Abstract

In this paper, a theoretical investigation on plasmon modes in a circular cylindrical double-layer graphene structure is presented. Due to the interlayer electromagnetic interaction, there exist two branches of plasmon modes, the optical plasmon mode and the acoustic plasmon mode. The characteristics of these two modes, such as mode pattern, effective mode index and propagation loss, are analyzed. The modal behaviors can be effectively tuned by changing the distance between two graphene layers, the chemical potential of graphene and the permittivity of interlayer dielectric. Importantly, the breakup of tradeoff between mode confinement and propagation loss is discovered in the distance-dependent modal behavior, which originates from the unique dispersion properties of a double-layer graphene system. As a consequence, both strong mode confinement and longer propagation length can be achieved. Our results may provide good opportunities for developing applications based on graphene plasmonics in circular cylindrical structure.

© 2016 Optical Society of America

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  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,” Science 306(5696), 666–669 (2004).
    [Crossref] [PubMed]
  2. 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(7065), 197–200 (2005).
    [Crossref] [PubMed]
  3. A. Neto, F. Guinea, N. Peres, K. Novoselov, and A. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
  4. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
    [Crossref] [PubMed]
  5. J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
    [Crossref] [PubMed]
  6. 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(7349), 64–67 (2011).
    [Crossref] [PubMed]
  7. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
    [Crossref]
  8. M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys. 46(8), L151–L153 (2007).
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  9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  10. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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  11. 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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  15. S. G. Liu, C. Zhang, M. Hu, X. X. Chen, P. Zhang, S. Gong, T. Zhao, and R. B. Zhong, “Coherent and tunable terahertz radiation from graphene surface plasmon polaritons excited by an electron beam,” Appl. Phys. Lett. 104(20), 201104 (2014).
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  18. S. Gong, T. Zhao, M. Sanderson, M. Hu, R. Zhong, X. Chen, P. Zhang, C. Zhang, and S. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
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    [Crossref] [PubMed]
  20. Y. S. Ang, S. Sultan, and C. Zhang, “Nonlinear optical spectrum of bilayer graphene in the terahertz regime,” Appl. Phys. Lett. 97(24), 243110 (2010).
    [Crossref]
  21. K. Yang, S. Arezoomandan, and B. S. Rodriguez, “The linear and nonlinear THz properties of graphene,” Int. J. THz Sci. Technol. 6, 223 (2013).
  22. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
    [Crossref] [PubMed]
  23. M. Farhat, C. Rockstuhl, and H. Bağcı, “A 3D tunable and multi-frequency graphene plasmonic cloak,” Opt. Express 21(10), 12592–12603 (2013).
    [Crossref] [PubMed]
  24. E. H. Hwang and S. Das Sarma, “Plasmon modes of spatially separated double-layer graphene,” Phys. Rev. B 80(20), 205405 (2009).
    [Crossref]
  25. R. E. V. Profumo, R. Asgari, M. Polini, and A. H. MacDonald, “Double-layer graphene and topological insulator thin-film plasmons,” Phys. Rev. B 85(8), 085443 (2012).
    [Crossref]
  26. J. J. Zhu, S. M. Badalyan, and F. M. Peeters, “Plasmonic excitations in Coulomb-coupled N-layer graphene structures,” Phys. Rev. B 87(8), 085401 (2013).
    [Crossref]
  27. S. Kim, I. Jo, J. Nah, Z. Yao, S. K. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83(16), 161401 (2011).
    [Crossref]
  28. R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
    [Crossref]
  29. J. A. Seamons, C. P. Morath, J. L. Reno, and M. P. Lilly, “Coulomb drag in the exciton regime in electron-hole bilayers,” Phys. Rev. Lett. 102(2), 026804 (2009).
    [Crossref] [PubMed]
  30. X. He, Z. Liu, D. N. Wang, M. Yang, T. Y. Hu, and J. G. Tian, “Saturable absorber based on graphene-covered-microfiber,” IEEE Photon. Technol. Lett. 25(14), 1392–1394 (2013).
    [Crossref]
  31. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
    [Crossref] [PubMed]
  32. Y. Wu, B. Yao, A. Zhang, Y. Rao, Z. Wang, Y. Cheng, Y. Gong, W. Zhang, Y. Chen, and K. S. Chiang, “Graphene-coated microfiber Bragg grating for high-sensitivity gas sensing,” Opt. Lett. 39(5), 1235–1237 (2014).
    [Crossref] [PubMed]
  33. J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
    [Crossref] [PubMed]
  34. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
    [Crossref] [PubMed]
  35. T. Zhao, S. Gong, M. Hu, R. Zhong, D. Liu, X. Chen, P. Zhang, X. Wang, C. Zhang, P. Wu, and S. Liu, “Coherent and tunable terahertz radiation from graphene surface plasmon polarirons excited by cyclotron electron beam,” Sci. Rep. 5, 16059 (2015).
    [Crossref] [PubMed]
  36. D. Correas-Serrano, J. S. Gomez-Diaz, and A. Alvarez-Melcon, “Surface plasmons in graphene cylindrical waveguides,” AP-S 8, 896–897 (2014).
  37. J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 11(3), 703–711 (2016).
    [Crossref]
  38. P. Longe and S. M. Bose, “Collective excitations in metallic graphene tubules,” Phys. Rev. B Condens. Matter 48(24), 18239–18243 (1993).
    [Crossref] [PubMed]
  39. A. Moradi and H. Khosravi, “Collective excitations in single-walled carbon nanotubes,” Phys. Rev. B 76(11), 113411 (2007).
    [Crossref]
  40. J. Yang, J. Yang, W. Deng, F. Mao, and M. Huang, “Transmission properties and molecular sensing application of CGPW,” Opt. Express 23(25), 32289–32299 (2015).
    [Crossref] [PubMed]
  41. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
    [Crossref] [PubMed]
  42. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
    [Crossref]
  43. B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
    [Crossref]
  44. Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
    [Crossref]
  45. S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano 6(2), 1766–1775 (2012).
    [Crossref] [PubMed]
  46. P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248 (2008).
    [Crossref]
  47. P. Berini, “Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
    [Crossref]
  48. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
    [Crossref] [PubMed]
  49. P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006).
    [Crossref] [PubMed]

