Abstract

The coupling between a single emitter and surface plasmons in paired graphene layers and in paired graphene ribbons are studied. For paired graphene layers, the coupling between surface plasmons in graphene layers is strong at low photon energy and small gap between layers, which results in strong enhancement of the emitter’s emission. The excitation efficiency of surface plasmons by a single emitter can be increased to nearly 1 in paired graphene layers. With the increase of the photon energy, emitter’s emission in paired layers is weakened and could be lower than that in graphene monolayer. For graphene paired ribbons, numerical simulations show similar properties of emission enhancement and high excitation efficiency of surface plasmons. The emission enhancement and the excitation efficiency of surface plasmons can be improved by narrowing the ribbon width.

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    [CrossRef]
  2. D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  6. F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interaction,” Nano Lett.11, 3370–3377 (2011).
    [CrossRef] [PubMed]
  7. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. H. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4, 532–535 (2008).
    [CrossRef]
  8. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett.105, 256805 (2010).
    [CrossRef]
  9. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
    [CrossRef]
  10. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
    [CrossRef]
  11. C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
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    [CrossRef]
  13. 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]
  14. Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
    [CrossRef]
  15. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113, 195–287 (1984).
    [CrossRef]
  16. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
    [CrossRef]
  17. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New. J. Phys.8, 318 (2006).
    [CrossRef]
  18. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75, 205418 (2007).
    [CrossRef]
  19. 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]
  20. 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]
  21. S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
    [CrossRef] [PubMed]
  22. S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
    [CrossRef]
  23. A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
    [CrossRef]

2012 (5)

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
[CrossRef]

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. Nano. 6, 431–440 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
[CrossRef]

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

2011 (3)

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. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

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

2010 (2)

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett.105, 256805 (2010).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

2009 (1)

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

2008 (2)

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

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

2007 (1)

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

2006 (2)

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

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

2005 (2)

K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation,” Phys. Rev. A72, 022317 (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]

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]

1998 (1)

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[CrossRef]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

1984 (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113, 195–287 (1984).
[CrossRef]

Basov, D. H.

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

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

Briegel, H. J.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[CrossRef]

Brongersma, M. L.

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

Buljan, H.

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

Chang, D. E.

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

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

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [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. Nano. 6, 431–440 (2012).
[CrossRef]

Chu, H. S.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
[CrossRef]

Cirac, J. I.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[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).
[CrossRef]

DiVincenzo, D. P.

K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation,” Phys. Rev. A72, 022317 (2005).
[CrossRef]

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,” 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]

Dur, W.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[CrossRef]

Efetov, D. K.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett.105, 256805 (2010).
[CrossRef]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [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,” 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]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113, 195–287 (1984).
[CrossRef]

Gan, C. H.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
[CrossRef]

García de Abajo, F. 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. Nano. 6, 431–440 (2012).
[CrossRef]

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

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

García de Abajo, F. Javier

S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-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]

Geim, A. K.

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]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

Grigorieva, I. 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,” 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]

Guinea, F.

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. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

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

Hao, Z.

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

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

Hemmer, P. R.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

Henriksen, E. A.

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

Hwang, E. H.

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

Jablan, M.

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

Jiang, D.

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]

Jiang, Z.

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

Jun, Y. C.

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

Katsnelson, M. I.

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]

Kekatpure, R.D.

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

Kim, P.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett.105, 256805 (2010).
[CrossRef]

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

Koppens, F. H. L.

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. Nano. 6, 431–440 (2012).
[CrossRef]

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

Li, E. P.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
[CrossRef]

Li, Z. Q.

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

Lukin, M. D.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

Manjavacas, A.

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. Nano. 6, 431–440 (2012).
[CrossRef]

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

Martin, M. C.

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

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-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]

Morozov, 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,” 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]

Nikitin, A. Y.

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. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

Novoselov, K. S.

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]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

Silveiro, Iván

S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
[CrossRef]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljacic, “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]

Sorensen, A. S.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [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]

Stormer, H. L.

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

Svore, K. M.

K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation,” Phys. Rev. A72, 022317 (2005).
[CrossRef]

Terhal, B. M.

K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation,” Phys. Rev. A72, 022317 (2005).
[CrossRef]

Thongrattanasiri, S.

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. Nano. 6, 431–440 (2012).
[CrossRef]

S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
[CrossRef]

S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

Weber, W. H.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113, 195–287 (1984).
[CrossRef]

White, J. S.

