Abstract

Multilayer graphene can support multiple plasmon bands. If structured into graphene ribbons, they can support multiple localized plasmonic modes with interesting optical properties. However, not all such plasmonic modes can be excited directly due to the constrains of the structural symmetry. We show by numerical simulations that by breaking the symmetry all plasmonic modes can be excited. We discuss the general principles and properties of two-layer graphene ribbons and then extend to multilayer graphene ribbons. In multilayer graphene ribbons with different ribbon widths, a tunable broadband absorption can be attained due to the excitations of all plasmonic modes. Our results suggest that these symmetry-broken multilayer graphene ribbons could offer more degrees of freedom in designing photonic devices.

© 2016 Optical Society of America

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2015 (3)

Y. Y. Dai, X. L. Zhu, N. A. Mortensen, J. Zi, and S. S. Xiao, “Nanofocusing in a tapered graphene plasmonic waveguide,” J. Opt. 17(6), 065002 (2015).
[Crossref]

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

N. K. Emani, D. Wang, T.-F. Chung, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Plasmon resonance in multilayer graphene nanoribbons,” Laser Photonics Rev. 9(6), 650–655 (2015).
[Crossref]

2014 (7)

A. Kumar, K. H. Fung, M. T. Homer Reid, and N. X. Fang, “Photon emission rate engineering using graphene nanodisc cavities,” Opt. Express 22(6), 6400–6415 (2014).
[Crossref] [PubMed]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref] [PubMed]

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14(5), 2907–2913 (2014).
[Crossref] [PubMed]

P. Wachsmuth, R. Hambach, G. Benner, and U. Kaiser, “Plasmon bands in multilayer graphene,” Phys. Rev. B 90(23), 235434 (2014).
[Crossref]

T. Liu, Y. Shen, W. Shin, Q. Zhu, S. Fan, and C. Jin, “Dislocated double-layer metal gratings: an efficient unidirectional coupler,” Nano Lett. 14(7), 3848–3854 (2014).
[Crossref] [PubMed]

F. J. García de Abajo, “Plasmonics: challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

2013 (8)

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (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]

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21(23), 28438–28443 (2013).
[Crossref] [PubMed]

A. Ishikawa and T. Tanaka, “Plasmon hybridization in graphene metamaterials,” Appl. Phys. Lett. 102(25), 253110 (2013).
[Crossref]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

2012 (7)

T. Stauber and G. Gómez-Santos, “Plasmons in layered structures including graphene,” New J. Phys. 14(10), 105018 (2012).
[Crossref]

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]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

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]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

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]

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]

2011 (4)

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]

V. B. Jovanović, I. Radović, D. Borka, and Z. L. Mišković, “High-energy plasmon spectroscopy of freestanding multilayer graphene,” Phys. Rev. B 84(15), 155416 (2011).
[Crossref]

F. H. L. 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]

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

2010 (2)

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

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

2009 (3)

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]

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

2008 (2)

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[Crossref] [PubMed]

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008).
[Crossref] [PubMed]

2007 (2)

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

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007).
[Crossref]

2006 (1)

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8(12), 318 (2006).
[Crossref]

2005 (1)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

1996 (1)

D. J. Gross, “The role of symmetry in fundamental physics,” Proc. Natl. Acad. Sci. U.S.A. 93(25), 14256–14259 (1996).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[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]

Altug, H.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

Alù, A.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (2013).
[Crossref] [PubMed]

Avouris, P.

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

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]

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]

Badioli, M.

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]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Benner, G.

P. Wachsmuth, R. Hambach, G. Benner, and U. Kaiser, “Plasmon bands in multilayer graphene,” Phys. Rev. B 90(23), 235434 (2014).
[Crossref]

Bøggild, P.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14(5), 2907–2913 (2014).
[Crossref] [PubMed]

Boltasseva, A.

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D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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F. H. L. 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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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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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).
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F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (2013).
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Nat. Nanotechnol. (3)

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Figures (4)

Fig. 1
Fig. 1 (a) Plasmon dispersion (solid lines) for two-layer graphene with a interlayer separation of 100 nm. That of a single-layer graphene (dashed line) is also shown for comparison. Dots represent the resonant frequencies of two-layer graphene ribbons of equal ribbon width for different ribbon widths extracted from the simulated absorption spectra, according to Eq. (2). The inset shows the schematics of an individual two-layer graphene ribbon and the cross-sectioned electric field distributions of the symmetric mode. (b) Absorption spectra of two-layer graphene ribbons of equal width for different interlayer separations: 100 nm (red line), 200 nm (green line), and 500 nm (blue line). The ribbon width is 200 nm. The dashed black line represents the absorption spectrum of a single graphene ribbon with a ribbon width of 200 nm. (c) Absorption spectra for two-layer graphene ribbons of unequal ribbon width at different interlayer separation as schematically shown in the inset. (d) Normalized electric (upper panels) and magnetic (lower panels) field amplitude distributions for the two-layer graphene ribbons of unequal ribbon width at two resonant frequencies. Arrows indicate the current direction within the constituent graphene ribbons.
Fig. 2
Fig. 2 (a) Absorption spectra for two-layer graphene ribbons with a different ribbon width different ΔW as labeled at intervals of 20 nm. The interlayer separation is 100 nm. The period of the supercell used is 1 μm. (b) Q factors of the symmetric (red dots) and anti-symmetric (black dots) modes as a function of the ribbon width difference. (c) Normalized amplitudes of the electric (upper panel) and magnetic (lower panel) dipole moment densities in a contour plot as a function of ΔW and frequency.
Fig. 3
Fig. 3 (a) Plasmon dispersion for ten-layer graphene. Symbols represent the resonant frequencies obtained from the calculated absorption spectra according to Eq. (2). (b) Absorption spectra for ten-layer graphene ribbons of equal ribbon width. Red, green, and blue lines are for the ribbon width of 200, 300, and 400 nm, respectively. The interlayer separation in ten-layer graphene and ten-layer graphene ribbons is both 100 nm.
Fig. 4
Fig. 4 Absorption spectra for ten-layer graphene ribbons of equal ribbon width (black lines) and of unequal ribbon width (red lines). The ribbon width of the former is 200 nm while that of the latter varies nearly from 120 nm for the top to 300 nm for the bottom graphene ribbon. The interlayer separation is 200 nm. The period of the supercell used is 1 μm. In (a), the Fermi energy is 0.4 eV. The dotted and solid lines are for the relaxation time of 0.4 and 0.04 ps, respectively. In (b), the Fermi energy is 0.6 eV. The dotted and solid lines are for the relaxation time of 0.6 and 0.06 ps, respectively.

Equations (4)

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σ(ω)= e 2 E F π 2 i ω+i τ 1 + e 2 4 [ θ( ω2 E F )+ i π log| ω2 E F ω+2 E F | ],
k eff =(n+3/4)π/W.
P= 1 iω j d 2 r ,
M= 1 2 r×j d 2 r ,

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