Abstract

The tunable hyperbolic metamaterial (HMM) based on the graphene-dielectric layered structure at THz frequency is presented, and the surface and bulk polaritons of the graphene-based HMM are theoretically studied. It is found that the dispersions of the polaritons can be tuned by varying the Fermi energy of graphene sheets, the graphene-dielectric layers and the layer number of graphene sheets. In addition, the highly confined bulk polariton mode can be excited and is manifested in an attenuated total reflection configuration as a sharp drop in the reflectance. Such properties can be used in tunable optical reflection modulation with the assistance of bulk polaritons.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  34. X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2014

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Y. J. Xiang, J. Guo, X. Y. Dai, S. C. Wen, D. Y. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[CrossRef] [PubMed]

2013

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

M. A. K. Othman, C. Guclu, F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[CrossRef] [PubMed]

B. Zhu, G. Ren, S. Zheng, Z. Lin, S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
[CrossRef] [PubMed]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21(16), 19113–19127 (2013).
[CrossRef] [PubMed]

T. Zhang, L. Chen, X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013).
[CrossRef] [PubMed]

W. R. Zhu, I. D. Rukhlenko, M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
[CrossRef]

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

F. Liu, E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013).
[CrossRef]

2012

P. Tassin, T. Koschny, M. Kafesaki, C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012).
[CrossRef]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

O. Kidwai, S. V. Zhukovsky, J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (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(7419), 192–200 (2012).
[CrossRef] [PubMed]

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

Z. Zhang, H. Li, Z. Gong, Y. Fan, T. Zhang, H. Chen, “Extend the omnidirectional electronic gap of Thue-Morse aperiodic gapped graphene superlattices,” Appl. Phys. Lett. 101(25), 252104 (2012).
[CrossRef]

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

H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012).
[CrossRef]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[CrossRef]

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

2011

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

B. D. Guo, L. Fang, B. H. Zhang, J. R. Gong, “Graphene Doping: A Review,” Insciences J. 1(2), 80–89 (2011).
[CrossRef]

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

A. Vakil, N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

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

2009

A. Reina, X. T. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[CrossRef] [PubMed]

A. A. Avetisyan, B. Partoens, F. M. Peeters, “Electric-field control of the band gap and Fermi energy in graphene multilayers by top and back gates,” Phys. Rev. B 80(19), 195401 (2009).
[CrossRef]

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

2008

G. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys. 104(8), 084314 (2008).
[CrossRef]

D. G. Cooke, P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008).
[CrossRef] [PubMed]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[CrossRef]

2007

I. Avrutsky, I. Salakhutdinov, J. Elser, V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

2005

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. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Alù, A.

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

Andreev, G. O.

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

Avetisyan, A. A.

A. A. Avetisyan, B. Partoens, F. M. Peeters, “Electric-field control of the band gap and Fermi energy in graphene multilayers by top and back gates,” Phys. Rev. B 80(19), 195401 (2009).
[CrossRef]

Avrutsky, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[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. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Bao, W.

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

Basov, D. N.

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

Belic, M. R.

Belov, P. A.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

Berger, C.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Boudouris, B. W.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Bulovic, V.

A. Reina, X. T. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[CrossRef] [PubMed]

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Capolino, F.

Castro Neto, A. H.

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

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

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Chabot, V.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Chen, C. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Chen, H.

Z. Zhang, H. Li, Z. Gong, Y. Fan, T. Zhang, H. Chen, “Extend the omnidirectional electronic gap of Thue-Morse aperiodic gapped graphene superlattices,” Appl. Phys. Lett. 101(25), 252104 (2012).
[CrossRef]

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Chen, L.

Chen, P. Y.

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

Chen, Z. W.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Chi, H.

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

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(7419), 192–200 (2012).
[CrossRef] [PubMed]

Cooke, D. G.

Crommie, M. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Cubukcu, E.

F. Liu, E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013).
[CrossRef]

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

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B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
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H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012).
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S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
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Mukhin, I. S.

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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
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A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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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(7419), 192–200 (2012).
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A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
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S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
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I. Avrutsky, I. Salakhutdinov, J. Elser, V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
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A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
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Protasenko, V.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Rafique, S.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Reina, A.

A. Reina, X. T. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[CrossRef] [PubMed]

Ren, G.

