Three-band plasmon induced transparency effect based on four-disk resonator coupled waveguide system

Zhu Zi-Hao; Gao You-Kang; Zeng Yan; Cheng Zheng; Ma Hong-Hua; Yi Xu-Nong

doi:10.7498/aps.71.20221397

Abstract

In order to reduce power consumption and realize ultrafast response time and dynamic tunability, a plasmonic waveguide system based on four disk resonators is designed. A plasmon induced transparency effect is theoretically analyzed by using two different methods: one is the direct destructive interference between bright mode resonator and dark mode resonator, and the other is the indirect coupling through a plasmonic waveguide. Owing to the giant effective nonlinear Kerr coefficient of the graphene-Ag composite material structure and the enhancement characteristics of slow light response to optical Kerr effect, the pump intensity of PIT system for changing the phase shift of transmission spectrum is greatly reduced. An ultrafast response time of 1 ps is achieved, and 0.4π, 0.8π, 1.2π, 1.6π and 2π-phase shift of the transmission spectrum in the plasmon induced transparency system are achieved with the intensity of the pump light as low as 2.34, 4.68, 7.02, 9.36, 11.7 MW/cm^–2, respectively. In this work, a plasmonic waveguide coupled directly by two small disk resonators is employed, because two small disk resonators play a role of the slit between the waveguide and the resonators, and also act as two separate resonators side-coupled with a plasmonic waveguide, which leads to the more efficient coupling of electromagnetic energy in the waveguide into the big disk resonators to form resonance and easier storage of light in the resonator. The triple-band plasmon induced transparency (PIT) effect and slow light properties of the model are analyzed by the expression of the deduced theoretical transmittance based on the coupled mode theory, indicating that they are very consistent with the finite-difference time-domain simulations. The results show that the transmission peak of the system is over 80% and the maximum group index is as high as 368. Furthermore, the disk resonators are easy to fabricate and the size of the entire PIT structure is < 0.5 μm², which is beneficial to the design of optoelectronic device on-chip integration. The research results have important application prospects in highly integrating optical circuits and networks, and also provide the ideas for the design and fabrication of multi-channel optical filter and light storage devices with low power consumption, ultrafast nonlinear response, ultracompact and dynamical tunability.

Keywords:

Authors and contacts

1.
School of Physics and Electronic Information Engineering, Hubei Engineering University, Xiaogan 432000, China
2.
Institute of Photonic Technology, Jinan University, Guangzhou 510632, China

Corresponding author: Ma Hong-Hua, mhh_0708@hbeu.edu.cn ; Yi Xu-Nong, xnyi@szu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11547017).

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References

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图 1 (a) 小盘形谐振腔直接耦合MIM波导的结构; (b) 小盘形谐振腔的半径r不同时, 结构的透射光谱 (图(b)插图为r = 65 nm、波长为749 nm时透射凹陷处的磁场分布)

Figure 1. (a) Schematic diagram of a small disk resonator directly coupled to a MIM waveguide; (b) transmission spectra of thestructure with the different radius of the small disk resonator r (The inset in panel (b) shows the magnetic field distribution at the transmission dip wavelength of 749 nm with r = 65 nm).

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图 2 四盘形谐振腔耦合MIM波导的模型图

Figure 2. Schematic of four-disk resonators coupled to a MIM waveguide system.

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图 3 三波段PIT效应的实现原理示意图

Figure 3. Schematic diagram of realizing principle of triple PIT effect.

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图 4 (a)—(c) 不同ΔR下系统的透射谱, 其中(a) ΔR = 6 nm, (b) ΔR = 4 nm, (c) ΔR = 2 nm; (d)—(j)当ΔR = 6 nm时, 系统在不同波长处的磁场分布, 其中(d) λ_I = 758 nm, (e) λ_II= 782 nm, (f) λ_III = 803 nm, (g) λ_A = 747 nm, (h) λ_B = 773 nm, (i) λ_C = 789 nm, (j) λ_D = 811 nm

Figure 4. (a)–(c) Transmission spectra with various radius detuning ΔR: (a) ΔR = 6 nm; (b) ΔR = 4 nm; (c) ΔR = 2 nm. (d)–(j) Magnetic field distributions corresponding to different wavelengths with ΔR = 6 nm: (d) λ_I = 758 nm; (e) λ_II = 782 nm; (f) λ_III = 803 nm; (g) λ_A = 747 nm; (h) λ_B = 773 nm; (i) λ_C = 789 nm; (j) λ_D = 811 nm.

