Abstract

Miniaturizing optical devices with desired functionality is a key prerequisite for nanoscale photonic circuits. Based on Fano resonance, an on-chip high-sensitivity sensor, composed of two waveguides coupling with a symmetry breaking ring resonator, is theoretically and numerically investigated. The established theoretical model agrees well with the finite-difference time-domain simulations, which reveals the physics of Fano resonance. Differing with the coupled cavities, the Fano resonance originates from the interference between symmetry-mode and asymmetry-mode in a single symmetry-broken cavity. The spectral responses and sensing performances of the plasmonic structure rely on the degree of asymmetry of cavity. In particular, the plasmonic sensor can detect the refractive index changes as small as 10−5, and the figure of merit (FOM) of symmetry-breaking cavity structure is 17 times larger than that of symmetrical cavity system. Additionally, the sensitivity to temperature of ethanol analyte achieves 0.701 nm/C. Compared with the coupled cavities, the on-chip high-sensitivity sensor using a single cavity is more compact, which paves the way toward highly integrated photonic devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (6)

X. X. Niu, X. Y. Hu, Q. C. Yan, J. K. Zhu, H. T. Cheng, Y. F. Huang, C. C. Lu, Y. L. Fu, and Q. H. Gong, “Plasmon-induced transparency effect for ultracompact on-chip devices,” Nanophotonics 8(7), 1125–1149 (2019).
[Crossref]

C. X. Xiong, H. J. Li, H. Xu, M. Z. Zhao, B. H. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

B. Zhang, H. Li, H. Xu, M. Zhao, C. Xiong, C. Liu, and K. Wu, “Absorption and slow-light analysis based on tunable plasmon-induced transparency in patterned graphene metamaterial,” Opt. Express 27(3), 3598–3608 (2019).
[Crossref]

E. Gao, Z. Liu, H. Li, H. Xu, Z. Zhang, X. Luo, C. Xiong, C. Liu, B. Zhang, and F. Zhou, “Dynamically tunable dual plasmon-induced transparency and absorption based on a single-layer patterned graphene metamaterial,” Opt. Express 27(10), 13884–13894 (2019).
[Crossref]

Z. Yi, C. P. Liang, X. F. Chen, Z. G. Zhou, Y. J. Tang, X. Ye, Y. G. Yi, J. Q. Wang, and P. H. Wu, “Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application,” Micromachines 10(7), 443 (2019).
[Crossref]

M. Wang, M. Zhang, Y. Wang, R. Zhao, and S. Yan, “Fano resonance in an asymmetric MIM waveguide structure and its application in a refractive index nanosensor,” Sensors 19(4), 791 (2019).
[Crossref]

2018 (3)

D. V. Nesterenko, S. Hayashi, and Z. Sekkat, “Asymmetric surface plasmon resonances revisited as Fano resonances,” Phys. Rev. B 97(23), 235437 (2018).
[Crossref]

J. Chen, F. Gan, Y. Wang, and G. Li, “Plasmonic sensing and modulation based on Fano resonances,” Adv. Opt. Mater. 6(9), 1701152 (2018).
[Crossref]

C. Zhou, G. Liu, G. Ban, S. Li, Q. Huang, J. Xia, Y. Wang, and M. Zhan, “Tunable Fano resonator using multilayer graphene in the near-infrared region,” Appl. Phys. Lett. 112(10), 101904 (2018).
[Crossref]

2017 (7)

A. Li and W. Bogaerts, “Tunable electromagnetically induced transparency in integrated silicon photonics circuit,” Opt. Express 25(25), 31688–31695 (2017).
[Crossref]

Y. Deng, G. Cao, H. Yang, G. Li, X. Chen, and W. Lu, “Tunable and high-sensitivity sensing based on Fano resonance with coupled plasmonic cavities,” Sci. Rep. 7(1), 10639 (2017).
[Crossref]

S. Li, Y. Wang, R. Jiao, L. Wang, G. Duan, and L. Yu, “Fano resonances based on multimode and degenerate mode interference in plasmonic resonator system,” Opt. Express 25(4), 3525–3533 (2017).
[Crossref]

I. Haddouche and L. Cherbi, “Comparison of finite element and transfer matrix methods for numerical investigation of surface plasmon waveguides,” Opt. Commun. 382, 132–137 (2017).
[Crossref]