Rodin, A. S.

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

Rukhlenko, I. D.

W. R. Zhu, I. D. Rukhlenko, M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
[CrossRef]

Salakhutdinov, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

Schneider, H.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Schwab, M. G.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Segalman, R. A.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

Shi, X. L.

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

Sipe, J. E.

O. Kidwai, S. V. Zhukovsky, J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[CrossRef]

Son, H.

A. Reina, X. T. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Tassin, T. Koschny, M. Kafesaki, C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012).
[CrossRef]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Sprinkle, M.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Sreekanth, K. V.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Strangi, G.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Tang, D. Y.

Y. J. Xiang, J. Guo, X. Y. Dai, S. C. Wen, D. Y. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[CrossRef] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Tassin, P.

P. Tassin, T. Koschny, M. Kafesaki, C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012).
[CrossRef]

Thiemens, M.

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

Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Vakil, A.

A. Vakil, N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Vukovic, S.

Wagner, M.

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

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Wang, F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Wen, S. C.

Winnerl, S.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Winzer, T.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Xiang, Y. J.

Xiao, X. C.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Xing, H. G.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Xu, H. J.

H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012).
[CrossRef]

Yan, R.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Yu, A. P.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Zapata-Rodríguez, C. J.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zettl, A.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Zhang, B. H.

B. D. Guo, L. Fang, B. H. Zhang, J. R. Gong, “Graphene Doping: A Review,” Insciences J. 1(2), 80–89 (2011).
[CrossRef]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Zhang, J. J.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Zhang, L. M.

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

Zhang, T.

T. Zhang, L. Chen, X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013).
[CrossRef] [PubMed]

Z. Zhang, H. Li, Z. Gong, Y. Fan, T. Zhang, H. Chen, “Extend the omnidirectional electronic gap of Thue-Morse aperiodic gapped graphene superlattices,” Appl. Phys. Lett. 101(25), 252104 (2012).
[CrossRef]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zhang, X. M.

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

Zhang, Z.

Z. Zhang, H. Li, Z. Gong, Y. Fan, T. Zhang, H. Chen, “Extend the omnidirectional electronic gap of Thue-Morse aperiodic gapped graphene superlattices,” Appl. Phys. Lett. 101(25), 252104 (2012).
[CrossRef]

Zhang, Z. M.

Zhao, Z.

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

Zheng, S.

Zheng, S. L.

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

Zhu, B.

Zhu, M.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Zhu, W.

H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012).
[CrossRef]

Zhu, W. R.

W. R. Zhu, I. D. Rukhlenko, M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
[CrossRef]

Zhukovsky, S. V.

O. Kidwai, S. V. Zhukovsky, J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[CrossRef]

ACS Nano

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

Appl. Phys. Lett.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Z. Zhang, H. Li, Z. Gong, Y. Fan, T. Zhang, H. Chen, “Extend the omnidirectional electronic gap of Thue-Morse aperiodic gapped graphene superlattices,” Appl. Phys. Lett. 101(25), 252104 (2012).
[CrossRef]

W. R. Zhu, I. D. Rukhlenko, M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013).
[CrossRef]

H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012).
[CrossRef]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[CrossRef]

Energy Environ. Sci.

V. Chabot, D. Higgins, A. P. Yu, X. C. Xiao, Z. W. Chen, J. J. Zhang, “A review of graphene and graphene oxide sponge: material synthesis and applications to energy and the environment,” Energy Environ. Sci. 7(5), 1564–1596 (2014).

Insciences J.

B. D. Guo, L. Fang, B. H. Zhang, J. R. Gong, “Graphene Doping: A Review,” Insciences J. 1(2), 80–89 (2011).
[CrossRef]

J. Appl. Phys.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[CrossRef]

G. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys. 104(8), 084314 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Nano Lett.

A. Reina, X. T. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[CrossRef] [PubMed]

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, H. G. Xing, “Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[CrossRef] [PubMed]

Nat. Photonics

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

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

P. Tassin, T. Koschny, M. Kafesaki, C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012).
[CrossRef]

Nature

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[CrossRef] [PubMed]

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

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, F. H. L. Koppens, “Plasmon-Induced Doping of Graphene,” Nature 487, 77–81 (2012).

