Abstract

Surface plasmon modes at terahertz-infrared waveband in subwavelength graphene wedge and groove waveguides are investigated, which can be categorized into perfect electric conductor and perfect magnetic conductor symmetric modes with different propagation characteristics. The electromagnetic near-fields are localized strongly in different regions for these two kinds of modes. Moreover, these modes can be interpreted by the folded graphene ribbon modes. The brim width of the waveguides and the Fermi energy of the graphene strongly influence the dispersion and propagation distances of the plasmon modes, which can be used for tuning the plasmon modes in graphene wedge and groove waveguides efficiently.

© 2013 Optical Society of America

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2013 (2)

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

2012 (8)

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

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

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
[CrossRef]

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and kerr-type nonlinear media,” Opt. Lett.37, 2730–2732 (2012).
[CrossRef] [PubMed]

2011 (5)

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

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

2009 (3)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett.9, 1285–1289 (2009).
[CrossRef]

J. Dintinger and O. J. F. Martin, “Channel and wedge plasmon modes of metallic v-grooves with finite metal thickness,” Opt. Express17, 2364–2374 (2009).
[CrossRef] [PubMed]

2008 (3)

E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

2007 (3)

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

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007).
[CrossRef]

M. Yan and M. Qiu, “Guided plasmon polariton at 2d metal corners,” J. Opt. Soc. Am. B24, 2333–2342 (2007).
[CrossRef]

2006 (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
[CrossRef] [PubMed]

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8, 318 (2006).
[CrossRef]

2005 (2)

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95, 046802 (2005).
[CrossRef] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

2002 (1)

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B66, 035403 (2002).
[CrossRef]

1999 (1)

1997 (1)

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

Aksay, I. A.

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Alonso-Gonzalez, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

Avouris, P.

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

Badioli, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Bechtel, H. A.

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

Berini, P.

Bozhevolnyi, S.

E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95, 046802 (2005).
[CrossRef] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

Cai, W.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and kerr-type nonlinear media,” Opt. Lett.37, 2730–2732 (2012).
[CrossRef] [PubMed]

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Car, R.

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Castro-Neto, A. H.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Chandra, B.

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

Chang, D. E.

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

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
[CrossRef]

Das Sarma, S.

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
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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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
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Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
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F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett.11, 3370–3377 (2011).
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A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett.9, 1285–1289 (2009).
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E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
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A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. 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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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol.6, 630–634 (2011).
[CrossRef] [PubMed]

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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
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A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. 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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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. 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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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
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E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007).
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V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol.6, 630–634 (2011).
[CrossRef] [PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
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Koppens, F. H. L.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
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F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett.11, 3370–3377 (2011).
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H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
[CrossRef] [PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
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H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

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

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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. 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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P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

Ma, L.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett.9, 1285–1289 (2009).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol.6, 630–634 (2011).
[CrossRef] [PubMed]

Martin, O. J. F.

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
[CrossRef]

E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

Martín-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

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E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

Morimoto, A.

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Neto, A. H. C.

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Nikitin, A. Y.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
[CrossRef]

Nordlander, P.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B66, 035403 (2002).
[CrossRef]

Novoselov, K. S.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

Osmond, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

Pesquera, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

Prudlomme, R. K.

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Qiu, M.

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Rodrigo, S.

E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

Saville, D. A.

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Schlather, A.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

Schniepp, H. C.

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Shen, Y. R.

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

Sherrott, M.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

Sols, F.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8, 318 (2006).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

Stauber, T.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8, 318 (2006).
[CrossRef]

Stewart, M. K.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Takahara, J.

Taki, H.

Tauber, M. J.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Thongrattanasiri, S.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

Tulevski, G.

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

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95, 046802 (2005).
[CrossRef] [PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Wang, C.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Wang, F.

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

Wang, L.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and kerr-type nonlinear media,” Opt. Lett.37, 2730–2732 (2012).
[CrossRef] [PubMed]

Wang, Y.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

Wu, Y.

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

Wunsch, B.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8, 318 (2006).
[CrossRef]

Xia, F.

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

Xu, J.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and kerr-type nonlinear media,” Opt. Lett.37, 2730–2732 (2012).
[CrossRef] [PubMed]

Yamagishi, S.

Yan, H.

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

Yan, M.

Zettl, A.

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

Zhang, L. 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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Zhang, X.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and kerr-type nonlinear media,” Opt. Lett.37, 2730–2732 (2012).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Zhao, 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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

Zhu, W.

