Abstract

Graphene-based plasmonic structures feature large tunability, high spatial confinement, and potentially low loss, and are therefore an emerging technology for unconventional manipulation of light. In this paper, we demonstrate electrically tunable terahertz plasmonic crystals consisting of square-lattice graphene periodic anti-dot arrays on a SiO2/Si substrate. Transmission spectroscopy reveals multiple distinct resonances arising from excitations of graphene surface-plasmon–polariton (SPP) modes on different branches of the SPP dispersion curves inherent to the periodic structures. The resonance frequencies are readily tuned electrostatically with the Si back-gate and exhibit the dependency on the carrier density unique to SPP in graphene. Simulations show excellent agreement with the experiments and further illustrate the symmetry-based selection rule for the excited graphene SPP modes. Such graphene plasmonic crystals may lead to a broad range of applications including plasmonic waveguide and transformation optics. Exploiting higher-order graphene SPP modes is an effective way to further facilitate field localization and enhancement.

© 2015 Optical Society of America

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2014 (5)

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

2013 (4)

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

2012 (8)

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

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

2011 (4)

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

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

2009 (1)

M. Jablan, H. Buljan, M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).

2007 (2)

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

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

2006 (1)

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

2002 (1)

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

1999 (1)

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

1996 (1)

S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

1992 (1)

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

1991 (1)

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Adreev, G. O.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Ajayan, P. M.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Alonso-Gonzalez, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Antoniadis, D. A.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Avouris, P.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

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

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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

Badioli, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Bao, W.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

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, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Boggild, P.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Buljan, H.

M. Jablan, H. Buljan, M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Chandra, B.

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

Chang, D. E.

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

Chee, J.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Crassee, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Das Sarma, S.

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

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Engheta, N.

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

Faist, J.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Fal’ko, V. I.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

Fan, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

Farmer, D. B.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

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

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Gao, W.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
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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, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
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A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

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M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

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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, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

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B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

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K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

Krahne, R.

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

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I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

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X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Li, P.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Li, X.

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

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Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Liang, X.

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

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B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
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I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Lousse, V.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
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I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Meng, X.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

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Mosig, J. R.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
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I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

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A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
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A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
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I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Osgood, R. M.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

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J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

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I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

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X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

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M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
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K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
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I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

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Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
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K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
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B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

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I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

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Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
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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, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Sherrott, M.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Shi, G.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Shu, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Smith, H. I.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Solgaard, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Soljacic, M.

M. Jablan, H. Buljan, M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).

Song, Y.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Tamagnone, M.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Tsui, D. C.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Tulevski, G.

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

Vajtai, R.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Vakil, A.

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

Valmorra, F.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Walter, A. L.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Wang, F.

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

Wang, W.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Wu, Y.

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

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

Xia, F.

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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

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

Xiao, S.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Xing, X. G.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Xu, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Yan, H.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

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

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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

Yan, R.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Yan, W.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Yeung, K. Y. M.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Yoon, H.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Zettl, A.

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

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Zhang, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Zhang, Y. H.

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Zhao, Y.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Zhu, M.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Zhu, W.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

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

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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

Zhu, X.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Zi, J.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Ziegler, K.

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

Zurutuza Elorza, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

ACS Nano (1)

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

ACS Photonics (1)

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Appl. Phys. Lett. (4)

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Nano Lett. (7)

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Nat. Commun. (1)

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

Nat. Nanotechnol. (2)

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

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

Nat. Photonics (1)

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

Nature (3)

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Z. Fei, A. S. Rodin, G. O. Adreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Phys. Rev. B (7)

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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

M. Jablan, H. Buljan, M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

Phys. Rev. Lett. (2)

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

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

Science (1)

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

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

Supplementary Material (1)

» Supplement 1: PDF (1276 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of a square-lattice graphene periodic anti-dot array; (b) simulated transmission, reflection, and absorption spectra of a graphene periodic anti-dot array on a SiO 2 / Si substrate with a lattice constant of 3 μm and an aperture diameter of 2 μm. Fermi energy is set to 0.4 eV and the carrier relaxation time 1 ps; (c) simulated z -direction electric field profiles (in an x y –plane right above the graphene sheet) of the two resonances in part b (left) and the 2D fast Fourier-transform (FFT) of each field profile (right). Top, lower-frequency mode; bottom, higher-frequency mode. In the 2D FFT of the field profiles, each square pixel corresponds to a reciprocal lattice vector (e.g., the center pixel is for [0,0], the one above the center is for [0,1], and so on) and its brightness represents the amplitude of the corresponding spatial frequency component.

Fig. 2.
Fig. 2.

(a) Scanning electron microscopy (SEM) image of a fabricated graphene anti-dot array sample; (b) typical Raman spectrum of the graphene anti-dot array samples.

Fig. 3.
Fig. 3.

Transmission extinction spectra at various back-gate voltages for the following; (a)–(d) samples SQ1–SQ4; (e) unpatterned graphene sample; (f) symbols are the plasmonic resonance frequency (in wavenumbers) as a function of the square root of the carrier density and equivalently the Fermi energy for all the resonance peaks in SQ1–SQ4. Height of the symbols corresponds to the typical error bar in extracting the peak position using different fitting functions and ranges. Solid curves are fits of the data points (symbols in the matching color) with functions in the form of y = a x 1 / 2 with a being a fitting parameter. Experimental results on the other structures are included in Supplement 1.

Fig. 4.
Fig. 4.

Simulated transmission extinction spectra for the same graphene anti-dot arrays in Figs. 3(a)3(d) assuming two different carrier relaxation times: τ = 1 ps (blue curves) and τ = 0.1 ps (red curves) in comparison with the experimental results (black curves).

Fig. 5.
Fig. 5.

Simulated z -direction electric field profiles of the SPP modes corresponding to the four prominent resonance peaks in Fig. 4(d). Plots are numbered in the ascending order of the resonance frequency. Insets, 2D FFT of the field profiles plotted similarly as in Fig. 1(c).

Tables (1)

Tables Icon

Table 1. Details of Different Graphene Anti-Dot Arrays

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