G. N. Tsigaridas, “A study on refractive index sensors based on optical micro-ring resonators,” Photonic Sens. 7(3), 217–225 (2017).
[Crossref]

Y. C. Liu, B. B. Li, and Y. F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6(5), 789–811 (2017).
[Crossref]

Z. Tu, D. Gao, M. Zhang, and D. Zhang, “High-sensitivity complex refractive index sensing based on Fano resonance in the subwavelength grating waveguide micro-ring resonator,” Opt. Express 25(17), 20911–20922 (2017).
[Crossref]

2016 (3)

Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
[Crossref]

S. Wang, L. Yan, Q. Xu, and S. Li, “A MIM filter based on a side-coupled crossbeam square-ring resonator,” Plasmonics 11(5), 1291–1296 (2016).
[Crossref]

K. Wen, Y. Hu, L. Chen, J. Zhou, L. Lei, and Z. Meng, “Single/Dual Fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

2015 (5)

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on Fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Z. Chen, L. Yu, L. Wang, G. Duan, Y. Zhao, and J. Xiao, “Sharp asymmetric line shapes in a plasmonic waveguide system and its application in nanosensor,” J. Lightwave Technol. 33(15), 3250–3253 (2015).
[Crossref]

Z. Zhang, F. Shi, and Y. Chen, “Tunable multichannel plasmonic filter based on coupling-induced mode splitting,” Plasmonics 10(1), 139–144 (2015).
[Crossref]

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Sci. Appl. 4(6), e294 (2015).
[Crossref]

Y. Huang, C. Min, P. Dastmalchi, and G. Veronis, “Slow-light enhanced subwavelength plasmonic waveguide refractive index sensors,” Opt. Express 23(11), 14922–14936 (2015).
[Crossref]

2014 (6)

J. Chen, C. Sun, and Q. Gong, “Fano resonances in a single defect nanocavity coupled with a plasmonic waveguide,” Opt. Lett. 39(1), 52–55 (2014).
[Crossref]

T. S. Wu, Y. M. Liu, Z. Y. Yu, Y. W. Peng, C. G. Shu, and H. Ye, “The sensing characteristics of plasmonic waveguide with a ring resonator,” Opt. Express 22(7), 7669–7677 (2014).
[Crossref]

N. Nozhat and N. Granpayeh, “All-optical nonlinear plasmonic ring resonator switches,” J. Mod. Opt. 61(20), 1690–1695 (2014).
[Crossref]

G. Cao, H. Li, Y. Deng, S. Zhan, Z. He, and B. Li, “Systematic theoretical analysis of selective-mode plasmonic filter based on aperture-side-coupled slot cavity,” Plasmonics 9(5), 1163–1169 (2014).
[Crossref]

L. Tong, H. Wei, S. Zhang, and H. Xu, “Recent advances in plasmonic sensors,” Sensors 14(5), 7959–7973 (2014).
[Crossref]

L. Xu, S. Wang, and L. Wu, “Refractive index sensing based on plasmonic waveguide side coupled with bilaterally located double cavities,” IEEE Trans. Nanotechnol. 13(5), 875–880 (2014).
[Crossref]

2013 (5)

2012 (2)

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett. 12(2), 602–609 (2012).
[Crossref]

H. Lu, X. Liu, D. Mao, and G. Wang, “Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators,” Opt. Lett. 37(18), 3780–3782 (2012).
[Crossref]

2010 (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

2009 (1)

2006 (2)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[Crossref]

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
[Crossref]

2004 (1)

W. Suh, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref]

1991 (1)

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Ban, G.

C. Zhou, G. Liu, G. Ban, S. Li, Q. Huang, J. Xia, Y. Wang, and M. Zhan, “Tunable Fano resonator using multilayer graphene in the near-infrared region,” Appl. Phys. Lett. 112(10), 101904 (2018).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref]

Bogaerts, W.

Boller, K. J.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[Crossref]

Cai, W.

Cao, G.