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

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]

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]

Zoller, P.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[CrossRef]

ACS Nano (1)

S. Thongrattanasiri, A. Manjavacas, and F. Javier García de Abajo, “Quantum Finite-Size Effects in Graphene Plasmons,” ACS Nano6, 1766–1775 (2012).
[CrossRef] [PubMed]

ACS. Nano (1)

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. Nano. 6, 431–440 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

S. Thongrattanasiri, Iván Silveiro, and F. Javier García de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett.100, 201105 (2012).
[CrossRef]

Nano Lett. (1)

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

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

Nat. Phys. (1)

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

Nature (1)

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]

New. J. Phys. (2)

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

A. Manjavacas, S. Thongrattanasiri, D. E. Chang, and F. J. García de Abajo, “Temporal quantum control with graphene,” New. J. Phys.14, 123020 (2012).
[CrossRef]

Phys. Rep. (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113, 195–287 (1984).
[CrossRef]

Phys. Rev. A (1)

K. M. Svore, B. M. Terhal, and D. P. DiVincenzo, “Local fault-tolerant quantum computation,” Phys. Rev. A72, 022317 (2005).
[CrossRef]

Phys. Rev. B (6)

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

Y. C. Jun, R.D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78, 153111 (2008).
[CrossRef]

M. Jablan, H. Buljan, and M. Soljacic, “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, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84, 161407 (2011).
[CrossRef]

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B85, 125431 (2012).
[CrossRef]

Phys. Rev. Lett. (4)

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett.105, 256805 (2010).
[CrossRef]

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006).
[CrossRef] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell s theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998).
[CrossRef]

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]

Other (1)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of (a) paired graphene layers and (b) paired grapehene ribbons. Insets are the profiles of the electric field intensity (|E|) in their fundamental SPs modes. In the insets, the field directions in gaps are indicated by blue arrows. The optical dipole is placed in the center of structures and is polarized vertically to graphene. Distance between the dipole and graphene layers (or ribbons) is l, and the graphene structures are assumed to be surrounded by air.

Fig. 2
Fig. 2

(a) For graphene monolayer, the total decay rate Γ is plotted in black solid line and the SPs decay rate Γsp in red dashed line. (b) For paired graphene layers, the total decay rate Γ is plotted in black solid line and the SPs decay rate Γsp in red solid line. Inset: the excitation efficiency of SPs by an emitter in graphene monolayer is plotted in green and the efficiency of SPs in paired graphene layers in blue line. In (a) and (b), l = 50nm. The solid lines show (c) the real part of the propagation constant and (d) the propagation distance of SPs in paired graphene layers versus the photon energy, and l is taken as 10 nm, 20 nm, 50 nm, 100 nm and 200 nm from the top line to the bottom line. For SPs in graphene monolayer, the data are plotted in black dashed line.

Fig. 3
Fig. 3

(a)η versus photon energy with η’s range from 1 to 103. Inset: η versus photon energy with η’s range from 0.8 to 1.5 and dashed red line indicates the line that η=1. Emitter distance l is 50 nm and Fermi level Ef is 0.5eV. (b)η versus photon energy with l varied between 10 nm, 20 nm, 50 nm, 100 nm and 200 nm from the right curve to the left curve.

Fig. 4
Fig. 4

(a) Exact value of η in black and η by Fermi golden rule in red. (b)According to Fermi golden rule, η can be divided into three factors, effective mode volume (Leff,m/2Leff,p in red), phase velocity (υp,m/υp,p in blue) and group velocity (υg,m/υg,p in green).

Fig. 5
Fig. 5

log(η) at different photon energies and different emitter distances with (a) Ef =0.3 eV, (b) Ef =0.5 eV, (c) Ef =0.7 eV and (d) Ef =1.0 eV. Yellow solid lines in theses figures indicate positions that η=1.

Fig. 6
Fig. 6

(a) Theory results for Γ in PGL are plotted in black-square line and simulation results for Γ are in red-circle line. (b) Real part of wave vectors for the first four SPs’ modes in GPR. Ribbon width w is set to be 300 nm and emitter distance l is taken as 50 nm (c) Profiles for electric field vertical to graphene E for first four modes. Photon energies of these modes are marked by black dots in (b).

