Abstract

In this paper, dispersion properties and field distributions of surface magneto plasmons (SMPs) in double-layer graphene structures at room temperature are studied. It is found that, the dispersion curves of both symmetric and antisymmetric SMPs modes split into several branches/bands when a magnetic field is applied perpendicularly to the graphene surface. Surprisingly, the lowest energy SMP band has anomalous dependence on the applied magnetic field, different to the other higher bands. In addition, the symmetric and antisymmetric modes can be decoupled if the two graphene layers possess different properties, such as different Fermi energies. Furthermore, electric components of the surface modes which are parallel to the graphene surfaces but perpendicular to the propagation direction (i.e. the transverse-electric mode) are no longer zero caused by the Lorentz force on the free electrons.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref]
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  4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
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  5. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
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  6. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4(2), 83–91 (2010).
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  7. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
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  9. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
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  12. 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. B 84(16), 161407 (2011).
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  13. B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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  22. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
    [PubMed]
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    [PubMed]
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    [Crossref]
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    [PubMed]
  26. V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
    [Crossref] [PubMed]
  27. V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011).
    [Crossref] [PubMed]
  28. B. Hu, Q. J. Wang, S. W. Kok, and Y. Zhang, “Active focal length control of terahertz slitted plane lenses by magnetoplasmons,” Plasmonics 7(2), 191–199 (2011).
    [Crossref]
  29. B. Hu, Q. J. Wang, and Y. Zhang, “Slowing down terahertz waves with tunable group velocities in a broad frequency range by surface magneto plasmons,” Opt. Express 20(9), 10071–10076 (2012).
    [Crossref] [PubMed]
  30. B. Hu, Q. J. Wang, and Y. Zhang, “Voigt Airy surface magneto plasmons,” Opt. Express 20(19), 21187–21195 (2012).
    [Crossref] [PubMed]
  31. Y.-C. Lan and C.-M. Chen, “Long-range surface magnetoplasmon on thin plasmon films in the Voigt configuration,” Opt. Express 18(12), 12470–12481 (2010).
    [Crossref] [PubMed]
  32. E. P. Fitrakis, T. Kamalakis, and T. Sphicopoulos, “Slow-light dark solitons in insulator–insulator–metal plasmonic waveguides,” J. Opt. Soc. Am. B 27, 1701–1706 (2010).
    [Crossref]
  33. M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B Condens. Matter 36(11), 5960–5967 (1987).
    [Crossref] [PubMed]
  34. M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41(1-8), 1–416 (2001).
    [Crossref]
  35. R. E. Camley, “Nonreciprocal surface waves,” Surf. Sci. Rep. 7(3-4), 103–187 (1987).
    [Crossref]
  36. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
    [Crossref]
  37. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. 37(11), 1895–1897 (2012).
    [Crossref] [PubMed]
  38. Yu. A. Bychkov and G. Martinez, “Magnetoplasmon excitations in graphene for filling factors ν≤6,” Phys. Rev. B 77(12), 125417 (2008).
    [Crossref]
  39. O. Berman, G. Gumbs, and Y. Lozovik, “Magnetoplasmons in layered graphene structures,” Phys. Rev. B 78(8), 085401 (2008).
    [Crossref]
  40. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2010).
    [Crossref]
  41. W. Wang, J. Kinaret, and S. Apell, “Excitation of edge magnetoplasmons in semi-infinite graphene sheets: Temperature effects,” Phys. Rev. B 85(23), 235444 (2012).
    [Crossref]
  42. A. Ferreira, N. M. R. Peres, and A. H. Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
    [Crossref]
  43. E. Hwang and S. D. Sarma, “Plasmon modes of spatially separated double-layer graphene,” Phys. Rev. B 80(20), 205405 (2009).
    [Crossref]
  44. T. Stauber and G. Gómez-Santos, “Plasmons and near-field amplification in double-layer graphene,” Phys. Rev. B 85(7), 075410 (2012).
    [Crossref]
  45. 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. B 85(12), 125431 (2012).
    [Crossref]
  46. W.-L. You and X.-F. Wang, “Dynamic screening and plasmon spectrum in bilayer graphene,” Nanotechnology 23(50), 505204 (2012).
    [Crossref] [PubMed]
  47. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
    [Crossref]
  48. 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(7), 532–535 (2008).
    [Crossref]
  49. E. Hwang, B. Y.-K. Hu, and S. Das Sarma, “Inelastic carrier lifetime in graphene,” Phys. Rev. B 76(11), 115434 (2007).
    [Crossref]

2013 (1)

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: Combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013).
[Crossref]

2012 (16)

