
- high transmission /
- Mie resonance
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图 1 亚波长金属孔的(a)单元结构、(b)电场分布以及(c)功率损耗密度分布
Fig. 1. Unit cell (a), electric field distribution (b), and power loss density distribution (c) of the subwavelength metal aperture.
图 2 平面波通过亚波长金属孔的(a)透射率、(b)反射率和(c)吸收率
Fig. 2. (a) Transmissivity, (b) reflectivity and (c) absorptivity of plane waves passing through the subwavelength metal aperture.
图 3 放置在亚波长金属孔两边的硅立方谐振子的(a)正视图和(b)侧视图
Fig. 3. (a) Front view and (b) side view of silicon cube resonators placed at both sides of the subwavelength metal aperture.
图 4 亚波长金属孔的(a)透射率和(b)吸收率随两个硅谐振子之间耦合距离的变化
Fig. 4. (a) Transmissivity and (b) absorptivity of the subwavelength metal aperture varying with the coupling distance between two silicon resonators.
图 5 Mie谐振耦合的亚波长金属孔的透射率随(a)硅纳米颗粒边长和(b)金属孔周期的变化
Fig. 5. Transmissivity of Mie-resonance coupled subwavelength metal aperture varying with (a) side length of silicon nanoparticles and (b) period of metal aperture.
图 6 加载耦合谐振子的亚波长金属孔透射的等效电路模型
Fig. 6. Equivalent circuit model of transmission of the subwavelength metal aperture added with coupled resonators
图 7 加载耦合谐振子的亚波长金属孔透射的等效电路拟合
Fig. 7. Equivalent circuit fitting of transmission of the subwavelength metal aperture added with coupled resonators.
图 8 透射率随(a)耦合距离的归一化和(b)耦合系数的倒数的归一化的变化
Fig. 8. Transmissivity varying with (a) normalization of coupling distance and (b) normalization of reciprocal of coupling coefficient.
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[1] Ebbesen T W, Lezec H J, Ghaemi H F, Thio T 1998 Nature 391 667
Google Scholar
[2] Garcia-Vidal F J, Martin-Moreno L, Ebbesen T W, Kuipers L 2010 Rev. Mod. Phys. 82 729
Google Scholar
[3] 姚尧, 沈悦, 郝加明, 戴宁 2019 68 147802
Google Scholar
Yao Y, Shen Y, Hao J M, Dai N 2019 Acta Phys. Sin. 68 147802
Google Scholar
[4] Barnes W L, Murray W A, Dintinger J, Devaux E, Ebbesen T W 2004 Phys. Rev. Lett. 92 107401
Google Scholar
[5] 郑俊娟, 孙刚 2010 59 4008
Google Scholar
Zheng J J, Sun G 2010 Acta Phys. Sin. 59 4008
Google Scholar
[6] 易永祥, 汪国平, 龙拥兵, 单红 2003 52 604
Google Scholar
Yi Y X, Wang G P, Long Y B, Shan H 2003 Acta Phys. Sin. 52 604
Google Scholar
[7] 朱旭鹏, 张轼, 石惠民, 陈智全, 全军, 薛书文, 张军, 段辉高 2019 68 247301
Google Scholar
Zhu X P, Zhang S, Shi H M, Chen Z Q, Quan J, Xue S W, Zhang J, Duan H G 2019 Acta Phys. Sin. 68 247301
Google Scholar
[8] 周强, 林树培, 张朴, 陈学文 2019 68 147104
Google Scholar
Zhou Q, Lin S P, Zhang P, Chen X W 2019 Acta Phys. Sin. 68 147104
Google Scholar
[9] Peer A, Biswas R 2016 Nanoscale 8 4657
Google Scholar
[10] Xiao B, Pradhan S K, Santiago K C, Rutherford G N, Pradhan A K 2015 Sci. Rep. 5 10393
Google Scholar
[11] Guo Y S, Liu S Y, Bi K, Lei M, Zhou J 2018 Photonics Res. 6 1102
Google Scholar
[12] Guo Y S, Liang H, Hou X J, Lv X L, Li L F, Li J S, Bi K, Lei M, Zhou J 2016 Appl. Phys. Lett. 108 051906
Google Scholar
[13] Guo Y S, Zhou J 2015 Sci. Rep. 5 8144
Google Scholar
[14] Guo Y S, Zhou J 2014 Opt. Express 22 27136
Google Scholar
[15] Guo Y S, Zhou J, Lan C W, Wu H Y, Bi K 2014 Appl. Phys. Lett. 104 204103
Google Scholar
[16] Chong K E, Staude I, James A, Dominguez J, Liu S, Campione S, Subramania G S, Luk T S, Decker M, Neshev D N, Brener I, Kivshar Y S 2015 Nano Lett. 15 5369
Google Scholar
[17] Yang Y, Kravchenko I I, Briggs D P, Valentine J 2014 Nat. Commun. 5 5753
Google Scholar
[18] 杨玖龙, 元晴晨, 陈润丰, 方汉林, 肖发俊, 李俊韬, 姜碧强, 赵建林, 甘雪涛 2019 68 214207
Google Scholar
Yang J L, Yuan Q C, Chen R F, Fang H L, Xiao F J, Li J T, Jiang B Q, Zhao J L, Gan X T 2019 Acta Phys. Sin. 68 214207
Google Scholar
[19] Shcherbakov M R, Neshev D N, Hopkins B, Shorokhov A S, Staude I, Melik-Gaykazyan E V, Decker M, Ezhov A A, Miroshnichenko A E, Brener I, Fedyanin A A, Kivshar Y S 2014 Nano Lett. 14 6488
Google Scholar
[20] Zywietz U, Schmidt M K, Evlyukhin A B, Reinhardt C, Aizpurua J, Chichkov B N 2015 ACS Photonics 2 913
Google Scholar
[21] Groep J V D, Coenen T, Mann S A, Polman A 2016 Optica 3 93
Google Scholar
[22] Zeng Y, Hoyer W, Liu J, Koch S W, Moloney J V 2009 Phys. Rev. B 79 235109
Google Scholar
[23] Haus H A 1984 Waves and Fields in Optoelectronics (Englewood Cliffs: Prentice-Hall Inc.) pp211−212
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