Y. Deng, G. Cao, H. Yang, G. Li, X. Chen, and W. Lu, “Tunable and high-sensitivity sensing based on Fano resonance with coupled plasmonic cavities,” Sci. Rep. 7(1), 10639 (2017).
[Crossref]

G. Cao, H. Li, Y. Deng, S. Zhan, Z. He, and B. Li, “Systematic theoretical analysis of selective-mode plasmonic filter based on aperture-side-coupled slot cavity,” Plasmonics 9(5), 1163–1169 (2014).
[Crossref]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[Crossref]

Chen, J.

J. Chen, F. Gan, Y. Wang, and G. Li, “Plasmonic sensing and modulation based on Fano resonances,” Adv. Opt. Mater. 6(9), 1701152 (2018).
[Crossref]

J. Chen, C. Sun, and Q. Gong, “Fano resonances in a single defect nanocavity coupled with a plasmonic waveguide,” Opt. Lett. 39(1), 52–55 (2014).
[Crossref]

Chen, L.

K. Wen, Y. Hu, L. Chen, J. Zhou, L. Lei, and Z. Meng, “Single/Dual Fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

Chen, X.

Y. Deng, G. Cao, H. Yang, G. Li, X. Chen, and W. Lu, “Tunable and high-sensitivity sensing based on Fano resonance with coupled plasmonic cavities,” Sci. Rep. 7(1), 10639 (2017).
[Crossref]

Chen, X. F.

Z. Yi, C. P. Liang, X. F. Chen, Z. G. Zhou, Y. J. Tang, X. Ye, Y. G. Yi, J. Q. Wang, and P. H. Wu, “Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application,” Micromachines 10(7), 443 (2019).
[Crossref]

Chen, Y.

Z. Zhang, F. Shi, and Y. Chen, “Tunable multichannel plasmonic filter based on coupling-induced mode splitting,” Plasmonics 10(1), 139–144 (2015).
[Crossref]

Chen, Z.

Cheng, H. T.

X. X. Niu, X. Y. Hu, Q. C. Yan, J. K. Zhu, H. T. Cheng, Y. F. Huang, C. C. Lu, Y. L. Fu, and Q. H. Gong, “Plasmon-induced transparency effect for ultracompact on-chip devices,” Nanophotonics 8(7), 1125–1149 (2019).
[Crossref]

Cherbi, L.

I. Haddouche and L. Cherbi, “Comparison of finite element and transfer matrix methods for numerical investigation of surface plasmon waveguides,” Opt. Commun. 382, 132–137 (2017).
[Crossref]

Dastmalchi, P.

Deng, Y.

Y. Deng, G. Cao, H. Yang, G. Li, X. Chen, and W. Lu, “Tunable and high-sensitivity sensing based on Fano resonance with coupled plasmonic cavities,” Sci. Rep. 7(1), 10639 (2017).
[Crossref]

G. Cao, H. Li, Y. Deng, S. Zhan, Z. He, and B. Li, “Systematic theoretical analysis of selective-mode plasmonic filter based on aperture-side-coupled slot cavity,” Plasmonics 9(5), 1163–1169 (2014).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref]

Duan, G.

Duan, G. Y.

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on Fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref]

Fan, S.

Fan, S. H.

W. Suh, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

Fang, Y.

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Sci. Appl. 4(6), e294 (2015).
[Crossref]

Feng, J.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett. 12(2), 602–609 (2012).
[Crossref]

Fu, Y. L.

X. X. Niu, X. Y. Hu, Q. C. Yan, J. K. Zhu, H. T. Cheng, Y. F. Huang, C. C. Lu, Y. L. Fu, and Q. H. Gong, “Plasmon-induced transparency effect for ultracompact on-chip devices,” Nanophotonics 8(7), 1125–1149 (2019).
[Crossref]

Gan, F.

J. Chen, F. Gan, Y. Wang, and G. Li, “Plasmonic sensing and modulation based on Fano resonances,” Adv. Opt. Mater. 6(9), 1701152 (2018).
[Crossref]

Gao, D.

Gao, E.

Gong, Q.

Gong, Q. H.

