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Based on the diffraction principle and the mode coupling theory, a composite micro-nano structure of sub-wavelength dielectric grating/metal-dielectric-metal (MDM) waveguide/periodic photonic crystal is proposed. Combined with the angle spectrum of reflection, the transmission characteristics of the surface plasmon polaritons and the generation mechanism of double Fano resonances at different incident angles and fixed wavelength are analyzed. The studies show that the physical mechanism of double Fano resonances is that the surface plasmon resonance generated at the interface of sub-wavelength dielectric grating and upper metal Ag film, and the waveguide mode resonance occurring in the MDM waveguide, provide the independently tunable double discrete states, under the condition of satisfying wave vector matching, which can be respectively coupled in the near field with the continuous state formed by the photonic band gap effect in the photonic crystal, thereby achieving the double Fano resonances. Then the influence of the structural parameters on the double Fano characteristics is analyzed quantitatively, and the evolution law of the double Fano resonances is explored by the change of the reflection spectra of resonance curves. The results show that the tuning between double Fano resonance curves and the resonance angles can be realized by changing the structural parameters. And under optimal conditions, the figure of merit (FOM) values of FR a and FR b in resonance A region can be as high as 460.0 and
$ 4.00 \times {10^4} $ , and the FOM values of FR a and FR b in resonance B region can be as high as 269.2 and$ 2.22 \times {10^4} $ . The structure can provide an effective theoretical reference for designing the refractive index sensors based on Fano resonances.-
Keywords:
- diffraction principle /
- mode coupling /
- surface plasmon polaritons /
- double Fano resonances
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[9] Wang J Y, Wang Q, Li Y, Chen P, Huang T, Dai B, Huang Y S, Zhang D W 2016 J. Opt. 45 302
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[10] Zhao Y, Huo Y Y, Man B Y, Ning T Y 2019 Plasmonics 14 1911
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[11] Suresh R, Rao K D, Udupa D V, Kumar S, Prathap C, Sahoo N K 2017 Optik 136 112
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[12] Trabelsi Y, Ali N B, Belhadj W, Kanzari M 2019 J. Supercond. Novel Magn. 32 3541
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[14] Chen Y W, Bian L A, Liu P G, Li G S, Xie Y C 2018 Superlattice Microstruct. 124 185
Google Scholar
[15] Jiang H D, Zheng G G, Rao W F 2019 Results Phys. 13 102173
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[16] Zhao T G, Yu S L 2018 Plasmonics 13 1115
Google Scholar
[17] Gao H, Li P L, Yang S D 2020 Opt. Commun. 457 124688
Google Scholar
[18] 陈颖, 谢进朝, 周鑫德, 张灿, 杨惠, 李少华 2019 68 237301
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[19] Zhang J, Zhang X P 2015 Opt. Express 23 30429
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Google Scholar
[21] Yi X C, Tian J P, Yang R C 2018 Eur. Phys. J. D 72 60
Google Scholar
[22] Wen K H, Hu Y H, Chen L, Zhou J Y, Lei L, Meng Z M 2016 Plasmonics 11 315
Google Scholar
[23] Keleshtery M H, Mir A, Kaatuzian H 2018 Plasmonics 13 1523
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Google Scholar
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图 1 复合结构模型图
Figure 1. Composite structure model diagram.
图 2 结构曲线图 (a) 连续态光谱图; (b) 连续态角谱图; (c) 双离散态角谱图; (d) 相位角谱图; (e) 双Fano共振形成角谱图
Figure 2. Structural diagram: (a) Continuous spectrum; (b) continuous state angular spectrum diagram; (c) double discrete states angular spectrum diagram; (d) phase angular spectrum diagram; (e) double Fano resonances form angular spectrum diagram.
图 3 N对双Fano特性的影响 (a) N对连续态曲线的影响; (b) N对双Fano曲线的影响; (c) N对FOM值的影响
Figure 3. Effect of N on characteristics of double Fano resonances: (a) Effect of N on the continuous state curves; (b) effect of N on the double Fano curves; (c) effect of N on FOM values.
图 4
$ {d_{\rm{Ag}}} $ 对双Fano特性的影响 (a)$ {d_{\rm{Ag}}} $ 对双Fano曲线的影响; (b)$ {d_{{\rm{Ag}}}} $ 对FOM值的影响Figure 4. Effect of
$ {d_{{\rm{Ag}}}} $ on characteristics of double Fano resonances: (a) Effect of$ {d_{{\rm{Ag}}}} $ on the double Fano curves; (b) effect of$ {d_{\rm{A}}}_{\rm{g}} $ on FOM values.
