Abstract

In this study, the dispersion equations of a graphene-coated nanowire (GN) are solved. It is found that in this waveguide, besides the surface plasmon polaritons (SPPs), there is another branch of guided modes, called photonic-like modes. The propagation distances of the photonic-like modes can be five orders of magnitude longer than those of the SPPs. Moreover, they can be modulated in the range of 10−4 to 1 m by changing the chemical potential of graphene. In particular, the mode field distributions remain nearly unchanged during the modulation. Based on the analysis performed using COMSOL Multiphysics, we further demonstrated that the propagation losses of the photonic-like modes are dependent on not only the chemical potential of graphene, but also the mode power proportion inside graphene. The photonic-like modes have tremendous potential to be used in optical switches, modulators, and switches in magnetic fields at the nanoscale.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (6)

S. Xu, X. Zou, B. Ma, J. Chen, L. Yu, and W. Zou, “Deep-learning-powered photonic analog-to-digital conversion,” Light: Sci. Appl. 8(1), 66–76 (2019).
[Crossref]

K. Chiba, A. Yoshida, K. Tomioka, and J. Motohisa, “Vertical InGaAs Nanowire Array Photodiodes on Si,” ACS Photonics 6(2), 260–264 (2019).
[Crossref]

P. Meng, D. Zhao, D. Zhong, and W. Liu, “Topological plasmonic modes in graphene-coated nanowire arrays,” Opt. Quantum Electron. 51(5), 156 (2019).
[Crossref]

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

D. Teng, K. Wang, Z. Li, and Y. Zhao, “Graphene-coated nanowire dimers for deep subwavelength waveguiding in mid-infrared range,” Opt. Express 27(9), 12458–12469 (2019).
[Crossref]

W. R. Wong and P. Berini, “Integrated multichannel Young’ s interferometer sensor based on long-range surface plasmon waveguides,” Opt. Express 27(18), 25470–25484 (2019).
[Crossref]

2018 (4)

S. Ye, Z. Wang, C. Sun, C. Dong, B. Wei, B. Wu, and S. Jian, “Plasmon-phonon-polariton modes and field enhancement in graphene-coated hexagon boron nitride nanowire pairs,” Opt. Express 26(18), 23854–23867 (2018).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

T. Cao, L. Tian, H. Liang, and K. R. Qin, “Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability,” Microsyst. Nanoeng. 4(1), 7–14 (2018).
[Crossref]

2017 (3)

2016 (7)

Y. Kou and J. Forstner, “Discrete plasmonic solitons in graphene-coated nanowire arrays,” Opt. Express 24(5), 4714–4721 (2016).
[Crossref]

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
[Crossref]

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

2015 (3)

B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field Enhancement and Gradient Force in the Graphene-Coated Nanowire Pairs,” Plasmonics 10(4), 839–845 (2015).
[Crossref]

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

B. Zhu, G. Ren, Y. Gao, Y. Yang, B. Wu, Y. Lian, and S. Jian, “Nanofocusing in the graphene-coated tapered nanowire infrared probe,” J. Opt. Soc. Am. B 32(5), 955–960 (2015).
[Crossref]

2014 (5)

2013 (1)

Z. Tong and S. Radic, “Low-noise optical amplification and signal processing in parametric devices,” Adv. Opt. Photonics 5(3), 318–384 (2013).
[Crossref]

2012 (1)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

2009 (1)

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

Alù, A.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Asselberghs, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Bao, Q.

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Belic, M. R.

M. Naserpour, C. J. Zapata-Rodriguez, S. M. Vukovic, H. Pashaeiadl, and M. R. Belic, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017).
[Crossref]

Berini, P.

Cao, T.

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

T. Cao, L. Tian, H. Liang, and K. R. Qin, “Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability,” Microsyst. Nanoeng. 4(1), 7–14 (2018).
[Crossref]

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

B. Chen, C. Meng, Z. Yang, W. Li, S. Lin, T. Gu, X. Guo, D. Wang, S. Yu, C. W. Wong, and L. Tong, “Graphene coated ZnO nanowire optical waveguides,” Opt. Express 22(20), 24276–24285 (2014).
[Crossref]

Chen, D.

Chen, J.