J. C. Banthí, D. Meneses-Rodríguez, F. García, M. U. González, A. García-Martín, A. Cebollada, and G. Armelles, “High magneto-optical activity and low optical losses in metal-dielectric Au/Co/Au-SiO(2) magnetoplasmonic nanodisks,” Adv. Mater. 24(10), OP36–OP41 (2012).
[PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

B. Hu, Q. J. Wang, and Y. Zhang, “Slowing down terahertz waves with tunable group velocities in a broad frequency range by surface magneto plasmons,” Opt. Express 20(9), 10071–10076 (2012).
[Crossref] [PubMed]

B. Hu, Q. J. Wang, and Y. Zhang, “Voigt Airy surface magneto plasmons,” Opt. Express 20(19), 21187–21195 (2012).
[Crossref] [PubMed]

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. 37(11), 1895–1897 (2012).
[Crossref] [PubMed]

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (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 Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

A. Yu. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Slow-light dark solitons in insulator–insulator–metal plasmonic waveguides,” Phys. Rev. B 85, 081405 (2012).
[Crossref]

P. Huidobro, A. Nikitin, C. González-Ballestero, L. Martín-Moreno, and F. García-Vidal, “Superradiance mediated by graphene surface plasmons,” Phys. Rev. B 85(15), 155438 (2012).
[Crossref]

W. Wang, J. Kinaret, and S. Apell, “Excitation of edge magnetoplasmons in semi-infinite graphene sheets: Temperature effects,” Phys. Rev. B 85(23), 235444 (2012).
[Crossref]

A. Ferreira, N. M. R. Peres, and A. H. Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
[Crossref]

T. Stauber and G. Gómez-Santos, “Plasmons and near-field amplification in double-layer graphene,” Phys. Rev. B 85(7), 075410 (2012).
[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. B 85(12), 125431 (2012).
[Crossref]

W.-L. You and X.-F. Wang, “Dynamic screening and plasmon spectrum in bilayer graphene,” Nanotechnology 23(50), 505204 (2012).
[Crossref] [PubMed]

2011 (8)

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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (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(10), 630–634 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

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. B 84(16), 161407 (2011).
[Crossref]

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
[Crossref] [PubMed]

V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011).
[Crossref] [PubMed]

B. Hu, Q. J. Wang, S. W. Kok, and Y. Zhang, “Active focal length control of terahertz slitted plane lenses by magnetoplasmons,” Plasmonics 7(2), 191–199 (2011).
[Crossref]

2010 (5)

Y.-C. Lan and C.-M. Chen, “Long-range surface magnetoplasmon on thin plasmon films in the Voigt configuration,” Opt. Express 18(12), 12470–12481 (2010).
[Crossref] [PubMed]

E. P. Fitrakis, T. Kamalakis, and T. Sphicopoulos, “Slow-light dark solitons in insulator–insulator–metal plasmonic waveguides,” J. Opt. Soc. Am. B 27, 1701–1706 (2010).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4(2), 83–91 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photon. 4(9), 611–622 (2010).
[Crossref]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2010).
[Crossref]

2009 (2)

E. Hwang and S. D. Sarma, “Plasmon modes of spatially separated double-layer graphene,” Phys. Rev. B 80(20), 205405 (2009).
[Crossref]

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

2008 (4)

Yu. A. Bychkov and G. Martinez, “Magnetoplasmon excitations in graphene for filling factors ν≤6,” Phys. Rev. B 77(12), 125417 (2008).
[Crossref]

O. Berman, G. Gumbs, and Y. Lozovik, “Magnetoplasmons in layered graphene structures,” Phys. Rev. B 78(8), 085401 (2008).
[Crossref]

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

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(7), 532–535 (2008).
[Crossref]

2007 (5)

E. Hwang, B. Y.-K. Hu, and S. Das Sarma, “Inelastic carrier lifetime in graphene,” Phys. Rev. B 76(11), 115434 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[Crossref] [PubMed]

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

2001 (1)

M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41(1-8), 1–416 (2001).
[Crossref]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[Crossref]

1987 (2)

R. E. Camley, “Nonreciprocal surface waves,” Surf. Sci. Rep. 7(3-4), 103–187 (1987).
[Crossref]

M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B Condens. Matter 36(11), 5960–5967 (1987).
[Crossref] [PubMed]

1972 (1)

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Åkerman, J.

V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011).
[Crossref] [PubMed]

Akimov, I. A.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
[Crossref] [PubMed]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

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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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [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(7), 532–535 (2008).
[Crossref]

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photon. 4(9), 611–622 (2010).
[Crossref]

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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Teng, J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Thio, T.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[Crossref]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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(1), 431–440 (2012).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

van der Marel, D.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2010).
[Crossref]

Vavassori, P.