图 5 W对共振A区Fano特性的影响 (a) W对FR a曲线的影响; (b) W对FOM值的影响
Figure 5. Effect of W on Fano characteristics of resonance region A: (a) Effect of W on FR a curve; (b) effect of W on FOM values.
图 6
$ {d_z} $ 对共振B区Fano特性的影响 (a)$ {d_z} $ 对FR b曲线的影响; (b)$ {d_z} $ 对FOM值的影响Figure 6. Effect of
$ {d_z} $ on Fano characteristics of resonance region B: (a) Effect of$ {d_z} $ on FR b curve; (b) effect of$ {d_z} $ on FOM values. -
[1] Takashima Y, Haraguchi M, Naoi Y 2019 Opt. Rev. 26 466
Google Scholar
[2] Li L X, Liang Y Z, Lu M D, Peng W 2016 Plasmonics 11 139
Google Scholar
[3] Panda A, Pukhrambam P D 2021 Opt. Quantum Electron. 53 357
Google Scholar
[4] Ji C G, Yang C Y, Shen W D, Lee K T, Zhang Y G, Liu X, Guo L J 2019 Nano Res. 12 543
Google Scholar
[5] Liang C P, Yi Z, Chen X F, Tang Y J, Yi Y, Zhou Z G, Wu X G, Huang Z, Yi Y G, Zhang G F 2020 Plasmonics 15 93
Google Scholar
[6] 祁云平, 张婷, 郭嘉, 张宝和, 王向贤 2020 69 167301
Google Scholar
Qi Y P, Zhang T, Guo J, Zhang B H, Wang X X 2020 Acta Phys. Sin. 69 167301
Google Scholar
[7] Yu J, Men H J, Zhang J W, Zhang X W, Tian N 2020 J. Electron. Mater. 49 4469
Google Scholar
[8] Bellucci S, Fitio V, Yaremchuk I, Vernyhor O, Bendziak A, Bobitski Y 2020 Symmetry 12 1315
Google Scholar
[9] Wang J Y, Wang Q, Li Y, Chen P, Huang T, Dai B, Huang Y S, Zhang D W 2016 J. Opt. 45 302
Google Scholar
[10] Zhao Y, Huo Y Y, Man B Y, Ning T Y 2019 Plasmonics 14 1911
Google Scholar
[11] Suresh R, Rao K D, Udupa D V, Kumar S, Prathap C, Sahoo N K 2017 Optik 136 112
Google Scholar
[12] Trabelsi Y, Ali N B, Belhadj W, Kanzari M 2019 J. Supercond. Novel Magn. 32 3541
Google Scholar
[13] Klimov V V, Pavlov A A, Treshin L V, Zabkov L V 2017 J. Phys. D: Appl. Phys. 50 285101
Google Scholar
[14] Chen Y W, Bian L A, Liu P G, Li G S, Xie Y C 2018 Superlattice Microstruct. 124 185
Google Scholar
[15] Jiang H D, Zheng G G, Rao W F 2019 Results Phys. 13 102173
Google Scholar
[16] Zhao T G, Yu S L 2018 Plasmonics 13 1115
Google Scholar
[17] Gao H, Li P L, Yang S D 2020 Opt. Commun. 457 124688
Google Scholar
[18] 陈颖, 谢进朝, 周鑫德, 张灿, 杨惠, 李少华 2019 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
[19] Zhang J, Zhang X P 2015 Opt. Express 23 30429
Google Scholar
[20] Bahrami F, Aitchison J S, Mojahedi M 2015 IEEE Photon. J. 7 1
Google Scholar
[21] Yi X C, Tian J P, Yang R C 2018 Eur. Phys. J. D 72 60
Google Scholar
[22] Wen K H, Hu Y H, Chen L, Zhou J Y, Lei L, Meng Z M 2016 Plasmonics 11 315
Google Scholar
[23] Keleshtery M H, Mir A, Kaatuzian H 2018 Plasmonics 13 1523
Google Scholar
[24] Zhang J J, Yang J B, Liang L M, Wu W J 2018 Opt. Commun. 407 46
Google Scholar
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