Fig. 7
Fig. 7

(a) Simulation results of PGR and theory results of PGL. Γ are plotted in black-square line and Γsp are plotted in red-square line. Ribbons width w is varied between 100 nm, 200 nm and 300 nm. (b) Efficiencies for emitters in PGR at different widths, and efficiency for PGL in black solid line. Inset: schematic for interactions between PGR and single dipole.(c) Simulation results of GMR and theory results of GML. Γ are plotted in black-square line and Γsp are plotted in red-square line. Ribbons width w is varied between 100 nm, 200 nm and 300 nm. (d) Efficiencies for emitters in graphene mono ribbon at different widths, and efficiency for GML in black solid line. In all these figures, distance between emitter and graphene d is 50 nm, and Fermi level Ef is 0.5 eV. Inset: schematic for interactions between GMR and single dipole.

Fig. 8
Fig. 8

Emitter’s total emission rates at different Fermi levels and different graphene structures, with Ef0 = 0.5eV. (a) Analytical results for GML at different Fermi levels and (b) analytical results for equally doped PGL at different Fermi levels. (c) Analytical results for non-equally doped PGL with Ef1 = Ef0 at different Ef2. (d) Analytical results for PGL at three combinations of Ef1 and Ef2 (|Ef0, Ef0|, |1.5Ef0, 1.5Ef0|, and |Ef0, 1.5Ef0|). (e) Simulation results for non-equally doped PGR with Ef1 = Ef0 at different Ef2. (f) Simulation results for PGR at three combinations of Ef1 and Ef2 (|Ef0, Ef0|, |1.5Ef0, 1.5Ef0|, and |Ef0, 1.5Ef0|).

Equations (16)

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Γ Γ 0 + 2 h ¯ | p | 2 0 Im ( r ) q 2 e 2 q l d q ,
Γ s p Γ 0 3 π ε 1 + ε 2 ( λ 0 λ s p ) 3 e 4 π l λ s p .
r = ε 2 k 1 ε 1 k 2 + k 1 k 2 σ / ω ε 0 ε 2 k 1 + ε 1 k 2 + k 1 k 2 σ / ω ε 0
r pair = r e 2 i k l 1 r e 2 i k l .
r e 2 q s p 2 ε 1 k 0 2 l = 1 .
Γ Γ 0 1 + 3 k 0 3 0 Im ( r e 2 q l 1 r e 2 q l ) q 2 d q .
Γ s p Γ 0 = 3 π ( λ 0 λ s p ) 3 2 ε 1 e 4 π l λ s p ( ε 2 ε 1 ) 4 π l λ s p e 4 π l λ s p ( 1 e 4 π l λ s p ) + [ ( ε 1 + ε 2 ) ( ε 2 ε 1 ) e 4 π l λ s p ] Q ( l , λ s p ) .
Q ( l , λ s p ) = 1 e 4 π l λ s p + 4 π l λ s p e 4 π l λ s p
Γ s p Γ 0 = 3 π ( λ 0 λ s p ) 3 e 4 π l λ s p Q ( l , λ s p ) .
σ ( ω ) = e 2 E f π h ¯ 2 i ω + i τ 1 + e 2 4 h ¯ [ θ ( h ¯ ω 2 E f ) + i π log | h ¯ ω 2 E f h ¯ ω + 2 E f | ]
η = Γ s p , p 2 Γ s p , m = ( λ s p , m λ s p , p ) 3 e 4 π l ( 1 λ s p , p 1 λ s p , m ) Q ( l , λ s p , p ) .
| g | 2 = ω | p | 2 / ( 2 h ¯ ε r ε 0 V eff )
L eff = 1 2 { ε 0 d ( ε r ω ) d ω | E ( x , ω ) | 2 + μ 0 | H ( x , ω ) | 2 } d x / ( ε r ε 0 | E ( x p , ω ) | 2 )
η = L eff , m 2 L eff , p υ p , m υ p , p υ g , m υ g , p
L eff , m 2 L eff , p = λ s p , m λ s p , p e 4 π l ( 1 λ s p , p 1 λ s p , m ) 1 + ( 1 + 4 π l λ s p , p ) e 4 π l λ s p , p .
Γ E f 1 , E f 2 Γ 0 1 + 3 2 k 0 3 0 Im ( ( 1 + r 1 e 2 q l ) ( 1 + r 2 e 2 q l ) 1 r 1 r 2 e 4 q l 1 ) q 2 d q .

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