S. Xu, X. Zou, B. Ma, J. Chen, L. Yu, and W. Zou, “Deep-learning-powered photonic analog-to-digital conversion,” Light: Sci. Appl. 8(1), 66–76 (2019).
[Crossref]

Chiba, K.

K. Chiba, A. Yoshida, K. Tomioka, and J. Motohisa, “Vertical InGaAs Nanowire Array Photodiodes on Si,” ACS Photonics 6(2), 260–264 (2019).
[Crossref]

Contestabile, G.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Dai, D.

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Dong, C.

Fang, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Ferrari, A. C.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Forstner, J.

Gao, Y.

Goykhman, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Gu, T.

Guo, C.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Guo, X.

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

B. Chen, C. Meng, Z. Yang, W. Li, S. Lin, T. Gu, X. Guo, D. Wang, S. Yu, C. W. Wong, and L. Tong, “Graphene coated ZnO nanowire optical waveguides,” Opt. Express 22(20), 24276–24285 (2014).
[Crossref]

Han, Y.

Hu, G.

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
[Crossref]

Hu, Z.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Huang, J.

Huang, Y.

Huang, Z.

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Huyghebaert, C.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Jian, S.

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Kou, Y.

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Li, H.-J.

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

Li, I. L.

Y. Huang, L. Zhang, H. Yin, M. Zhang, H. Su, I. L. Li, and H. Liang, “Graphene-coated nanowires with a drop-shaped cross section for 10 nm confinement and 1 mm propagation,” Opt. Lett. 42(11), 2078–2081 (2017).
[Crossref]

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

Li, S.

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
[Crossref]

Li, W.

B. Chen, C. Meng, Z. Yang, W. Li, S. Lin, T. Gu, X. Guo, D. Wang, S. Yu, C. W. Wong, and L. Tong, “Graphene coated ZnO nanowire optical waveguides,” Opt. Express 22(20), 24276–24285 (2014).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Li, X.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Li, Y.

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

Li, Z.

Lian, Y.

Liang, H.

T. Cao, L. Tian, H. Liang, and K. R. Qin, “Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability,” Microsyst. Nanoeng. 4(1), 7–14 (2018).
[Crossref]

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

Y. Huang, L. Zhang, H. Yin, M. Zhang, H. Su, I. L. Li, and H. Liang, “Graphene-coated nanowires with a drop-shaped cross section for 10 nm confinement and 1 mm propagation,” Opt. Lett. 42(11), 2078–2081 (2017).
[Crossref]

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

Lin, Q.

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

Lin, S.

Liu, H.

Liu, J.-P.

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Liu, J.-Q.

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Liu, K.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Liu, L.

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Liu, W.

P. Meng, D. Zhao, D. Zhong, and W. Liu, “Topological plasmonic modes in graphene-coated nanowire arrays,” Opt. Quantum Electron. 51(5), 156 (2019).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Ma, B.

S. Xu, X. Zou, B. Ma, J. Chen, L. Yu, and W. Zou, “Deep-learning-powered photonic analog-to-digital conversion,” Light: Sci. Appl. 8(1), 66–76 (2019).
[Crossref]

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Meng, C.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

B. Chen, C. Meng, Z. Yang, W. Li, S. Lin, T. Gu, X. Guo, D. Wang, S. Yu, C. W. Wong, and L. Tong, “Graphene coated ZnO nanowire optical waveguides,” Opt. Express 22(20), 24276–24285 (2014).
[Crossref]

Meng, P.

P. Meng, D. Zhao, D. Zhong, and W. Liu, “Topological plasmonic modes in graphene-coated nanowire arrays,” Opt. Quantum Electron. 51(5), 156 (2019).
[Crossref]

Midrio, M.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Motohisa, J.

K. Chiba, A. Yoshida, K. Tomioka, and J. Motohisa, “Vertical InGaAs Nanowire Array Photodiodes on Si,” ACS Photonics 6(2), 260–264 (2019).
[Crossref]

Naserpour, M.

M. Naserpour, C. J. Zapata-Rodriguez, S. M. Vukovic, H. Pashaeiadl, and M. R. Belic, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017).
[Crossref]

Ott, A. K.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Pan, A.-L.