2016 (1)

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 11(3), 703–711 (2016).
[Crossref]

2015 (4)

T. Zhao, S. Gong, M. Hu, R. Zhong, D. Liu, X. Chen, P. Zhang, X. Wang, C. Zhang, P. Wu, and S. Liu, “Coherent and tunable terahertz radiation from graphene surface plasmon polarirons excited by cyclotron electron beam,” Sci. Rep. 5, 16059 (2015).
[Crossref] [PubMed]

J. Yang, J. Yang, W. Deng, F. Mao, and M. Huang, “Transmission properties and molecular sensing application of CGPW,” Opt. Express 23(25), 32289–32299 (2015).
[Crossref] [PubMed]

T. Zhao, R. B. Zhong, M. Hu, X. X. Chen, P. Zhang, S. Gong, and S. G. Liu, “Tunable terahertz radiation from arbitrary profile dielectric grating coated with graphene excited by an electron beam,” Chin. Phys. B 24(9), 094102 (2015).
[Crossref]

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. Zhong, X. Chen, P. Zhang, C. Zhang, and S. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

2014 (8)

S. G. Liu, C. Zhang, M. Hu, X. X. Chen, P. Zhang, S. Gong, T. Zhao, and R. B. Zhong, “Coherent and tunable terahertz radiation from graphene surface plasmon polaritons excited by an electron beam,” Appl. Phys. Lett. 104(20), 201104 (2014).
[Crossref]

T. Zhan, D. Han, X. Hu, X. Liu, S. Chui, and J. Zi, “Tunable terahertz radiation from graphene induced by moving electrons,” Phys. Rev. B 89(24), 245434 (2014).
[Crossref]

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Y. Wu, B. Yao, A. Zhang, Y. Rao, Z. Wang, Y. Cheng, Y. Gong, W. Zhang, Y. Chen, and K. S. Chiang, “Graphene-coated microfiber Bragg grating for high-sensitivity gas sensing,” Opt. Lett. 39(5), 1235–1237 (2014).
[Crossref] [PubMed]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
[Crossref] [PubMed]

D. Correas-Serrano, J. S. Gomez-Diaz, and A. Alvarez-Melcon, “Surface plasmons in graphene cylindrical waveguides,” AP-S 8, 896–897 (2014).

2013 (8)

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[Crossref]

X. He, Z. Liu, D. N. Wang, M. Yang, T. Y. Hu, and J. G. Tian, “Saturable absorber based on graphene-covered-microfiber,” IEEE Photon. Technol. Lett. 25(14), 1392–1394 (2013).
[Crossref]

K. Yang, S. Arezoomandan, and B. S. Rodriguez, “The linear and nonlinear THz properties of graphene,” Int. J. THz Sci. Technol. 6, 223 (2013).

