Abstract

We theoretically investigate the transport property of graphene surface plasmon polaritons (GSPPs) on curved graphene substrates. The dispersion relationship, propagation length, and field confinement are calculated by an analytical method and compared with those on planar substrates. Based on our theory, the bend of graphene nearly does not affect the property of GSPPs except for an extremely small shift to the lower frequency for the same effective mode index. The field distributions and the eigenfrequencies of GSPPs on planar and cylindrical substrates are calculated by the finite element method, which validates our theoretical analysis. Moreover, three types of graphene-guided optical interconnections of GSPPs, namely, planar to curved graphene film, curved to planar graphene film, and curved to curved graphene film, are proposed and examined in detail. The theoretical results show that the GSPPs propagation on curved graphene substrates and interconnections will not induce any additional losses if the phase-matching condition is satisfied. Additionally, the extreme tiny size of curved graphene for interconnection at a certain spectra range is predicted by our theory and validated by the simulation of 90° turning of GSPPs. The bending effect on the property of GSPPs is systematically analyzed and identified. Our studies would be helpful to instruct design of plasmonic devices involving curved GSPPs, such as nanophotonic circuits, flexible plasmonic, and biocompatible devices.

© 2015 Chinese Laser Press

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References

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2015 (1)

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110, 14001 (2015).
[Crossref]

2014 (2)

Y. G. Chen, Y. H. Chen, and Z. Y. Li, “Direct method to control surface plasmon polaritons on metal surfaces,” Opt. Lett. 39, 339–342 (2014).
[Crossref]

X. Y. He and R. Li, “Comparison of graphene-based transverse magnetic and electric surface plasmon modes,” IEEE J. Sel. Top. Quantum Electron. 20, C1 (2014).
[Crossref]

2013 (6)

Y.-H. Chen, M. Zhang, L. Gan, X. Wu, L. Sun, J. Liu, J. Wang, and Z.-Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21, 17558–17566 (2013).
[Crossref]

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

W. B. Lu, W. Zhu, H. J. Xu, Z. H. Ni, Z. G. Dong, and T. J. Cui, “Flexible transformation plasmonics using graphene,” Opt. Express 21, 10475–10482 (2013).
[Crossref]

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

X. L. Zhu, W. Yan, N. A. Mortensen, and S. S. Xiao, “Bends and splitters in graphene nanoribbon waveguides,” Opt. Express 21, 3486–3491 (2013).
[Crossref]

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103, 133104 (2013).
[Crossref]

2012 (4)

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
[Crossref]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

2011 (5)

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

2010 (2)

2007 (2)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref]

2003 (1)

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

Aksu, S.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Altug, H.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Andersen, D. R.

Artar, A.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Avouris, P.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Barnes, W. L.

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

Bechtel, H. A.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Boudouris, B. W.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Capasso, F.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Chandra, B.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Chen, C. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Chen, Y. G.

Chen, Y. H.

Chen, Y.-H.

Y.-H. Chen, M. Zhang, L. Gan, X. Wu, L. Sun, J. Liu, J. Wang, and Z.-Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21, 17558–17566 (2013).
[Crossref]

Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
[Crossref]

Chu, H. S.

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Crommie, M. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Cui, T. J.

de Abajo, F. J. G.

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Dereux, A.

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

Dokmeci, M. R.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Dong, Z. G.

Ebbesen, T. W.

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

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

Fal’ko, V. I.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Forati, E.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103, 133104 (2013).
[Crossref]

Freitag, M.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Gan, L.

Y.-H. Chen, M. Zhang, L. Gan, X. Wu, L. Sun, J. Liu, J. Wang, and Z.-Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21, 17558–17566 (2013).
[Crossref]

Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
[Crossref]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref]

Gellert, P. R.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Genevet, P.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

Geng, B. S.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Girit, C.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

Guo, H. L.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Hanson, G. W.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103, 133104 (2013).
[Crossref]

Hao, Z.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

He, X. Y.

