Abstract

Graphene nanoribbon (GNR), as a fundamental component to support the surface plasmon waves, are envisioned to play an important role in graphene plasmonics. However, to achieve extremely confinement of the graphene surface plasmons (GSPs) is still a challenging. Here, we propose a scheme to realize the excitation of localized surface plasmons with very strong field enhancement at the resonant frequency. By sinusoidally patterning the boundaries of GNRs, a new type of plasmon mode with field energy concentrated on the shaped grating crest (crest mode) can be efficiently excited, creating a sharp notch on the transmission spectra. Specifically, the enhanced field energies are featured by 3 times of magnitude stronger than that of the unpatterned classical GNRs. Through theoretical analyses and numerical calculations, we confirm that the enhanced fields of the crest modes can be tuned not only by changing the width, period and Fermi energy as traditional ribbons, but also by varying the grating amplitude and period. This new technique of manipulating the light-graphene interaction gives an insight of modulating plasmon resonances on graphene nanostrutures, making the proposed pattern method an attractive candidate for designing optical filters, spatial light modulators, and other active plasmonic devices.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. 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]
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    [Crossref]
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    [Crossref] [PubMed]
  35. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
    [Crossref]
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    [Crossref]
  37. S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons: erratum,” Opt. Express 24(7), 7436 (2016).
    [Crossref] [PubMed]
  38. 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]
  39. A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
    [Crossref] [PubMed]
  40. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (10)

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

W. Xu and T. W. Lee, “Recent progress on fabrication techniques of graphene nanoribbons,” Mater. Horiz. 3(3), 186–207 (2016).
[Crossref]

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

V. Gerasik, M. S. Wartak, A. V. Zhukov, and M. B. Belonenko, “Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range,” Mod. Phys. Lett. B 30(11), 1650185 (2016).
[Crossref]

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

H. Nasari, M. S. Abrishamian, and P. Berini, “Nonlinear optics of surface plasmon polaritons in subwavelength graphene ribbon resonators,” Opt. Express 24(1), 708–723 (2016).
[Crossref] [PubMed]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, S. X. Xia, X. J. Shang, and X. Luo, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24(5), 5376–5386 (2016).
[Crossref]

S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons: erratum,” Opt. Express 24(7), 7436 (2016).
[Crossref] [PubMed]

2015 (5)

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: a dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(2), 214 (2015).
[Crossref]

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

2014 (4)

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
[Crossref]

M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photonics Rev. 8(3), 394–408 (2014).
[Crossref]

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

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

2013 (7)

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

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

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

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
[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]

S. He, X. Zhang, and Y. He, “Graphene nano-ribbon waveguides of record-small mode area and ultra-high effective refractive indices for future VLSI,” Opt. Express 21(25), 30664–30673 (2013).
[Crossref] [PubMed]

2012 (6)

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. 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]

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

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (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]

2011 (4)

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]

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]

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

2010 (1)

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

2009 (1)

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[Crossref]

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]

Abbas, A. N.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Abrishamian, M. S.

Aitchison, J. S.

M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photonics Rev. 8(3), 394–408 (2014).
[Crossref]

Ajayan, P. M.

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]

Alam, M. Z.

M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photonics Rev. 8(3), 394–408 (2014).
[Crossref]

Alonso-González, P.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Atar, F. B.

Avouris, P.

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

Balci, O.

Balci, S.

Bao, Q.

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

Basov, D. N.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [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]

Belonenko, M. B.

V. Gerasik, M. S. Wartak, A. V. Zhukov, and M. B. Belonenko, “Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range,” Mod. Phys. Lett. B 30(11), 1650185 (2016).
[Crossref]

Berini, P.

H. Nasari, M. S. Abrishamian, and P. Berini, “Nonlinear optics of surface plasmon polaritons in subwavelength graphene ribbon resonators,” Opt. Express 24(1), 708–723 (2016).
[Crossref] [PubMed]

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]

Bezuglyi, E. V.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[Crossref]

Boltasseva, A.

N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: a dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(2), 214 (2015).
[Crossref]

Casanova, F.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Centeno, A.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Chakraborty, S.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Chan, M. W. C.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

Chang, D. E.

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]

Chen, S.

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

Chen, Z.

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Cheng, H.

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

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

Dai, N.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Dai, S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

de la Peña, F.

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
[Crossref] [PubMed]

Duan, X.

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

Ducati, C.

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
[Crossref] [PubMed]

Efetov, D. K.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

Emani, N. K.

N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: a dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(2), 214 (2015).
[Crossref]

Fang, Z.

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]

Fei, Z.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Fogler, M. M.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Folland, T. G.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Freitag, M.

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

Gao, W.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Garcia de Abajo, F. J.

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

García de Abajo, F. J.

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]

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]

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]

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

García-Vidal, F. J.

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]

Geng, B.

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]

Gerasik, V.