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

Zurutuza Elorza, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

ACS Nano (4)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6, 431–440 (2012).
[CrossRef]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. Garca de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano7, 2388–2395 (2013).
[CrossRef] [PubMed]

S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudłomme, R. Car, D. A. Saville, and I. A. Aksay, “Bending properties of single functionalized graphene sheets probed by atomic force microscopy,” ACS Nano2, 2577–2584 (2008).
[CrossRef]

Appl. Phys. Lett. (2)

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87, 061106 (2005).
[CrossRef]

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett.100, 153111 (2012).
[CrossRef]

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

Nano Lett. (4)

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett.11, 4701–4705 (2011).
[CrossRef] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.13, 2541–2547 (2013).
[CrossRef] [PubMed]

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

A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett.9, 1285–1289 (2009).
[CrossRef]

Nat. Mater. (1)

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

Nat. Nanotechnol. (2)

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

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

Nat. Photonics (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2, 496–500 (2008).
[CrossRef]

Nature (3)

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature487, 77–81 (2012).
[PubMed]

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. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature487, 82–85 (2012).
[PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440, 508–511 (2006).
[CrossRef] [PubMed]

New J. Phys. (1)

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8, 318 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (6)

I. V. Novikov and A. A. Maradudin, “Channel polaritons,” Phys. Rev. B66, 035403 (2002).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
[CrossRef]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007).
[CrossRef]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84, 195446 (2011).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

Phys. Rev. Lett. (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95, 046802 (2005).
[CrossRef] [PubMed]

E. Moreno, S. Rodrigo, S. Bozhevolnyi, L. Martin-Moreno, and F. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100, 023901 (2008).
[CrossRef] [PubMed]

Science (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Plasmon modes in the graphene wedge waveguide. (a) The geometry of the wedge waveguide. The plasmons propagate along the z-axis. (b) The dispersion of the plasmon modes in the wedge waveguide with θ = 20° and p = 20 nm. Blue lines are the normalized momenta, and gray lines are the normalized propagation distances, the green line in the center corresponds to the momenta of light in vacuum. The lower panels show the Ey and time averaged Sz of the near-fields for the four modes labeled in (b). The red arrows represent the flow direction of electric field lines.

Fig. 2
Fig. 2

The evolution of plasmon modes from the graphene wedge to the graphene ribbon. (a) The apex angle dependence of the plasmon modes in graphene wedges. The dispersion curves of the modes AD for the apex angle 20°, 60°, 100°, and 140° are shown in the top panels, which are compared with the dispersion curves of the corresponding modes in the flat ribbon, respectively. And the lower panels show the near-fields Ey for the points labeled in the dispersion curves of D with different apex angles. (b) The charge orderings for the plasmon modes in graphene ribbons and wedges. The PEC symmetric modes in graphene wedges correspond to the odd order modes in ribbons, whereas the PMC symmetric modes correspond to the even order modes.

Fig. 3
Fig. 3

(a) The plasmon modes in the graphene wedge waveguide with an apex angle θ = 20° and a brim width p = 60 nm, the blue and gray lines are the normalized momenta and propagation distances of plasmon modes, respectively. (b) – (d) The frequencies, momenta, and propagation distances of the PMC symmetric mode B and the PEC symmetric mode D as a function of the brim width.

Fig. 4
Fig. 4

Doping level dependences of the PMC symmetric mode B and PEC symmetric mode D. (a) – (c) show the frequencies, momenta, and absolute propagation distances of these two modes as a function of the Fermi energy of graphene.

Fig. 5
Fig. 5

The Fermi energy dependences of the momenta (a) and the propagation distances (b) for the PEC symmetric mode A and PMC symmetric mode B, with fixed plasmon frequency 30 THz. The geometric parameters of the waveguide keep the same with those in Fig. 3(a) and Fig. 4.

Fig. 6
Fig. 6

Plasmon modes in the graphene groove waveguide. (a) The geometry of the groove waveguide. (b) The dispersion of the plasmon modes in the groove waveguide with θ = 20° and p = 20 nm, the blue and gray lines are the normalized momenta and propagation distances respectively, the green line in the center corresponds to the momentum of light in vacuum. The lower eight plots show the Ey and time averaged Sz of the near-fields for the four modes labeled in (b), respectively.

Equations (1)

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σ intra = 2 i e 2 k B T 2 π ( ω + i / τ ) ln [ 2 cosh ( E F 2 k B T ) ] , σ inter = e 2 4 [ 1 2 + 1 π arctan ( ω 2 E F 2 k B T ) i 2 π ln ( ω + 2 E F ) 2 ( ω + 2 E F ) 2 + ( 2 k B T ) 2 ] .

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