X. Y. He and R. Li, “Comparison of graphene-based transverse magnetic and electric surface plasmon modes,” IEEE J. Sel. Top. Quantum Electron. 20, C1 (2014).
[Crossref]

Horng, J.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Huang, L.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
[Crossref]

Huang, M.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Ju, L.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Kats, M. A.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

Kim, K.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Koh, W. S.

Kong, J.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Li, E. P.

Li, J. F.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

Li, Q.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

Li, R.

X. Y. He and R. Li, “Comparison of graphene-based transverse magnetic and electric surface plasmon modes,” IEEE J. Sel. Top. Quantum Electron. 20, C1 (2014).
[Crossref]

Li, X. S.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Li, Z. Y.

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110, 14001 (2015).
[Crossref]

Y. G. Chen, Y. H. Chen, and Z. Y. Li, “Direct method to control surface plasmon polaritons on metal surfaces,” Opt. Lett. 39, 339–342 (2014).
[Crossref]

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Li, Z.-Y.

Y.-H. Chen, M. Zhang, L. Gan, X. Wu, L. Sun, J. Liu, J. Wang, and Z.-Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21, 17558–17566 (2013).
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Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
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Liang, X. G.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Liu, J.

Liu, S. Y.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
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Martin, M.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Meng, Z. M.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
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Ni, Z. H.

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
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A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

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K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
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S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
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V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
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L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Shi, Z.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

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Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
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Tulevski, G.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

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A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
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S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

Wang, F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
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L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Wu, X.

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H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

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H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

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Xu, H. J.

Xu, H. X.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

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H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Yan, W.

Yanik, A. A.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Yao, Y.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref]

Yu, N. F.

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
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Zettl, A.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Zhang, M.

Zhu, W.

Zhu, W. J.

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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Zhu, X. L.

Adv. Mater. (1)

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23, 4422–4430 (2011).
[Crossref]

Appl. Phys. Lett. (1)

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103, 133104 (2013).
[Crossref]

Europhys. Lett. (1)

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110, 14001 (2015).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Y. He and R. Li, “Comparison of graphene-based transverse magnetic and electric surface plasmon modes,” IEEE J. Sel. Top. Quantum Electron. 20, C1 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous excitation and emission enhancement of fluorescence assisted by double plasmon modes of gold nanorods,” J. Phys. Chem. C 117, 10636–10642 (2013).
[Crossref]

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Light Sci. Appl. (1)

Y.-H. Chen, L. Huang, L. Gan, and Z.-Y. Li, “Wavefront shaping of infrared light through a subwavelength hole,” Light Sci. Appl. 1, e26 (2012).
[Crossref]

Nano Lett. (2)

Y. Yao, M. A. Kats, P. Genevet, N. F. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
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F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref]

Nat. Nanotechnol. (2)

H. G. Yan, X. S. Li, B. Chandra, G. Tulevski, Y. Q. Wu, M. Freitag, W. J. Zhu, P. Avouris, and F. N. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Nat. Photonics (1)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

Nature (3)