V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011).
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V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
[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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

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J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
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I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2010).
[Crossref]

Wang, B.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (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(10), 630–634 (2011).
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W. Wang, J. Kinaret, and S. Apell, “Excitation of edge magnetoplasmons in semi-infinite graphene sheets: Temperature effects,” Phys. Rev. B 85(23), 235444 (2012).
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W.-L. You and X.-F. Wang, “Dynamic screening and plasmon spectrum in bilayer graphene,” Nanotechnology 23(50), 505204 (2012).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
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W.-L. You and X.-F. Wang, “Dynamic screening and plasmon spectrum in bilayer graphene,” Nanotechnology 23(50), 505204 (2012).
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B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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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(10), 630–634 (2011).
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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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Zhang, X.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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Zhang, Y.

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 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 grapheme–SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
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S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
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V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, “Enhanced magneto-optical effects in magnetoplasmonic crystals,” Nat. Nanotechnol. 6(6), 370–376 (2011).
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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 Nano 6(1), 431–440 (2012).
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Adv. Mater. (1)

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F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (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(10), 630–634 (2011).
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I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2010).
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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(7), 532–535 (2008).
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Nature (4)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
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W. Wang, J. Kinaret, and S. Apell, “Excitation of edge magnetoplasmons in semi-infinite graphene sheets: Temperature effects,” Phys. Rev. B 85(23), 235444 (2012).
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S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
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B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the SMPs propagating in a double-layer graphene structure when a magnetic field is applied along the –x axis. (b) Graphene conductivity elements Im(σyy) and Re(σyz) as a function of frequency without the magnetic field (black dotted line), and with a magnetic field of E1 = EF (red solid and blue dashed lines). The solid black lines indicate the electron-electron transitions between LLs of intraband (E1-E0, E2-E1) and interband (E2-E-1). The parameters are chosen as EF = 0.05eV, d = T = 300K, Γ = 0.03EF.
Fig. 2
Fig. 2 Dispersion relations of SMPs without (black lines) and with (red and blue lines) external magnetic fields. The symmetric modes (SMs) and antisymmetric modes (AMs) are denoted by solid and dashed lines, respectively. The green line is the dispersion of light in free space. The spacing between the two graphene layer is d = 0.003λ. The intensity of the magnetic field is E1 = EF. The other parameters are the same as Fig. 1.
Fig. 3
Fig. 3 Electric field distributions of ħω = 1.5EF with and without the external magnetic fields. (a) Re(Ez); (b) Im(Ex); (c) Im(Ey). The parameters are the same as used in Fig. 2. The black solid and dashed lines denote the symmetric and antisymmetric modes of B = 0, respectively. The red solid and blue dashed lines denote the symmetric and antisymmetric modes of E1 = EF, respectively.
Fig. 4
Fig. 4 Effects of the magnetic field on the SMP modes of the GDS structure. The symmetric and antisymmetric modes are denoted by solid and dashed lines, respectively. 3 magnetic fields with intensities of E1 = 0.9EF (green lines), E1 = 1.0EF (blue lines), and E1 = 1.1EF (blue lines) are compared. (a) Band 3; (b) Band 2; (c) Band 1; (d) Comparison of Im(σyy) under the 3 magnetic fields. The other parameters are the same as those in Fig. 2.
Fig. 5
Fig. 5 Effects of the spacing d on the symmetric (red lines) and antisymmetric (blue lines) SMP modes of the GDS structure. (a)-(c) Dispersions of SMPs with various graphene separations of band 3, band2, and band1, respectively. The separations are chosen as d = 0.003λ (solid lines), d = 0.01λ (dashed lines) and d = 0 (dotted lines). (d)-(e), Ez intensity distributions above the GDS structure of the symmetric and antisymmetric modes, respectively. d is increased form 0.003λ (solid lines) to 0.006λ (dashed lines) and 0.01λ (dotted lines).
Fig. 6
Fig. 6 (a) SMPs modes of band 2 of a GDS when the Fermi energies of the two graphene sheets are different (the red and blue solid lines). The upper graphene sheet is EF1 = 0.05eV while the lower is EF1 = 0.06eV. For comparison, SMPs on SLG with magnetic fields of EF = 0.05eV and EF = 0.06eV are also plotted (the dashed lines). (b) Field distribution of Re(Ez) of the two modes at ħω = 1.3EF. The other parameters are the same as Fig. 2.
Fig. 7
Fig. 7 (a) SMPs modes (solid lines) of band 2 of a GDS structure with ε1 = 6, ε2 = 3.8, ε3 = 1. Compared with SMP modes on SLG interfaces of Al2O3 / Air (red dashed line) and Al2O3 / SiO2 (blue dashed line). (b) Field distribution of Re(Ez) of the MS and MA modes at ħω = 1.1EF withε1 = 6, ε2 = 3.8, ε3 = 1. The other parameters are the same as Fig. 2.