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图 5 MIM波导宽度w = 52 nm时, 有效折射率实部曲线和相移曲线

Figure 5. Real part of the effective refractive index and phase shift curve in the MIM waveguide with w = 52 nm.

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图 6 泵浦光诱导信号光相移与泵浦光强之间的关系

Figure 6. Relationship between the phase shift of the induced signal light and the pump light intensity.

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图 7 不同泵浦光强调谐下, (a1)—(e1)三波段PIT效应归一化透射谱及(a2)—(e2)相应的相移响应和群折射率　(a1), (a2) I = 2.34 MW/cm², Δϕ = 0.8π; (b1), (b2) I = 4.68 MW/cm², Δϕ = 0.6π; (c1), (c2) I = 7.02 MW/cm², Δϕ = 0.4π; (d1), (d2) I = 9.36 MW/cm², Δϕ = 0.2π; (e1), (e2) I = 11.70 MW/cm², Δϕ = 0

Figure 7. (a1)–(e1) Transmission spectra of tiple PIT effect with (a2)—(e2) corresponding phase shift responses and group indexunder different pump light intensity: (a1), (a2) I = 2.34 MW/cm², Δϕ = 0.8π; (b1), (b2) I = 4.68 MW/cm², Δϕ = 0.6π; (c1), (c2) I = 7.02 MW/cm², Δϕ = 0.4π; (d1), (d2) I = 9.36 MW/cm², Δϕ = 0.2π; (e1), (e2) I = 11.70 MW/cm², Δϕ = 0.

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图 8 三波段PIT效应透射光谱随泵浦光强变化的演化图

Figure 8. Evolution of the triple PIT effect with the pump light intensity.

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表 1 不同结构模型的PIT波段数量、最大透射率和最大群折射率的对比

Table 1. Comparison of the number of PIT band, maximum transmission and maximum group index of different structural models.

结构模型	PIT波段数量	最大透射率/%	最大群折射率
大小盘形谐振腔耦合波导结构	三波段	81	368.0
三盘形谐振腔边耦合波导结构	双波段	50	35.0^[18]
四盘形谐振腔耦合波导结构	三波段	86	14.5^[36]
双盘形谐振腔耦合波导结构	单波段	60	53.2^[37]