M. Farhat, C. Rockstuhl, and H. Bağcı, “A 3D tunable and multi-frequency graphene plasmonic cloak,” Opt. Express 21(10), 12592–12603 (2013).
[Crossref] [PubMed]

J. J. Zhu, S. M. Badalyan, and F. M. Peeters, “Plasmonic excitations in Coulomb-coupled N-layer graphene structures,” Phys. Rev. B 87(8), 085401 (2013).
[Crossref]

M. Amin, M. Farhat, and H. Baǧcı, “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref] [PubMed]

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
[Crossref] [PubMed]

2012 (4)

R. E. V. Profumo, R. Asgari, M. Polini, and A. H. MacDonald, “Double-layer graphene and topological insulator thin-film plasmons,” Phys. Rev. B 85(8), 085443 (2012).
[Crossref]

S. Thongrattanasiri, A. Manjavacas, and F. J. García de Abajo, “Quantum finite-size effects in graphene plasmons,” ACS Nano 6(2), 1766–1775 (2012).
[Crossref] [PubMed]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

2011 (6)

S. Kim, I. Jo, J. Nah, Z. Yao, S. K. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83(16), 161401 (2011).
[Crossref]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (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(7349), 64–67 (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]

2010 (1)

Y. S. Ang, S. Sultan, and C. Zhang, “Nonlinear optical spectrum of bilayer graphene in the terahertz regime,” Appl. Phys. Lett. 97(24), 243110 (2010).
[Crossref]

2009 (5)

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

A. Neto, F. Guinea, N. Peres, K. Novoselov, and A. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

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

J. A. Seamons, C. P. Morath, J. L. Reno, and M. P. Lilly, “Coulomb drag in the exciton regime in electron-hole bilayers,” Phys. Rev. Lett. 102(2), 026804 (2009).
[Crossref] [PubMed]

2008 (1)

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248 (2008).
[Crossref]

2007 (4)

A. Moradi and H. Khosravi, “Collective excitations in single-walled carbon nanotubes,” Phys. Rev. B 76(11), 113411 (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]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
[Crossref]

M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys. 46(8), L151–L153 (2007).
[Crossref]

2006 (1)

2005 (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,” Nature 438(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
[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]

2000 (1)

P. Berini, “Plasmon polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[Crossref]

1993 (1)

P. Longe and S. M. Bose, “Collective excitations in metallic graphene tubules,” Phys. Rev. B Condens. Matter 48(24), 18239–18243 (1993).
[Crossref] [PubMed]

Alaee, R.

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Alvarez-Melcon, A.

D. Correas-Serrano, J. S. Gomez-Diaz, and A. Alvarez-Melcon, “Surface plasmons in graphene cylindrical waveguides,” AP-S 8, 896–897 (2014).

Amin, M.

M. Amin, M. Farhat, and H. Baǧcı, “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013).
[Crossref] [PubMed]

Ang, Y. S.

Y. S. Ang, S. Sultan, and C. Zhang, “Nonlinear optical spectrum of bilayer graphene in the terahertz regime,” Appl. Phys. Lett. 97(24), 243110 (2010).
[Crossref]

Arezoomandan, S.

K. Yang, S. Arezoomandan, and B. S. Rodriguez, “The linear and nonlinear THz properties of graphene,” Int. J. THz Sci. Technol. 6, 223 (2013).

Asgari, R.

R. E. V. Profumo, R. Asgari, M. Polini, and A. H. MacDonald, “Double-layer graphene and topological insulator thin-film plasmons,” Phys. Rev. B 85(8), 085443 (2012).
[Crossref]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Badalyan, S. M.

J. J. Zhu, S. M. Badalyan, and F. M. Peeters, “Plasmonic excitations in Coulomb-coupled N-layer graphene structures,” Phys. Rev. B 87(8), 085401 (2013).
[Crossref]

Bagci, H.

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M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
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X. He, Z. Liu, D. N. Wang, M. Yang, T. Y. Hu, and J. G. Tian, “Saturable absorber based on graphene-covered-microfiber,” IEEE Photon. Technol. Lett. 25(14), 1392–1394 (2013).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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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(7349), 64–67 (2011).
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Liu, J. P.

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Figures (6)
Fig. 1
Fig. 1 Schematic of CDLG structure, the radii of the inner and outer graphene layers are ra and rb, respectively.

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Fig. 2
Fig. 2 (a) Mode patterns of the first four modes at the frequency of 40THz. (b) Normalized Ez field of m = 0 mode at 10THz, 20THz, 30THz and 40THz. (c) Dispersion of SPPs modes (d) Normalized propagation length of SPPs modes.

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Fig. 3
Fig. 3 Effective mode index (a) and normalized propagation length (b) as a function of the distance between two graphene layers at the frequency of 40THz.

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Fig. 4
Fig. 4 Effective mode index (a) and normalized propagation length (b) as a function of the chemical potential at the frequency of 40THz.

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Fig. 5
Fig. 5 Effective mode index (a) and normalized propagation length (b) as a function of the permittivity of dielectric sandwiched between two grpahene layers at the frequency of 20THz.

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Fig. 6
Fig. 6 Comparison of SPPs properties between CDLG and monolayer graphene structure. (a) Effective mode index and (b) Normalized propagation length of fundamental mode as a function of frequency. Mode patterns in the (c) X-Y and (d) Y-Z planes.