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[CrossRef] [PubMed]

Opt. Express

Opt. Laser Technol.

X. L. Shi, S. L. Zheng, H. Chi, X. F. Jin, X. M. Zhang, “All-optical modulator with longrange surface plasmon resonance,” Opt. Laser Technol. 49, 316–319 (2013).
[CrossRef]

Phys. Rev. A

O. Kidwai, S. V. Zhukovsky, J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[CrossRef]

Phys. Rev. B

A. A. Avetisyan, B. Partoens, F. M. Peeters, “Electric-field control of the band gap and Fermi energy in graphene multilayers by top and back gates,” Phys. Rev. B 80(19), 195401 (2009).
[CrossRef]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

F. Liu, E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013).
[CrossRef]

I. Avrutsky, I. Salakhutdinov, J. Elser, V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

Phys. Rev. Lett.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, M. Helm, “Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point,” Phys. Rev. Lett. 107(23), 237401 (2011).
[CrossRef] [PubMed]

Rev. Mod. Phys.

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

Science

A. Vakil, N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of graphene-based HMM consisting of alternating graphene sheets and dielectric layers, the layers are infinite in x-y plane. (b) Illustration of the graphene-based HMM (medium B) with thickness of d sandwiched by media A and C.

Fig. 2
Fig. 2

(a) Effective permittivity of the graphene-based HMM. (b) The EFCs of a graphene-based HMM at 8THz, 9THz and 10THz respectively, the solid (dotted and dashed) line is calculated from EMT, the hollow circles are the results based on Bloch’s theorem.

Fig. 3
Fig. 3

The dependences of dispersion relations of p-polarized surface and bulk polaritons on (a) the Fermi energy EF, (b) the number of graphene sheets (i.e., Ns). and (c) the period number of the graphene-based HMM (i.e., N), where Ns = 1, N = 6, td = 50nm in (a), N = 6, td = 50nm, EF = 0.2eV in (b), and Ns = 1, td = 50nm, EF = 0.2eV in (c). Curves (I), (II) and (III) correspond to kz = 0 in air, HMM and prism, respectively, curve (IV) in (a) denotes k x = n p k 0 sin(θ) with incident angle θ= 68.55 0 and n p =4 .

Fig. 4
Fig. 4

The two-dimensional map of reflectance of the Otto configuration (inset), where Ns = 1, N = 6, td = 50nm and EF = 0.2eV, dielectric A is air with h = 1um.

Fig. 5
Fig. 5

(a) Reflectance of the Otto configuration with HMM vs incident angles at different Fermi energy EF. (b) Reflectance vs EF, the frequency of the incident wave is 10THz (11THz), θ= 68.55 0 (51.86°) for case 1 (2).

Fig. 6
Fig. 6

(a)The two-dimensional map of reflectance of the Otto configuration at different frequency and incident angles, (b) at different frequency and Fermi energy, where the dielectric A is MF2 with ε A = 1.9, h = 1.5um.

Equations (7)

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σ intra = i e 2 K B T π 2 (ω+i/τ) ( E F K B T +2ln(1+ e E F K B T )), σ inter = i e 2 π 2 ln| 2 E F (ω+i/τ) 2 E F +(ω+i/τ) |
ε p =( t g ε g + t d ε d )/( t g + t d ), ε t =( t g + t d ) ε g ε d /( t g ε d + t d ε g )
{ H Ay (z)= A 0 e i K Az z E Ax (z)= K Az ε A ε 0 ω A 0 e i K Az z (z<0)
{ H By (z)= B 0 e i K Bz z + C 0 e i K Bz z E Bx (z)= K Bz ε 0 ε p ω ( B 0 e i K Bz z C 0 e i K Bz z ) (0<z<d)
{ H Cy (z)= D 0 e i K Cz z E Cx (z)= K Cz ε C ε 0 ω D 0 e i K Cz z (z>d)
( ε C k Bz ε p k Cz ) ( ε C k Bz + ε p k Cz ) ( ε A k Bz ε p k Az ) ( ε A k Bz + ε p k Az ) = e i2 k Bz d
( ε C k Bz ε p k Cz ) ( ε C k Bz + ε p k Cz ) ( ε A k Bz ε p k Az ) ( ε A k Bz + ε p k Az ) = e 2 k Bz d

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