X. X. Niu, X. Y. Hu, Q. C. Yan, J. K. Zhu, H. T. Cheng, Y. F. Huang, C. C. Lu, Y. L. Fu, and Q. H. Gong, “Plasmon-induced transparency effect for ultracompact on-chip devices,” Nanophotonics 8(7), 1125–1149 (2019).
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S. Wang, L. Yan, Q. Xu, and S. Li, “A MIM filter based on a side-coupled crossbeam square-ring resonator,” Plasmonics 11(5), 1291–1296 (2016).
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[Crossref]

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M. Wang, M. Zhang, Y. Wang, R. Zhao, and S. Yan, “Fano resonance in an asymmetric MIM waveguide structure and its application in a refractive index nanosensor,” Sensors 19(4), 791 (2019).
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Y. Deng, G. Cao, H. Yang, G. Li, X. Chen, and W. Lu, “Tunable and high-sensitivity sensing based on Fano resonance with coupled plasmonic cavities,” Sci. Rep. 7(1), 10639 (2017).
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Ye, X.

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Z. Yi, C. P. Liang, X. F. Chen, Z. G. Zhou, Y. J. Tang, X. Ye, Y. G. Yi, J. Q. Wang, and P. H. Wu, “Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application,” Micromachines 10(7), 443 (2019).
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Yu, Z. Y.

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C. Zhou, G. Liu, G. Ban, S. Li, Q. Huang, J. Xia, Y. Wang, and M. Zhan, “Tunable Fano resonator using multilayer graphene in the near-infrared region,” Appl. Phys. Lett. 112(10), 101904 (2018).
[Crossref]

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G. Cao, H. Li, Y. Deng, S. Zhan, Z. He, and B. Li, “Systematic theoretical analysis of selective-mode plasmonic filter based on aperture-side-coupled slot cavity,” Plasmonics 9(5), 1163–1169 (2014).
[Crossref]

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Zhang, B. H.

Zhang, D.

Zhang, M.

M. Wang, M. Zhang, Y. Wang, R. Zhao, and S. Yan, “Fano resonance in an asymmetric MIM waveguide structure and its application in a refractive index nanosensor,” Sensors 19(4), 791 (2019).
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Zhang, Z.

Zhao, M.

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Zhao, R.

M. Wang, M. Zhang, Y. Wang, R. Zhao, and S. Yan, “Fano resonance in an asymmetric MIM waveguide structure and its application in a refractive index nanosensor,” Sensors 19(4), 791 (2019).
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Zhao, Y. F.

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on Fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

Zheng, M.

Zhou, C.

C. Zhou, G. Liu, G. Ban, S. Li, Q. Huang, J. Xia, Y. Wang, and M. Zhan, “Tunable Fano resonator using multilayer graphene in the near-infrared region,” Appl. Phys. Lett. 112(10), 101904 (2018).
[Crossref]

Zhou, F.

Zhou, J.

K. Wen, Y. Hu, L. Chen, J. Zhou, L. Lei, and Z. Meng, “Single/Dual Fano resonance based on plasmonic metal-dielectric-metal waveguide,” Plasmonics 11(1), 315–321 (2016).
[Crossref]

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Z. Yi, C. P. Liang, X. F. Chen, Z. G. Zhou, Y. J. Tang, X. Ye, Y. G. Yi, J. Q. Wang, and P. H. Wu, “Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application,” Micromachines 10(7), 443 (2019).
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X. X. Niu, X. Y. Hu, Q. C. Yan, J. K. Zhu, H. T. Cheng, Y. F. Huang, C. C. Lu, Y. L. Fu, and Q. H. Gong, “Plasmon-induced transparency effect for ultracompact on-chip devices,” Nanophotonics 8(7), 1125–1149 (2019).
[Crossref]

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
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Adv. Opt. Mater. (1)

J. Chen, F. Gan, Y. Wang, and G. Li, “Plasmonic sensing and modulation based on Fano resonances,” Adv. Opt. Mater. 6(9), 1701152 (2018).
[Crossref]

Appl. Phys. Lett. (1)

C. Zhou, G. Liu, G. Ban, S. Li, Q. Huang, J. Xia, Y. Wang, and M. Zhan, “Tunable Fano resonator using multilayer graphene in the near-infrared region,” Appl. Phys. Lett. 112(10), 101904 (2018).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Z. Chen, L. Yu, L. L. Wang, G. Y. Duan, Y. F. Zhao, and J. H. Xiao, “A refractive index nanosensor based on Fano resonance in the plasmonic waveguide system,” IEEE Photonics Technol. Lett. 27(16), 1695–1698 (2015).
[Crossref]

