Theoretical analysis of tunable double plasmon induced transparency in three-ellipse-shaped resonator coupled waveguide

Gu Xin; Zhang Hui-Fang; Li Ming-Yu; Chen Jun-Ya; He Ying

doi:10.7498/aps.71.20221365

Abstract

The tunable double plasmon-induced transparency (PIT) effects are investigated in a waveguide coupled by the three ellipse-shaped resonators. By the finite element method, we study the influences of coupling modes of the three ellipse-shaped resonators, waveguide structure parameters and the refractive indices of dielectric in three ellipse-shaped resonators on double PIT effects. The waveguide structure consists of three ellipse-shaped resonators, and is similar to a four-level structure of the atomic system. The bottom ellipse-shaped resonator can be named a bright mode, the middle and top ellipse-shaped resonators each can be seen as a dark mode. In order to obtain an ideal double PIT transparency window, we also numerically analyze the optical transmission characteristics of structures of several three-ellipse-shaped resonator coupled waveguides. Furthermore, we mainly discuss the transmission spectra in the better three-ellipse-shaped resonator coupled waveguide structure as a function of the radii of the long axis in ellipse-shaped resonators, the coupling distance between the bottom ellipse-shaped resonator and the bus waveguide, the coupling distance between ellipse-shaped resonators, and the symmetry broken degree. In addition, we also consider the effect of the refractive indices of dielectric in three ellipse-shaped resonators on double PIT spectra. It is found that the transmission spectra in the three-ellipse-shaped resonator coupled waveguide have obvious red shift when the refractive indices of dielectric in the three ellipse-shaped resonators increase. All the simulation results may provide the theoretical basis for the potential application of multiple PIT in plasma switches and sensors.

Keywords:

Authors and contacts

Department of Physics, Shanghai University, Shanghai 200444, China

Corresponding author: Zhang Hui-Fang, hfzhang1967@shu.edu.cn

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11804219).

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References

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Cited By

图 1 (a) 三椭圆谐振腔耦合波导结构(三椭圆腔左右放置且s₁ = s₂); (b) 双椭圆(黑色虚线)和三椭圆(红色实线)波导结构透射谱;(c)−(g) 三椭圆腔波导结构中波长分别为849, 855, 860, 866, 883 nm时的电场分布

Figure 1. (a) Schematic diagram of three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed left and right and s₁= s₂); (b) transmission spectra of the two (black dash) and three (red solid) ellipse-shaped resonators waveguide structure; (c)−(g) electric field distribution of three ellipse-shaped resonators waveguide structure at wavelength of 849, 855, 860, 866, 883 nm, respectively.

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图 2 (a) 三椭圆谐振腔耦合波导结构(三椭圆腔左右放置且s₁ = 0); (b) 双椭圆(黑色虚线)和三椭圆(红色实线)波导结构透射谱;(c)−(g) 三椭圆腔波导结构中波长分别为844, 851, 867, 877, 888 nm时的电场分布

Figure 2. (a) Schematic diagram of three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed left and right and s₁ = 0); (b) transmission spectra of two (black dash) and three (red solid) ellipse-shaped resonators waveguide structure; (c)−(g) electric field distribution of three ellipse-shaped resonators waveguide structure at wavelength of 844, 851, 867, 877, 888 nm, respectively.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 三椭圆谐振腔耦合波导结构(三椭圆腔左右放置且s₂ = 0); (b) 双椭圆(黑色虚线)和三椭圆(红色实线)波导结构透射谱;(c)−(g) 三椭圆腔波导结构中波长分别为846, 858, 866, 883, 897 nm时的电场分布

Figure 3. (a) Schematic diagram of three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed left and right and s₂ = 0); (b) transmission spectra of two (black dash) and three (red solid) ellipse-shaped resonators waveguide structure; (c)−(g) electric field distribution of three ellipse-shaped resonators waveguide structure at wavelength of 846, 858, 866, 883, 897 nm, respectively.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 三椭圆谐振腔耦合波导结构(三椭圆腔在一条直线上竖直放置); (b) 双椭圆(黑色虚线)和三椭圆(红色实线)波导结构透射谱; (c)−(g) 三椭圆腔波导结构中波长分别为845, 851, 867, 878, 889 nm时的电场分布

Figure 4. (a) Schematic diagram of three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed vertically in a straight line); (b) transmission spectra of two (black dash) and three (red solid) ellipse-shaped resonators waveguide structure; (c)−(g) electric field distribution of three ellipse-shaped resonators waveguide structure at wavelength of 845, 851, 867, 878, 889 nm, respectively.