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

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Science (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Schematic of the theoretical model for GSPPs transporting on graphene deposited on a cylindrical substrate.
Fig. 2.
Fig. 2. GSPP magnetic field ( H z ) distributions of first six order modes on cylindrical substrate. Radius of the cylindrical substrate is 50 nm.
Fig. 3.
Fig. 3. (a) Dispersion relationship, (b) propagation length, and (c) decay lengths in air and (d) substrate of GSPP on planar substrate and on cylindrical substrates whose radii are 500, 50, and 5 nm, as illustrated. Discrete points of each color, which represent the correspondent values of GSPP on the cylindrical substrates with different radii, are the first 20 order modes.
Fig. 4.
Fig. 4. GSPPs magnetic field ( H z ) distributions at the same eigenfrequency on the cylindrical substrates with different radii. (a) and (b), respectively, correspond to 81.5 and 92.7 THz. Radius of the cylindrical substrate on the right is 50 nm, which is twice that of the left one in both (a) and (b).
Fig. 5.
Fig. 5. Comparison of the GSPP magnetic field ( H z ) distributions of the same GSPP wavelength ( λ GSPP ) on the planar and cylindrical substrates. Lengths of graphene on the planar and cylindrical substrates are equal. Radius of the cylindrical substrate is 5 nm. Frequency is (a) 194.3 and (b) 194.4 THz.
Fig. 6.
Fig. 6. GSPP magnetic field ( H z ) distributions on planar and curved graphene films excited by the electric dipoles with different frequencies. (a) and (b) are excited at 110 THz, while (c) and (d) are excited at 120 THz. Lengths of planar and curved graphene films are equal. Curvature radius of the curved graphene film is 50 nm.
Fig. 7.
Fig. 7. Comparison of GSPP propagating on (a) U-shaped and (b) planar graphene films. GSPPs in (a) and (b) are excited by the electric dipoles with the frequency of 199 THz. Length of U-shaped graphene film is equal to that of the planar. Curvature radius of the curved part in a U-shaped film is 50 nm. (c) GSPP transmission spectra of these two shapes of graphene films.
Fig. 8.
Fig. 8. Comparison of GSPP propagating on (a) S-shaped and (b) planar graphene films. GSPPs in (a) and (b) are excited by the electric dipoles with the frequency of 199 THz. Length of S-shaped graphene film is equal to that of the planar. The curvature radii of the two curved graphene films connected in an S shape are 35 and 70 nm. (c) GSPP transmission spectra of GSPPs on these two shapes of graphene films.
Fig. 9.
Fig. 9. Comparison of GSPP propagating on (a) G shape and (b) graphene films. GSPPs in (a) and (b) are excited by the electric dipoles with the frequency of 199 THz. Length of G-shaped graphene film is equal to that of the planar. The curvature radii of the two curved graphene films connected in the G shape are 35 and 70 nm. (c) GSPP transmission spectra of GSPPs on these two shapes of graphene films.
Fig. 10.
Fig. 10. Realization of 90° turning of GSPP by utilizing curved graphene. GSPPs in panels (a) and (b) are excited by the electric dipoles with the frequency of 198 THz. Curvature radius of the quarter-circle-shaped graphene film that is used to interconnect the two planar films is 10 nm in panel (a). As a comparison, the transport of GSPPS on a planar graphene film with the equal length to that of the L shape is illustrated in panel (b). (c) GSPP transmission spectra of these two shapes of graphene films.

Equations (7)

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H c z = m n = G n J n ( m k 0 r ) · e i n ϕ , E c r = 1 i ω ε m r H c z ϕ = n m ω ε m r n = G n J n ( m k 0 r ) · e i n ϕ , E c ϕ = 1 i ω ε m H c z r = k 0 i ω ε 0 n = G n J n ( m k 0 r ) · e i n ϕ ,
H s z = n = F n H n ( k 0 r ) · e i n ϕ , E s r = 1 i ω ε 0 r H s z ϕ = n ω ε 0 r n = F n H n ( k 0 r ) · e i n ϕ , E s ϕ = 1 i ω ε 0 H s z r = k 0 i ω ε 0 n = F n H n ( k 0 r ) · e i n ϕ ,
e ^ r × ( E⃗ s ϕ E⃗ c ϕ ) = 0 , e ^ r × ( H ^ s z H ^ c z ) = σ E⃗ c ϕ ,
( k 0 i ω ε 0 H n ( k 0 r ) k 0 i ω ε 0 J n ( m k 0 r ) H n ( k 0 r ) σ k 0 i ω ε 0 J n ( m k 0 r ) m J n ( m k 0 r ) ) ( F n G n ) = 0 .
| k 0 i ω ε 0 H n ( k 0 r ) k 0 i ω ε 0 J n ( m k 0 r ) H n ( k 0 r ) σ k 0 i ω ε 0 J n ( m k 0 r ) m J n ( m k 0 r ) | = 0 .
m J n ( m k 0 a ) J n ( m k 0 a ) H n ( k 0 a ) H n ( k 0 a ) + i σ k 0 ω ε 0 = 0 ,
ε 0 k 0 2 k 2 ε 0 + ε m k 0 2 k 2 ε m + i σ ω ε 0 = 0 ,

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