Equations (16)

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σ ¯ g =( 0 0 0 0 σ yy σ yz 0 σ yz σ yy ),
σ yy = e 2 iπ ( ω+i2Γ ) n=0 | eB | v F 2 { n F ( E n ) n F ( E n+1 )+ n F ( E n+1 ) n F ( E n ) [ Δ intra,n 2 ( ω+i2Γ ) 2 ] Δ intra,n + n F ( E n ) n F ( E n+1 )+ n F ( E n+1 ) n F ( E n ) [ Δ inter,n 2 ( ω+i2Γ ) 2 ] Δ inter,n },
σ yz = e 2 π n=0 | eB | v F 2 [ n F ( E n ) n F ( E n+1 ) n F ( E n+1 )+ n F ( E n ) ] ×{ 1 [ Δ intra,n 2 ( ω+i2Γ ) 2 ] + 1 [ Δ inter,n 2 ( ω+i2Γ ) 2 ] },
σ intra,yy = σ intra,yy1 + σ intra,yy2 ,
σ intra,yy1 = e 2 iπ ( ω+i2Γ )| eB | v F 2 n F ( E 0 ) n F ( E 1 ) [ ( E 1 E 0 ) 2 ( ω+i2Γ ) 2 ]( E 1 E 0 ) ,
σ intra,yy2 = e 2 iπ ( ω+i2Γ )| eB | v F 2 n F ( E 1 ) n F ( E 2 ) [ ( E 2 E 1 ) 2 ( ω+i2Γ ) 2 ]( E 2 E 1 ) .
E x/y/z ={ A x/y/z e κ 1 x + B x/y/z e κ 1 x C x/y/z e κ 2 (xd/2) D x/y/z e κ 3 (x+d/2) d/2xd/2 xd/2 xd/2 ,
ψ 2 ψ 3 [ sin( κ 1 d) ] 2 { 1+ [ sin( κ 1 d) ] 2 [ φ 2 φ 3 + η 1 2 σ 1yz 2 φ 3 ψ 2 ] }{ 1+ [ sin( κ 1 d) ] 2 [ φ 2 φ 3 + η 1 2 σ 2yz 2 φ 2 ψ 3 ] } + { 1+ [ sin( κ 1 d) ] 2 [ φ 2 φ 3 η 1 2 σ 1yz σ 2yz ] } 2 =0
φ 2(3) =icoth( κ 1 d)+ σ 1(2)yy ω μ 0 μ 1 κ 1 +i μ 1 κ 2(3) μ 2(3) κ 1
ψ 2(3) =icoth( κ 1 d)+ σ 1(2)zz κ 1 ω ε 1 ε 0 i ε 2(3) κ 1 ε 1 κ 2(3)
1 [ sinh( κ 1 d) ] 2 [ φ 2 2 μ 0 μ r1 ε 0 ε r1 σ 1zy 2 ] ψ 2 sinh( κ 1 d){ 1 [ sinh( κ 1 d) ] 2 [ φ 2 2 + μ 0 μ r1 ε 0 ε r1 σ 1zy 2 φ 2 ψ 2 ] }=0
1 [ sinh( κ 1 d) ] 2 [ φ 2 2 μ 0 μ r1 ε 0 ε r1 σ 1zy 2 ]+ ψ 2 sinh( κ 1 d){ 1 [ sinh( κ 1 d) ] 2 [ φ 2 2 + μ 0 μ r1 ε 0 ε r1 σ 1zy 2 φ 2 ψ 2 ] }=0
[ tanh( κ 1 d 2 )+1+i σ 1zz κ 1 ω ε r1 ε 0 ][ tanh( κ 1 d 2 )+1i σ 1zz ω μ 0 κ 1 ] η 1 2 σ 1yz 2 =0
[ coth( κ 1 d 2 )+1+i σ 1zz κ 1 ω ε 1 ε 0 ][ coth( κ 1 d 2 )+1i σ 1zz ω μ 0 κ 1 ]+ η 1 2 σ 1yz 2 =0
tanh( β 2 k 0 2 d 2 )+1Im( σ 1zz ) β 2 k 0 2 ω ε r1 ε 0 =0
coth( β 2 k 0 2 d 2 )+1Im( σ 1zz ) β 2 k 0 2 ω ε r1 ε 0 =0

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