V. Gerasik, M. S. Wartak, A. V. Zhukov, and M. B. Belonenko, “Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range,” Mod. Phys. Lett. B 30(11), 1650185 (2016).
[Crossref]

Girit, C.

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]

Goldflam, M. D.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Grigorenko, A. N.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

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

Guan, Y.

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Guinea, F.

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

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]

Halas, N. J.

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]

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Hao, J.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Hao, Z.

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]

He, Q.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

He, S.

He, Y.

Hillenbrand, R.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Holland, D. J.

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
[Crossref] [PubMed]

Horng, J.

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]

Huang, W. Q.

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
[Crossref]

Huang, Z.

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

Hueso, L. E.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Ishikawa, A.

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

Janssen, G. C. A. M.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Ju, L.

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]

Kakenov, N.

Kats, A. V.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[Crossref]

Kevek, J. W.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

Kildishev, A. V.

N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: a dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(2), 214 (2015).
[Crossref]

Kim, P.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

Kim, Y. J.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Knight, M. W.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Kocabas, C.

Koppens, F. H.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

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]

Koppens, F. H. L.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Leary, R. K.

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
[Crossref] [PubMed]

Lee, T. W.

W. Xu and T. W. Lee, “Recent progress on fabrication techniques of graphene nanoribbons,” Mater. Horiz. 3(3), 186–207 (2016).
[Crossref]

Levchenko, A.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[Crossref]

Li, H.

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

Li, H. J.

Li, X.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

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

Li, X. F.

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
[Crossref]

Liang, X.

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]

Lin, Q.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons: erratum,” Opt. Express 24(7), 7436 (2016).
[Crossref] [PubMed]

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

Liu, B.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Liu, G.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Liu, G. D.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

Liu, H.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Liu, J. P.

Liu, M. K.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Liu, Z.

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]

Loh, K. P.

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

Low, T.

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

Luo, X.

Ma, L.

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]

Ma, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

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]

Manolatou, C.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

Marshall, O. P.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Martin, M.

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]

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
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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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A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
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McEuen, P. L.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
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Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
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Miao, Z.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
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M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photonics Rev. 8(3), 394–408 (2014).
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Nasari, H.

Nene, P.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
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Nicoletti, O.

O. Nicoletti, F. de la Peña, R. K. Leary, D. J. Holland, C. Ducati, and P. A. Midgley, “Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles,” Nature 502(7469), 80–84 (2013).
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A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

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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I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
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Nordlander, P.

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).
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M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
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Novoselov, K. S.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y. J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
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A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
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Pesquera, A.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
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A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
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W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
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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).
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N. K. Emani, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Graphene: a dynamic platform for electrical control of plasmonic resonance,” Nanophotonics 4(2), 214 (2015).
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Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Shang, X. J.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, S. X. Xia, X. J. Shang, and X. Luo, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24(5), 5376–5386 (2016).
[Crossref]

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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).
[Crossref] [PubMed]

Shu, J.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Sobhani, H.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Spevak, I. S.

I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B 79(16), 161406 (2009).
[Crossref]

Strait, J. H.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

Sun, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

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

Tao, N.

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Thongrattanasiri, S.

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]

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]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

Tian, J.

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

Tiwari, S.

J. H. Strait, P. Nene, M. W. C. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, “Confined plasmons in graphene microstructures: experiments and theory,” Phys. Rev. B 87(24), 241410 (2013).
[Crossref]

Vélez, S.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

Wagner, M.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Wang, B. X.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
[Crossref]

Wang, F.

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]

Wang, G. Z.

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
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Wang, L.

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

Wang, L. L.

Wang, S.

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Wang, Y.

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]

Wartak, M. S.

V. Gerasik, M. S. Wartak, A. V. Zhukov, and M. B. Belonenko, “Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range,” Mod. Phys. Lett. B 30(11), 1650185 (2016).
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Wen, S. C.

Wu, J. S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Wu, W.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Wu, Y.

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

Xia, F.

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

Xia, S.

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
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Xia, S. X.

Xiao, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Xie, B.

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

Xie, F.

Xu, Q.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

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W. Xu and T. W. Lee, “Recent progress on fabrication techniques of graphene nanoribbons,” Mater. Horiz. 3(3), 186–207 (2016).
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Yan, H.

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

Yu, P.

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

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).
[Crossref] [PubMed]

Zhai, X.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons: erratum,” Opt. Express 24(7), 7436 (2016).
[Crossref] [PubMed]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, S. X. Xia, X. J. Shang, and X. Luo, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24(5), 5376–5386 (2016).
[Crossref]

S. Xia, X. Zhai, L. Wang, H. Li, Z. Huang, and Q. Lin, “Dynamically tuning the optical coupling of surface plasmons in coplanar graphene nanoribbons,” Opt. Commun. 352, 110–115 (2015).
[Crossref]

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Theoretical investigation of broadband and wide-angle terahertz metamaterial absorber,” IEEE Photonics Technol. Lett. 26(2), 111–114 (2014).
[Crossref]

Zhang, L.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Zhang, X.