DownLoad: Full-Size Img PowerPoint

图 5 (a) 轴对称三椭圆谐振腔耦合波导结构(三椭圆腔倒等腰三角形放置且O₃O₁ = O₃O₂); (b) 非轴对称(黑色虚线)和轴对称(红色实线)三椭圆腔波导结构透射谱; (c)−(e) 轴对称波导结构中波长分别为865, 876, 883 nm时的电场分布

Figure 5. (a) Schematic diagram of the axisymmetric three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed in an inverted isosceles triangle and O₃O₁ = O₃O₂); (b) transmission spectra of the non-axisymmetric (black dash) and the axisymmetric (red solid) three ellipse-shaped resonators waveguide structure; (c)−(e) electric field distribution of the axisymmetric three ellipse-shaped resonators waveguide structure at wavelength of 865, 876, 883 nm, respectively.

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图 6 (a) 轴对称三椭圆谐振腔耦合波导结构(三椭圆腔正等腰三角形放置且O₂O₁ = O₂O₃); (b) 非轴对称(黑色虚线)和轴对称(红色实线)三椭圆腔波导结构透射谱; (c)−(e) 轴对称波导结构中波长分别为853, 879, 895 nm时的电场分布

Figure 6. (a) Schematic diagram of the axisymmetric three ellipse-shaped resonators coupled waveguide structure (three ellipse-shaped resonators are placed in a positive isosceles triangle and O₂O₁ = O₂O₃); (b) transmission spectra of the non-axisymmetric (black dash) and the axisymmetric (red solid) three ellipse-shaped resonators waveguide structure; (c)−(e) electric field distribution of the axisymmetric three ellipse-shaped resonators waveguide structure at wavelength of 853, 879, 895 nm, respectively.

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图 7 三椭圆腔耦合波导结构双PIT效应实验设计示意简图

Figure 7. Schematic diagram of experimental design of double PIT effects for the three ellipse-shaped resonators coupled waveguide structure.

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图 8 当改变椭圆腔长轴半径时, 三椭圆谐振腔波导结构的透射谱　(a)−(c) 改变顶部椭圆腔长轴半径r₁; (d)−(f) 改变中部椭圆腔长轴半径r₂; (g)−(i) 改变底部椭圆腔长轴半径r₃; (j)—(l) 改变r₁和r₃

Figure 8. Transmission spectra in the three ellipse-shaped resonators coupled waveguide structure when changing the long-axis radius of the elliptical cavity: (a)−(c) Change radiusof the long axis r₁in the top ellipse-shaped resonator; (d)−(f) change r₂in the middle ellipse-shaped resonator; (g)−(i) change r₃in the bottom ellipse-shaped resonator; (j)−(l) change r₁andr₃.

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图 9 三椭圆谐振腔波导结构透射谱随结构参数的变化　(a) 当x₁ = x₂ = 0, h = c = 10 nm时, 透射谱随H的变化; (b) 当x₁ = x₂ = 0, H = c = 10 nm时, 透射谱随h的变化; (c) 当x₁ = x₂ = 0, H = h = 10 nm时, 透射谱随c的变化; (d), (e) 当H = h = c = 10 nm时, 透射谱随x₁和x₂的变化; (f) 当x₁ = x₂ = 0, H = h = 10 nm时, 透射谱随n的变化

Figure 9. Transmission spectra in the three ellipse-shaped resonators coupled waveguide structure with different parameters: (a) With H when x₁ = x₂ = 0, h = c = 10 nm; (b) with h when x₁ = x₂ = 0, H = c =10 nm; (c) with c when x₁ = x₂ = 0, H = h = 10 nm; (d), (e) with x₁ and x₂when H = h = c = 10 nm; (f) with n when x₁ = x₂ = 0, H = h = 10 nm.