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Pashaeiadl, H.

M. Naserpour, C. J. Zapata-Rodriguez, S. M. Vukovic, H. Pashaeiadl, and M. R. Belic, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017).
[Crossref]

Qi, Z.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Qin, K.

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

Qin, K. R.

T. Cao, L. Tian, H. Liang, and K. R. Qin, “Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability,” Microsyst. Nanoeng. 4(1), 7–14 (2018).
[Crossref]

Qin, S.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Qiu, C.-W.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Radic, S.

Z. Tong and S. Radic, “Low-noise optical amplification and signal processing in parametric devices,” Adv. Opt. Photonics 5(3), 318–384 (2013).
[Crossref]

Ren, G.

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Romagnoli, M.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Ruan, S.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

Shen, Y. R.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Sorianello, V.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Su, H.

Y. Huang, L. Zhang, H. Yin, M. Zhang, H. Su, I. L. Li, and H. Liang, “Graphene-coated nanowires with a drop-shaped cross section for 10 nm confinement and 1 mm propagation,” Opt. Lett. 42(11), 2078–2081 (2017).
[Crossref]

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
[Crossref]

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

Sun, C.

S. Ye, Z. Wang, C. Sun, C. Dong, B. Wei, B. Wu, and S. Jian, “Plasmon-phonon-polariton modes and field enhancement in graphene-coated hexagon boron nitride nanowire pairs,” Opt. Express 26(18), 23854–23867 (2018).
[Crossref]

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Teng, D.

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Tian, L.

T. Cao, Y. Li, L. Tian, H. Liang, and K. Qin, “Fast Switching “On/Off” Chiral Surface Plasmon Polaritons in Graphene-Coated Ge2Sb2Te5 Nanowire,” ACS Appl. Nano Mater. 1(2), 759–767 (2018).
[Crossref]

T. Cao, L. Tian, H. Liang, and K. R. Qin, “Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability,” Microsyst. Nanoeng. 4(1), 7–14 (2018).
[Crossref]

Tomioka, K.

K. Chiba, A. Yoshida, K. Tomioka, and J. Motohisa, “Vertical InGaAs Nanowire Array Photodiodes on Si,” ACS Photonics 6(2), 260–264 (2019).
[Crossref]

Tong, L.

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

B. Chen, C. Meng, Z. Yang, W. Li, S. Lin, T. Gu, X. Guo, D. Wang, S. Yu, C. W. Wong, and L. Tong, “Graphene coated ZnO nanowire optical waveguides,” Opt. Express 22(20), 24276–24285 (2014).
[Crossref]

Tong, Z.

Z. Tong and S. Radic, “Low-noise optical amplification and signal processing in parametric devices,” Adv. Opt. Photonics 5(3), 318–384 (2013).
[Crossref]

Tu, L.

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Van Campenhout, J.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Vukovic, S. M.

M. Naserpour, C. J. Zapata-Rodriguez, S. M. Vukovic, H. Pashaeiadl, and M. R. Belic, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017).
[Crossref]

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Wang, D.

Wang, H.

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Wang, J.

B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field Enhancement and Gradient Force in the Graphene-Coated Nanowire Pairs,” Plasmonics 10(4), 839–845 (2015).
[Crossref]

Y. Gao, G. Ren, B. Zhu, J. Wang, and S. Jian, “Single-mode graphene-coated nanowire plasmonic waveguide,” Opt. Lett. 39(20), 5909–5912 (2014).
[Crossref]

Wang, K.

Wang, L.-L.

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

Wang, Z.

S. Ye, Z. Wang, C. Sun, C. Dong, B. Wei, B. Wu, and S. Jian, “Plasmon-phonon-polariton modes and field enhancement in graphene-coated hexagon boron nitride nanowire pairs,” Opt. Express 26(18), 23854–23867 (2018).
[Crossref]

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Wei, B.

Wen, S.-C.

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Wong, C. W.

Wong, W. R.

Wu, B.

Wu, H.

H. Wu, Q. Bao, X. Guo, D. Dai, and L. Tong, “Low-loss photonic-like guided mode in metal-supported optical nanofibers,” Appl. Phys. Lett. 114(3), 031104 (2019).
[Crossref]

Xia, S.-X.