Zhou, C.

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

Zhou, L.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete Phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Zhu, J. J.

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

Zhu, S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. McLeod, M. K. Liu, K. W. Post, S. Zhu, G. C. A. M. Janssen, M. M. Fogler, and D. N. Basov, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15(12), 8271–8276 (2015).
[Crossref] [PubMed]

Zhu, W.

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

Zhukov, A. V.

V. Gerasik, M. S. Wartak, A. V. Zhukov, and M. B. Belonenko, “Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range,” Mod. Phys. Lett. B 30(11), 1650185 (2016).
[Crossref]

Zurutuza, A.

A. Y. Nikitin, P. Alonso-González, S. Vélez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016).
[Crossref]

ACS Nano (7)

Z. Chen, X. Shan, Y. Guan, S. Wang, J. J. Zhu, and N. Tao, “Imaging local heating and thermal diffusion of nanomaterials with plasmonic thermal microscopy,” ACS Nano 9(12), 11574–11581 (2015).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. 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]

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

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

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]

A. N. Abbas, G. Liu, B. Liu, L. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

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

Appl. Phys. Lett. (2)

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

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

IEEE Photonics Technol. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1

Schematic of the designed periodic GNRs with two sinusoidally shaped boundaries. The insert shows top-view illustration of a typical period.

Fig. 2
Fig. 2

Transmission, reflection, and absorption spectra of GNRs with two sinusoidal grating (grating-grating) boundaries (a) and with two linear (line-line) boundaries (b). The insets shows one period of the shaped GNRs and the polarization direction of electromagnetic excitation. Electric field norms (c) and Ez components (d) in a unit cell of sinusoidally shaped GNRs for the nature of the enhanced crest modes 1-4, respectively. Electric field norms (e) and Ez components (f) in a unit cell of GNRs with line-line boundaries for the excited modes 1-4, respectively. The parameters are set as W = 100 nm, Ef = 1.0 eV, A = 40 nm, Λ = 100 nm and P = 200 nm.

Fig. 3
Fig. 3

Geometrically tuning of the enhanced plasmon modes. Transmission spectra with different geometrical parameters of grating amplitude A (a), ribbon width W (c), grating period Λ (e) and ribbon period P (g), respectively. Plasmon resonant frequency (left) and fwhm (right) as a function of A (b), W (d), Λ (f) and P (h), respectively. Except for the tunable variable, the other parameters are set as Ef = 1.0 eV, A = 40 nm, W = 100 nm, Λ = 100 nm, and P = 200 nm.

Fig. 4
Fig. 4

Electrostatic tuning of the crest plasmon modes. (a) Transmission spectra with different Fermi energy level in graphene when W = 100 nm, A = 40 nm, Λ = 100 nm and P = 200 nm. (b) Scaling rule of plasmon resonant frequencies (left) and fwhm (right) as a function of Ef.

Fig. 5
Fig. 5

Schematic of the designed periodic GNRs with only one sinusoidally shaped boundary. The insert shows top-view illustration of a typical period.

Fig. 6
Fig. 6

(a) Transmission, reflection, and absorption spectra of GNRs with one sinusoidally shaped (grating-line) boundary. The inset shows one period of the shaped GNRs and the polarization direction of electromagnetic excitation. Electric field norms (b) and Ez components (c) in a unit cell of asymmetrically shaped GNRs for the nature of the excited crest modes 1-4, respectively. The parameters are set as W = 100 nm, Ef = 1.0 eV, A = 40 nm, Λ = 100 nm and P = 200 nm.

Fig. 7
Fig. 7

(a) Transmission spectra with different grating amplitude A of GNRs with one sinusoidally shaped boundary. (b) Plasmon resonant frequency (left) and fwhm (right) as a function of A. The parameters are set as W = 100 nm, Ef = 1.0 eV, Λ = 100 nm and P = 200 nm. (c) Distribution of the |E|-field intensity at the y-direction along the dotted line that lies at the middle of a period, as shown in the insert of (c). The green lines are for the line-line (L-L) boundaries, the blue lines are for the grating-line (G-L) boundaries, while the red lines are for the grating-grating (G-G) boundaries, respectively. The parameters are set as W = 100 nm, Ef = 1.0 eV, A = 40 nm, Λ = 100 nm and P = 200 nm.

Equations (5)

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y up =Asin( 2πx /Λ + φ 0 )+W/2 , y lo =Asin( 2πx /Λ + φ 0 )W/2 ,
σ( ω )= i e 2 π 2 E f ω+i τ 1 + e 2 4 [ θ( ω2 E f )+ i π log| ω2 E f ω+2 E f | ],
ω p = e E f πη ε avg W eff = e E f πη ε avg ( W+2A ) .
η= Im[ σ( ω p ) ] ε avg W eff ω p .
ω p = e E f πη ε avg W eff = e E f πη ε avg ( W+A ) .

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