Abstract

We investigate the performance of bends and splitters in graphene nanoribbon waveguides. Although the graphene waveguides are lossy themselves, we show that bends and splitters do not induce any additional loss provided that the nanoribbon width is sub-wavelength. We use transmission line theory to qualitatively interpret the behavior observed in our simulation. Our results pave a promising way to realize ultra-compact devices operating in the terahertz region.

© 2013 OSA

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  7. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  31. J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
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    [PubMed]

2012 (9)

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

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef] [PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. Garcia de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
[CrossRef] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. Koppens, and F. J. Garcia de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

F. Yang, J. R. Sambles, and G. W. Bradberry, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nature Nanotechnol. 7, 330–334 (2012).
[CrossRef]

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86, 165416 (2012).
[CrossRef]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

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

2011 (4)

A. Y. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (R) (2011).
[CrossRef]

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]

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

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

2010 (1)

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, “Nealy-zero transmission through periodically modulated ultrathin metal films,” Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

2009 (2)

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef] [PubMed]

M. Jablan, H. Buljan, and Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

2008 (4)

K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef] [PubMed]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16, 16314–16325 (2008).
[CrossRef] [PubMed]

2007 (2)

E. H. Hwand and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

2006 (1)

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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

2005 (3)

S. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A 340, 474–479 (2005).
[CrossRef]

G. Veronis and S. H. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

2004 (2)

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,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004).
[CrossRef] [PubMed]

2003 (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef] [PubMed]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

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. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 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, G. Thiemens, M. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. K., and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef] [PubMed]

Avouris, P.

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[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. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef] [PubMed]

Bao, W.

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

Basov, D. N.

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

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

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]

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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nature Nanotechnol. 7, 330–334 (2012).
[CrossRef]

Buljan, H.

M. Jablan, H. Buljan, and Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, G. Thiemens, M. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. K., and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[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. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[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. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. Koppens, and F. J. Garcia de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Das Sarma, S.

E. H. Hwand and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

Devaux, E.

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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Dominguez, M.

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

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[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,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Ebbesen, T. W.

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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Elorza, A. Z.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Engheta, N.

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

Falkovsky, L. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Fan, S. H.

G. Veronis and S. H. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Fei, Z.

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

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

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K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef] [PubMed]

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]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Shu, J.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
[CrossRef] [PubMed]

Soljacic,

M. Jablan, H. Buljan, and Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[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. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Stormer, H. L.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Thiemens, G.

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

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. Koppens, and F. J. Garcia de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. Garcia de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef] [PubMed]

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

Vakil, A.

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

Valdes-Garcia, A.

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef] [PubMed]

Varlamov, A. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Veronis, G.

G. Veronis and S. H. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Wagner, M.

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

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

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]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Winn, J.

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Modling the Flow of Light, 1st. ed. (Princeton Univ., 1995).

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef] [PubMed]

Xia, F.

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, “Nealy-zero transmission through periodically modulated ultrathin metal films,” Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Xiao, S. S.

S. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A 340, 474–479 (2005).
[CrossRef]

Xu, Q.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
[CrossRef] [PubMed]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nature Nanotechnol. 7, 330–334 (2012).
[CrossRef]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

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]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Zhan, T. R.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86, 165416 (2012).
[CrossRef]

Zhang, J.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, “Nealy-zero transmission through periodically modulated ultrathin metal films,” Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Zhang, L. M.

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

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [PubMed]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

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,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Zhao, F. Y.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86, 165416 (2012).
[CrossRef]

Zhao, Z.

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

Zi, J.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86, 165416 (2012).
[CrossRef]

ACS Nano (3)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
[CrossRef] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. Koppens, and F. J. Garcia de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, “Nealy-zero transmission through periodically modulated ultrathin metal films,” Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

G. Veronis and S. H. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Eur. Phys. J. B (1)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[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]

F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

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

Nat. Phys. (1)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Nature (5)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[CrossRef] [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,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

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

Nature Nanotechnol. (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nature Nanotechnol. 7, 330–334 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

S. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A 340, 474–479 (2005).
[CrossRef]

Phys. Rev. B (4)

E. H. Hwand and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86, 165416 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (R) (2011).
[CrossRef]

M. Jablan, H. Buljan, and Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. Garcia de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Science (3)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[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,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 206, 206–209 (2008).
[CrossRef]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Modling the Flow of Light, 1st. ed. (Princeton Univ., 1995).

S. A. Maier, Plasmonics: Fundamentals and Applications, 1st ed. (Springer, 2007).

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Figures (4)

Fig. 1
Fig. 1

(a) Effective refractive indices of GPP modes as a function of wavelength for free-standing graphene ribbons of 20 nm (the solid line) and 30 nm (the dashed line) widths. Inset illustrates a cross-section graphene nanoribbon waveguide with the width d, where the axis indicates light propagation along the z direction. (b) Propagation lengths as a function of wavelength for the freestanding graphene ribbons. Inset shows field distributions of the GPP mode at λ = 15 μm for the case of d = 30 nm.

Fig. 2
Fig. 2

Transmission spectra of graphene nanoribbon waveguide bends for d = 20, 30 nm. Inset illustrates its top-view corresponding structure and the top-view magnetic amplitude at y = 0 when λ0 = 15 μm and d = 30 nm.

Fig. 3
Fig. 3

Transmission spectra of graphene nanoribbon T-shape splitters (shown in the inset with the top view) for d = 20, 30 nm. In this case we choose din = dout = d.

Fig. 4
Fig. 4

Reflection coefficient of a graphene nanoribbon T-shape splitter as a function of din/dout at λ = 12 μm. Inset shows its top-view corresponding structure and illustrates zero-reflection when din/dout = 2.25 at λ = 12 μm.

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