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[1]	Ritchie R H 1957 Phys. Rev. 106 874 Google Scholar
[2]	Barnes W L, Dereux A, Ebbesen T W 2003 Nature 424 824 Google Scholar
[3]	Dionne J A, Sweatlock L A, Atwater H A, Polman A 2006 Phys. Rev. B 73 035407 Google Scholar
[4]	Galvez F, del Valle J, Gomez A, Osorio M R, Granados D, Perez de Lara D, Garcia M A, Vicent J L 2016 Opt. Materials Express 6 3086 Google Scholar
[5]	Yang X Y, Hua E, Su H, Guo J, Yan S B 2020 Sensors 20 4125 Google Scholar
[6]	陈颖, 谢进朝, 周鑫德, 张灿, 杨惠, 李少华 2019 物理学报 68 237301 Google Scholar Chen Y, Xie J C, Zhou X D, Zhang C, Yang H, Li S H 2019 Acta Phys. Sin. 68 237301 Google Scholar
[7]	Han X, Wang T, Li X, Zhu Y 2016 Plasmonics 11 729 Google Scholar
[8]	杨韵茹, 关建飞 2016 物理学报 65 057301 Google Scholar Yang Y R, Guan J F 2016 Acta Phys. Sin. 65 057301 Google Scholar
[9]	Liu X, Li J N, Chen J F, Rohimah S, Tian H, Wang J F 2021 Opt. Express 29 20829 Google Scholar
[10]	祁云平, 张雪伟, 周培阳, 胡兵兵, 王向贤 2018 物理学报 67 197301 Google Scholar Qi Y P, Zhang X W, Zhou P Y, Hu B B, Wang X Y 2018 Acta Phys. Sin. 67 197301 Google Scholar
[11]	Hao X X, Huo Y P, He Q, Guo Y Y, Niu Q Q, Cui P F, Wang Y Y, Song M N 2021 Phys. Scripta 96 075505 Google Scholar
[12]	Amrani M, Khattou S, Rezzouk Y, Mouadili A, Noual A, El Boudouti E H, Djafari-Rouhani B 2022 J. Phys. D: Appl. Phys. 55 075106 Google Scholar
[13]	Zhang Z, Yang J, He X, Han Y, Zhang J, Huang J, Chen D 2018 Appl. Sci. 8 462 Google Scholar
[14]	Harris S E, Field J E, Imamoğlu A 1990 Phys. Rev. Lett. 64 1107 Google Scholar
[15]	褚培新, 张玉斌, 陈俊学 2020 物理学报 69 134205 Google Scholar Chu P X, Zhang Y B, Chen J X 2020 Acta Phys. Sin. 69 134205 Google Scholar
[16]	Chen M M, Xiao Z Y, Lu X J 2020 Carbon 159 273 Google Scholar
[17]	Li M W, Liang C P, Zhang Y B, Yi Z, Chen X F, Zhou Z G, Yang H, Tang Y J, Yi Y G 2019 Results Phys. 15 102603 Google Scholar
[18]	Wang X J, Meng H Y, Deng S Y, Lao C D, Wei Z C, Wang F H, Tan C G, Huang X 2019 Nanomaterials 9 385 Google Scholar
[19]	Liu L, Xia S X, Luo X, Zhai X, Yu Y B, Wang L L 2018 Opt. Commun. 418 27 Google Scholar
[20]	Waks E, Vuckovic J 2006 Phys. Rev. Lett. 96 153601 Google Scholar
[21]	Marco P, Dario G, Liam O F, Claudio A L 2018 Opt. Express 26 8470 Google Scholar
[22]	Li J J, Tian J P, Yang R C 2019 Eur. Phys. J. D 73 230 Google Scholar
[23]	Han X, Wang T, Li X M, Liu B, He Y, Tang J 2015 J. Phys. D: Appl. Phys. 48 235102 Google Scholar
[24]	Niu Y Y, Wang J C, Liu D D, Hu Z D, Sang T, Gao S M 2017 Optik 140 1038 Google Scholar
[25]	Wang G X, Lu H, Liu X M 2012 Opt. Express 20 020902 Google Scholar
[26]	Wen K H, Yan L S, Pan W, Luo B, Guo Z, Guo Y H, Luo X G 2014 J. Light. Technol. 32 1701 Google Scholar
[27]	Cao G T, Li H J, Zhan S P, Xu H Q, Liu Z M, He Z H, Wang Y 2013 Opt. Express 21 9198 Google Scholar
[28]	Wang Y Q, He Z H, Cui W, Ren X C, Li C J, Xue W W, Cao D M, Li G, Lei W L 2020 Results Phys. 16 102981 Google Scholar
[29]	李继军, 吴耀德, 宋明玉 2007 长江大学学报(自科版)理工卷 4 1673 Google Scholar Li J J, Wu Y D, Song M Y 2007 J. Yangtze University (Nat. Sci. Edit) Sci. Eng. V. 4 1673 Google Scholar
[30]	Li Z F, Wen K H, Fang Y H, Guo Z C 2020 IEEE J. Quantum Electron. 56 2982249 Google Scholar
[31]	Qiong Z, Wang Z 2019 Opt. Express 27 303 Google Scholar
[32]	Yin X G, Feng T H, Yip S, Liang Z X, Hui A, Ho J C, Li J S 2013 Appl. Phys. Lett. 103 021115 Google Scholar
[33]	Xu H, Lu Y, Lee Y, Ham B S 2010 Opt. Express 18 17736 Google Scholar
[34]	Zhu Y, Hu X Y, Yang H, Gong Q H 2014 Sci. Rep. UK 4 3752 Google Scholar
[35]	闫西成 2018 硕士学位论文(武汉:华中科技大学) (Wuhan: Huazhong University of Science & Technology) Yan X C 2018 M. S. Thesis (Wuhan: Huazhong University of Science & Technology
[36]	Ye C G, Zhang L 2008 Opt. Lett. 33 1911 Google Scholar

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