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Xiao, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Xie, F.

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

Xin, H.

Xu, S.

S. Xu, X. Zou, B. Ma, J. Chen, L. Yu, and W. Zou, “Deep-learning-powered photonic analog-to-digital conversion,” Light: Sci. Appl. 8(1), 66–76 (2019).
[Crossref]

Xu, W.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Xu, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Yang, J.

Yang, Y.

Yang, Z.

Ye, S.

Yin, H.

Yoshida, A.

K. Chiba, A. Yoshida, K. Tomioka, and J. Motohisa, “Vertical InGaAs Nanowire Array Photodiodes on Si,” ACS Photonics 6(2), 260–264 (2019).
[Crossref]

Yu, L.

S. Xu, X. Zou, B. Ma, J. Chen, L. Yu, and W. Zou, “Deep-learning-powered photonic analog-to-digital conversion,” Light: Sci. Appl. 8(1), 66–76 (2019).
[Crossref]

Yu, S.

Yuan, X.

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

Zapata-Rodriguez, C. J.

M. Naserpour, C. J. Zapata-Rodriguez, S. M. Vukovic, H. Pashaeiadl, and M. R. Belic, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017).
[Crossref]

Zhai, X.

J.-P. Liu, X. Zhai, L.-L. Wang, H.-J. Li, F. Xie, Q. Lin, and S.-X. Xia, “Analysis of Mid-Infrared Surface Plasmon Modes in a Graphene-Based Cylindrical Hybrid Waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

S.-X. Xia, X. Zhai, L.-L. Wang, J.-P. Liu, H.-J. Li, J.-Q. Liu, A.-L. Pan, and S.-C. Wen, “Excitation of surface plasmons in graphene-coated nanowire arrays,” J. Appl. Phys. 120(10), 103104 (2016).
[Crossref]

Zhan, P.

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Zhang, C.

C. Zhang, L. Tu, Z. Huang, L. Liu, P. Zhan, C. Sun, and Z. Wang, “An electrically tunable plasmonic optical modulator with high modulation depth based on graphene-wrapped silver nanowire,” J. Opt. 18(12), 125007 (2016).
[Crossref]

Zhang, J.

J. Yang, H. Xin, Y. Han, D. Chen, J. Zhang, J. Huang, and Z. Zhang, “Ultra-compact beam splitter and filter based on a graphene plasmon waveguide,” Appl. Opt. 56(35), 9814–9821 (2017).
[Crossref]

Z. Qi, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Electrically tuneable directional coupling and switching based on multimode interference effect in dielectric loaded graphene plasmon waveguides,” J. Opt. 18(6), 065003 (2016).
[Crossref]

H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
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Y. Huang, L. Zhang, H. Yin, M. Zhang, H. Su, I. L. Li, and H. Liang, “Graphene-coated nanowires with a drop-shaped cross section for 10 nm confinement and 1 mm propagation,” Opt. Lett. 42(11), 2078–2081 (2017).
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H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
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P. Meng, D. Zhao, D. Zhong, and W. Liu, “Topological plasmonic modes in graphene-coated nanowire arrays,” Opt. Quantum Electron. 51(5), 156 (2019).
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H. Wang, H. Zhao, G. Hu, S. Li, H. Su, and J. Zhang, “Graphene Based Surface Plasmon Polariton Modulator Controlled by Ferroelectric Domains in Lithium Niobate,” Sci. Rep. 5(1), 18258 (2016).
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P. Meng, D. Zhao, D. Zhong, and W. Liu, “Topological plasmonic modes in graphene-coated nanowire arrays,” Opt. Quantum Electron. 51(5), 156 (2019).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of the GN cross-section and coordinate system. (b) Normalized time-averaged Poynting vectors $\left\langle {{S_Z}} \right\rangle$ of the TM, TE, and EH modes, respectively. (c) The amplitudes and polarizations of these modes. Wavelength of the incident light $\lambda {\kern 1pt} {\kern 1pt} = {\kern 1pt} {\kern 1pt} 1.55{\kern 1pt} {\kern 1pt} \mu {\textrm{m}}$.
Fig. 2.
Fig. 2. Dependences of (a) effective refractive index and (b) mode loss on the chemical potential of graphene. The solid lines show the calculation results obtained by solving the dispersion equations. The dots, triangles, and rectangles on the solid lines are the calculation results obtained using COMSOL. (The above scheme is also used in Figs. 35).
Fig. 3.
Fig. 3. Dependences of (a) effective refractive index, (b) mode loss, and (c) mode power proportion inside graphene on the relative permittivity of the nanowire.
Fig. 4.
Fig. 4. Dependences of (a) effective refractive index and (b) mode loss on the cross-sectional radius of the nanowire.
Fig. 5.
Fig. 5. Dependences of (a) effective refractive index and (b) mode loss on the wavelength.