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[1]	Harris S E, Field J E, Imamoglu A 1990 Phys. Rev. Lett. 64 1107 Google Scholar
[2]	Kekatpure R D, Barnard E S, Cai W, Brongersma M L 2010 Phys. Rev. Lett. 104 243902 Google Scholar
[3]	Luk'yanchuk B, Zheludev N I, Maier S A, Halas N J, Nordlander P, Giessen H, Chong C T 2010 Nat. Mater. 9 707 Google Scholar
[4]	Zhao F, Lin J, Lei Z, Yi Z, Qin F, Zhang J, Liu L, Wu X, Yang W, Wu P 2022 Phys. Chem. Chem. Phys. 24 4871 Google Scholar
[5]	Lai G, Liang R S, Zhang Y J, Bian Z Y, Yi L X, Zhan G Z, Zhao R T 2015 Opt. Express 23 6554 Google Scholar
[6]	Wang B Y, Zeng Q D, Xiao S Y, Xu C, Xiong L B, Lv H, Du J, Yu H Q 2017 J. Phys. D: Appl. Phys. 50 455107 Google Scholar
[7]	王波云, 朱子豪, 高有康, 曾庆栋, 刘洋, 杜君, 王涛, 余华清 2022 物理学报 71 024201 Google Scholar Wang B Y, Zhu Z H, Gao Y K, Zeng Q D, Liu Y, Du J, Wang T, Yu H Q 2022 Acta Phys. Sin. 71 024201 Google Scholar
[8]	Zeng Y, Ling Z X, Liu G D, Wang L L, Lin Q 2022 Opt. Express 30 14103 Google Scholar
[9]	Zheng Z, Luo Y, Yang H, Yi Z, Zhang J, Song Q, Yang W, Liu C, Wu X, Wu P 2022 Phys. Chem. Chem. Phys. 24 8846 Google Scholar
[10]	Huang H L, Xia H, Guo Z B, Li H J, Xie D 2018 Opt. Commun. 424 163 Google Scholar
[11]	Zhang S, Genov D A, Wang Y, Liu M, Zhang X 2008 Phys. Rev. Lett. 101 047401 Google Scholar
[12]	Zhang T, Liu Q, Dan Y H, Yu S, Han X, Dai J, Xu K 2020 Opt. Express 28 18899 Google Scholar
[13]	Liu Z M, Zhang X, Zhang Z B, Gao E D, Zhou F Q, Hong J L, Luo X 2020 New J. Phys. 22 083006 Google Scholar
[14]	Zheng Z, Zheng Y, Luo Y, Yi Z, Zhang J, Liu Z, Yang W, Yu Y, Wu X, Wu P 2022 Phys. Chem. Chem. Phys. 24 2527 Google Scholar
[15]	Zhang X, Zhou F Q, Liu Z M, Zhang Z B, Qin Y P, Zhuo S S, Luo X, Gao E D, Li H J 2021 Opt. Express 29 29387 Google Scholar
[16]	Zentgraf T, Zhang S, Oulton R F, Zhang X 2009 Phys. Rev. B 80 195415 Google Scholar
[17]	Wu X, Zheng Y, Luo Y, Zhang J, Yi Z, Wu X, Cheng S, Yang W, Yu Y, Wu P 2021 Phys. Chem. Chem. Phys. 23 26864 Google Scholar
[18]	Lu H, Liu X, Mao D 2012 Phys. Rev. A 85 053803 Google Scholar
[19]	Han X, Wang T, Li X, Xiao S, Zhu Y 2015 Opt. Express 23 31945 Google Scholar
[20]	Saraswat V, Jacobberger R M, Arnold M S 2021 ACS Nano 15 3674 Google Scholar
[21]	Zhou F, Qin F, Yi Z, Yao W, Liu Z, Wu X, Wu P 2021 Phys. Chem. Chem. Phys. 23 17041 Google Scholar
[22]	Zhang T, Zhou J Z, Dai J, Dai Y T, Han X, Li J Q, Yin F F, Zhou Y, Xu K 2018 J. Phys. D: Appl. Phys. 51 055103 Google Scholar
[23]	Nikolaenko A E, Papasimakis N, Atmatzakis E, Luo Z, Shen Z X, Angelis F D, Boden S A, Fabrizio E D, Zheludev N I 2012 Appl. Phys. Lett. 100 181109 Google Scholar
[24]	Li X, Cai W, An J, Kim S, Nah J, Yang D, Piner R, Velamakanni A, Jung I, Tutuc E 2009 Science 324 1312 Google Scholar
[25]	Suk J W, Kitt A, Magnuson C W, Hao Y, Ahmed S, An J, Swan A K, Goldberg B B, Ruoff R S 2011 ACS Nano 5 6916 Google Scholar
[26]	Wu J B, Jin B B, Wan J, Liang L J, Zhang Y G, Jia T, Cao C H, Kang L, Xu W W, Chen J, Wu P H 2011 Appl. Phys. Lett. 99 161113 Google Scholar
[27]	Lu H, Liu X, Wang L, Gong Y, Mao D 2011 Opt. Express 19 2910 Google Scholar
[28]	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
[29]	Lei F, Gao M, Du C, Jing Q L, Long G L 2015 Opt. Express 23 11508 Google Scholar
[30]	Zhu Y, Hu X Y, Yang H, Gong Q H 2014 Sci. Rep. 104 211108 Google Scholar
[31]	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
[32]	Ren T X, Chen L 2019 Opt. Lett. 44 5446 Google Scholar
[33]	Ma Q L, Hong W Y, Shui L L 2022 Opt. Express 30 3055 Google Scholar
[34]	Wang B K, Guo T, Gai K, Yan F, Wang R X, Li L 2022 Appl. Opt. 61 3218 Google Scholar
[35]	Xu H, Xiong C X, Chen Z Q, Zheng M F, Zhao M Z, Zhang B H, Li H J 2018 J. Opt. Soc. Am. B 35 1463 Google Scholar
[36]	Han X, Wang T, Li X, Liu B, He Y, Tang J 2015 J. Phys. D:Appl. Phys. 48 235102 Google Scholar
[37]	Wang B Y, Zhu Y H, Zhang J, Zeng Q D, Du J, Wang T, Yu H Q 2020 Chin. Phys. B 29 084211 Google Scholar

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