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Bends and splitters in graphene nanoribbon waveguidesXiaolong Zhu, Wei Yan, N. Asger Mortensen, and Sanshui Xiao »View Author Affiliations
Xiaolong Zhu,1,2
Wei Yan,1,2
N. Asger Mortensen,1,2
and Sanshui Xiao1,2,*
1DTU Fotonik - Department of Photonics Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark 2Center for Nanostructured Graphene (CNG), Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark *Corresponding author: saxi@fotonik.dtu.dk |
Optics Express, Vol. 21, Issue 3, pp. 3486-3491 (2013)
http://dx.doi.org/10.1364/OE.21.003486
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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
OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(240.6690) Optics at surfaces : Surface waves
ToC Category:
Integrated Optics
History
Original Manuscript: December 18, 2012
Revised Manuscript: January 23, 2013
Manuscript Accepted: January 23, 2013
Published: February 4, 2013
Citation
Xiaolong Zhu, Wei Yan, N. Asger Mortensen, and Sanshui Xiao, "Bends and splitters in graphene nanoribbon waveguides," Opt. Express 21, 3486-3491 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3486
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References
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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]
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- L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007). [CrossRef]
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- G. Veronis and S. H. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87, 131102 (2005). [CrossRef]
- 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,” Nature487, 82–85 (2012). [PubMed]
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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). [CrossRef] [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,” Nature487, 82–85 (2012). [PubMed]
- W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano6, 7806–7813 (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]
- 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 Nano6, 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,” Nature487, 77–81 (2012). [PubMed]
- A. Y. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (R) (2011). [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,” Nature438, 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,” Science306, 666–669 (2004). [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,” Nature474, 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]
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- F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009). [CrossRef] [PubMed]
- 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]
- S. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A340, 474–479 (2005). [CrossRef]
- W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano6, 7806–7813 (2012). [CrossRef] [PubMed]
- F. Yang, J. R. Sambles, and G. W. Bradberry, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nature Nanotechnol.7, 330–334 (2012). [CrossRef]
- M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474, 64–67 (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,” Nature474, 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,” Science206, 206–209 (2008). [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. B86, 165416 (2012). [CrossRef]
- 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]
- 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,” Nature487, 82–85 (2012). [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,” Nature474, 64–67 (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,” Science206, 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,” Science306, 666–669 (2004). [CrossRef] [PubMed]
- 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. B86, 165416 (2012). [CrossRef]
- 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,” Nature487, 82–85 (2012). [PubMed]
- 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. B86, 165416 (2012). [CrossRef]
ACS Nano
- Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano6, 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 Nano6, 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 Nano6, 431–440 (2012). [CrossRef]
Appl. Phys. Lett.
- 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
- L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007). [CrossRef]
Nat. Mater.
- 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.
- 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
- A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6, 749–758 (2012). [CrossRef]
Nat. Phys.
- 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
- 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,” Nature438, 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,” Nature474, 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,” Nature440, 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,” 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, 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,” Nature487, 82–85 (2012). [PubMed]
Nature Nanotechnol.
- 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
- Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express16, 16314–16325 (2008). [CrossRef] [PubMed]
Opt. Lett.
- 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]
Phys. Lett. A
- S. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A340, 474–479 (2005). [CrossRef]
Phys. Rev. B
- E. H. Hwand and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 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. B86, 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. B84, 161407 (R) (2011). [CrossRef]
- M. Jablan, H. Buljan, and Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009). [CrossRef]
Phys. Rev. Lett.
- 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
- A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332, 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,” Science306, 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,” Science206, 206–209 (2008). [CrossRef]
Other
- 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).
2012, Grigorenko, Nat. Photonics
- A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6, 749–758 (2012). [CrossRef]
- Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano6, 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 Nano6, 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 Nano6, 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. B86, 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,” 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, 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,” Nature487, 82–85 (2012). [PubMed]
- A. Y. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 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,” Science332, 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,” Nature474, 64–67 (2011). [CrossRef] [PubMed]
- 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]
- 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. B80, 245435 (2009). [CrossRef]
- 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,” Science206, 206–209 (2008). [CrossRef]
- E. H. Hwand and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007). [CrossRef]
- L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007). [CrossRef]
- 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. S. Xiao and M. Qiu, “Study of transmission properties for waveguide bends by use of a circular photonic crystal,” Phys. Lett. A340, 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,” Nature438, 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,” Science306, 666–669 (2004). [CrossRef] [PubMed]
- 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]
- 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]
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