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Equations (6)

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E z I = A 1 m k c 1 2 J m ( k c 1 r )                                                           H z I = A 2 m k c 1 2 J m ( k c 1 r ) E r I = j A 1 m k z k c 1 J m ′ ( k c 1 r ) − A 2 m ω μ 0 m r J m ( k c 1 r ) E θ I = − A 1 m k z m r J m ( k c 1 r ) − j A 2 m ω μ 0 k c 1 J m ′ ( k c 1 r )                     , H r I = A 1 m ω ε 0 ε 1 m r J m ( k c 1 r ) + j A 2 m k z k c 1 J m ′ ( k c 1 r )   H θ I = A 1 m j ω ε 0 ε 1 k c 1 J m ′ ( k c 1 r ) − A 2 m k z m r J m ( k c 1 r )
E z I I = A 3 m k c 2 2 I m ( k c 2 r ) + A 4 m k c 2 2 K m ( k c 2 r )   ,                             H z I I = A 5 m k c 2 2 I m ( k c 2 r ) + A 6 m k c 2 2 K m ( k c 2 r ) E r I I = − j k z k c 2 [ A 3 m I ′ m ( k c 2 r ) + A 4 m K m ′ ( k c 2 r ) ] + ω μ 0 m r [ A 5 m I m ( k c 2 r ) + A 6 m K m ( k c 2 r ) ] E θ I I = k z m r [ A 3 m I m ( k c 2 r ) + A 4 m K m ( k c 2 r ) ] + j ω μ 0 k c 2 [ A 5 m I ′ m ( k c 2 r ) + A 6 m K ′ m ( k c 2 r ) ]                             , H r I I = − j k z k c 2 [ A 5 m I ′ m ( k c 2 r ) + A 6 m K ′ m ( k c 2 r ) ] − ω ε 0 ε 2 r m [ A 3 m I m ( k c 2 r ) + A 4 m K m ( k c 2 r ) ] H θ I I = k z r m [ A 5 m I m ( k c 2 r ) + A 6 m K m ( k c 2 r ) ] − j ω ε 0 ε 2 k c 2 [ A 3 m I ′ m ( k c 2 r ) + A 4 m K ′ m ( k c 2 r ) ]
E z I I I = A 7 m k c 3 2 K m ( k c 3 r ) ,                                             H z I I I = A 8 m k c 3 2 K m ( k c 3 r ) E r I I I = − j k z k c 3 A 7 m K m ′ ( k c 3 r ) + ω μ 0 m r A 8 m K m ( k c 3 r ) E θ I I I = k z m r A 7 m K m ( k c 3 r ) + j ω μ 0 k c 3 A 8 m K ′ m ( k c 3 r )                         , H r I I I = − j k z k c 3 A 8 m K ′ m ( k c 3 r ) − ω ε 0 r m A 7 m K m ( k c 3 r ) H θ I I I = k z r m A 8 m K m ( k c 3 r ) − j ω ε 0 k c 3 A 7 m K ′ m ( k c 3 r )
E z I | r = r a = E z I I | r = r a ,                                                                                                                               E θ I | r = r a = E θ I I | r = r a ,         ( H z I − H z I I ) | r = r a = σ g E θ I | r = r a ,                 ( H θ I I − H θ I ) | r = r a = σ g E z I | r = r a .
E z I I | r = r b = E z I I I | r = r b ,                                                                                                                                                         E θ I I | r = r b = E θ I I I | r = r b ,         ( H z I I − H z I I I ) | r = r b = σ g E θ I I I | r = r b ,                             ( H θ I I I − H θ I I ) | r = r b = σ g E z I I I | r = r b .
[ σ g k c 3 K 0 ( k c 3 r b ) − j ω ε 0 ε 3 K 1 ( k c 3 r b ) ] k c 2 I 0 ( k c 2 r b ) k c 3 K 0 ( k c 3 r b ) − j ω ε 0 ε 2 I 1 ( k c 2 r b ) [ σ g k c 1 J 0 ( k c 1 r a ) − j ω ε 0 ε 1 J 1 ( k c 1 r a ) ] k c 2 I 0 ( k c 2 r a ) k c 1 J 0 ( k c 1 r a ) + j ω ε 0 ε 2 I 1 ( k c 2 r a ) = [ σ g k c 3 K 0 ( k c 3 r b ) − j ω ε 0 ε 3 K 1 ( k c 3 r b ) ] k c 2 K 0 ( k c 2 r b ) k c 3 K 0 ( k c 3 r b ) + j ω ε 0 ε 2 K 1 ( k c 2 r b ) [ σ g k c 1 J 0 ( k c 1 r a ) − j ω ε 0 ε 1 J 1 ( k c 1 r a ) ] k c 2 K 0 ( k c 2 r a ) k c 1 J 0 ( k c 1 r a ) − j ω ε 0 ε 2 K 1 ( k c 2 r a )       .

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