IEEE Trans. Nanotechnol. (1)

L. Xu, S. Wang, and L. Wu, “Refractive index sensing based on plasmonic waveguide side coupled with bilaterally located double cavities,” IEEE Trans. Nanotechnol. 13(5), 875–880 (2014).
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J. Lightwave Technol. (2)

J. Mod. Opt. (1)

N. Nozhat and N. Granpayeh, “All-optical nonlinear plasmonic ring resonator switches,” J. Mod. Opt. 61(20), 1690–1695 (2014).
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Light: Sci. Appl. (1)

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Sci. Appl. 4(6), e294 (2015).
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Mater. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[Crossref]

Micromachines (1)

Z. Yi, C. P. Liang, X. F. Chen, Z. G. Zhou, Y. J. Tang, X. Ye, Y. G. Yi, J. Q. Wang, and P. H. Wu, “Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application,” Micromachines 10(7), 443 (2019).
[Crossref]

Nano Lett. (1)

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett. 12(2), 602–609 (2012).
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Nanophotonics (2)

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the plasmonic structure. (a) 3-dimensional structure. (b) Equivalent theoretical model for Fig. 1(a).
Fig. 2.
Fig. 2. (a) The transmission spectrum of the structure with metal bar at θ = 0°. (b)–(d) Magnetic field distributions at wavelengths 919 nm, 1900nm, 2200 nm.
Fig. 3.
Fig. 3. (a) The transmission spectra of the plasmonic structure at different θ. (b)Evolution of the transmittance versus θ. (c)–(e) show the magnetic field (Hz) distributions, with θ = 15°, for λ = 907 nm (left peak), λ = 921 nm (dip), λ = 939 nm (right peak), respectively.
Fig. 4.
Fig. 4. (a) The transmission spectra versus the refractive index n with metal bar placed at θ = 75°. (b) Fano peak wavelengths versus refractive index n of the surrounding medium.
Fig. 5.
Fig. 5. (a) The FOM curve for the plasmonic symmetry-broken ring cavity system with θ = 15°. (b) The maximum value of FOM (MAX of FOM) around FR1 versus the position of metal bar θ. (c) The FOM curves for different ranges of refractive index with the metal bar at θ = 15°. (d) An enlarged view of the first Fano resonance. (e) The curves of FOM* for symmetrical cavity (blue line) and symmetry-breaking cavity (red line).
Fig. 6.
Fig. 6. (a) The transmission spectrum versus the temperature of ethanol. (b)The wavelengths of Fano peaks versus the temperature of ethanol.

Equations (9)

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t | a = i Ω | a Γ i | a Γ e | a + S + i n | K + S i n | K i M | a ,
S + o u t = S i n + K | a ,
S o u t = S + i n + K | ,
| a = ( a 1 a 2 a m ) ,   | K = ( κ 1 κ 2 κ m ) ,   K | = ( κ 1 κ 2 κ m ) ,
Ω = ( ω 11 ω 1 m ω m 1 ω m m ) , Γ i = ( γ i 11 γ i 1 m γ i m 1 γ i m m ) , Γ e = ( γ e 11 γ e 1 m γ e m 1 γ e m m ) , M = ( μ 11 μ 1 m μ m 1 μ m m ) .
I = | 1 τ ω 1 ( D 2 1 τ ω 1 ) j μ 12 1 τ ω 1 1 τ ω 2 + 1 τ ω 2 ( D 1 1 τ ω 2 ) j μ 21 1 τ ω 1 1 τ ω 2 D 1 D 2 + μ 12 μ 21 | 2 ,
F ( λ ) = F 0 [ q + 2 × ( 2 π c / 2 π c λ λ 2 π c / 2 π c λ 0 λ 0 ) / 2 × ( 2 π c / 2 π c λ λ 2 π c / 2 π c λ 0 λ 0 ) Γ Γ ] 2 1 + [ 2 × ( 2 π c / 2 π c λ λ 2 π c / 2 π c λ 0 λ 0 ) / 2 × ( 2 π c / 2 π c λ λ 2 π c / 2 π c λ 0 λ 0 ) Γ Γ ] 2 + A ( λ ) .
L O D = 0.02 S ,
n = 1.36048 3.94 × 10 4 ( T T 0 ) ,

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