Equations (7)

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σ g ( ω , μ c , Γ , T ) = σ intra ( ω , μ c , Γ , T ) + σ inter ( ω , μ c , Γ , T ) ,
σ intra ( ω , μ c , Γ , T ) = i e 2 k B T π 2 ( ω + i 2 Γ ) { μ c k B T + 2 ln [ exp ( μ c k B T ) + 1 ] } , and
σ inter ( ω , μ c , Γ , T ) = 0 i e 2 ( ω + i 2 Γ ) π 2 [ exp ( Ω μ c k B T ) + 1 ] 1 [ exp ( Ω μ c k B T ) + 1 ] 1 ( ω + i 2 Γ ) 2 4 ( Ω / ) 2 d Ω
1 h 1 h 2 I m ( h 1 a ) I m ( h 1 a ) K m ( h 2 a ) K m ( h 2 a ) i ω ε 0 σ g h 1 k 0 2 I m ( h 1 a ) I m ( h 1 a ) + i ω ε 0 σ g k 0 2 h 2 K m ( h 2 a ) K m ( h 2 a ) 1 h 2 K m ( h 2 a ) K m ( h 2 a ) + i ω ε 0 ( ε 2 ε 1 ) σ g h 2 2 × i β 2 m 2 σ g ω ε 0 h 1 2 h 2 2 a 2 + ε 1 h 1 I m ( h 1 a ) I m ( h 1 a ) ε 2 h 2 K m ( h 2 a ) K m ( h 2 a ) + i σ g ω ε 0 i σ g ω ε 0 h 1 I m ( h 1 a ) I m ( h 1 a ) ε 2 ε 1 h 1 2 = ( m β h 1 h 2 a ) 2
i ω ε 0 [ ε 1 h 1 I 1 ( h 1 a ) I 0 ( h 1 a ) + ε 2 h 2 K 1 ( h 2 a ) K 0 ( h 2 a ) ] = σ g and
i ω ε 0 k 0 2 [ h 1 I 0 ( h 1 a ) I 1 ( h 1 a ) + h 2 K 0 ( h 2 a ) K 1 ( h 2 a ) ] = σ g .
1 4 h 1 h 2 I 0 ( h 1 a ) + I 2 ( h 1 a ) I 1 ( h 1 a ) K 0 ( h 2 a ) + K 2 ( h 2 a ) K 1 ( h 2 a ) + i ω ε 0 2 σ g h 1 k 0 2 I 0 ( h 1 a ) + I 2 ( h 1 a ) I 1 ( h 1 a ) + i ω ε 0 2 σ g k 0 2 h 2 K 0 ( h 2 a ) + K 2 ( h 2 a ) K 1 ( h 2 a ) 1 2 h 2 K 0 ( h 2 a ) + K 2 ( h 2 a ) K 1 ( h 2 a ) i ω ε 0 ( ε 2 ε 1 ) σ g h 2 2 × i σ g β 2 ω ε 0 h 1 2 h 2 2 a 2 + i σ g ω ε 0 + ε 1 2 h 1 I 0 ( h 1 a ) + I 2 ( h 1 a ) I 1 ( h 1 a ) + ε 2 2 h 2 K 0 ( h 2 a ) + K 2 ( h 2 a ) K 1 ( h 2 a ) i σ g 2 ω ε 0 h 1 I 0 ( h 1 a ) + I 2 ( h 1 a ) I 1 ( h 1 a ) ( ε 2 ε 1 ) h 1 2 = ( β h 1 h 2 a ) 2