Abstract

We investigate the optical exceptional points (EPs) in the graphene incorporated multilayer metamaterial manifesting Fano resonance. The system is non-Hermitian and possesses EPs where both the eigenvalues and eigenvectors of the Hamiltonian coalesce. In the aid of Fano resonance, the reflection may reach minimum approaching to zero, resulting in the degeneration of both eigenvalues and eigenvectors and thus the emergence of EPs. The transmission and reflection of light through the metamaterial change sharply by varying slightly the incident wavelength and chemical potential of graphene in the parameter space when encircling the EPs. In addition, the unidirectional invisibility can be achieved at EPs. The study paves a way to precisely controlling the transmission and reflection through metamaterials and may find applications in optoelectronic switches, modulators, absorbers, and optical sensors.

© 2017 Optical Society of America

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  1. M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
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    [Crossref] [PubMed]
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    [PubMed]

2017 (3)

2016 (7)

X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
[Crossref]

M. Pan, Z. Liang, Y. Wang, and Y. Chen, “Tunable angle-independent refractive index sensor based on Fano resonance in integrated metal and graphene nanoribbons,” Sci. Rep. 6(1), 29984 (2016).
[Crossref] [PubMed]

H. Ramezani, Y. Wang, E. Yablonovitch, and X. Zhang, “Unidirectional perfect absorber,” IEEE J. Sel. Top. Quantum Electron. 22(5), 115–120 (2016).
[Crossref]

C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Nonreciprocal phase shift and mode modulation in dynamic graphene waveguides,” J. Lightwave Technol. 34(16), 3877–3883 (2016).

Z. Wang, B. Wang, K. Wang, H. Long, and P. Lu, “Vector plasmonic lattice solitons in nonlinear graphene-pair arrays,” Opt. Lett. 41(15), 3619–3622 (2016).
[Crossref] [PubMed]

S. Feng, “Loss-induced super scattering and gain-induced absorption,” Opt. Express 24(2), 1291–1304 (2016).
[Crossref] [PubMed]

S. Ke, B. Wang, C. Qin, H. Long, K. Wang, and P. Lu, “Exceptional points and asymmetric mode switching in plasmonic waveguides,” J. Lightwave Technol. 34(22), 5258–5262 (2016).
[Crossref]

2015 (4)

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

R. Yu, V. Pruneri, and F. J. García de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(4), 8969 (2015).
[Crossref] [PubMed]

2014 (5)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
[Crossref]

M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
[Crossref]

L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22(2), 1760–1767 (2014).
[Crossref] [PubMed]

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
[Crossref] [PubMed]

2013 (6)

H. X. Cui, X. W. Cao, M. Kang, T. F. Li, M. Yang, T. J. Guo, Q. H. Guo, and J. Chen, “Exceptional points in extraordinary optical transmission through dual subwavelength metallic gratings,” Opt. Express 21(11), 13368–13379 (2013).
[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]

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

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
[Crossref] [PubMed]

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4(3), 1987–1995 (2013).
[PubMed]

2012 (3)

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012).
[Crossref] [PubMed]

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

2011 (4)

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
[Crossref] [PubMed]

B. Dietz, H. L. Harney, O. N. Kirillov, M. Miski-Oglu, A. Richter, and F. Schäfer, “Exceptional points in a microwave billiard with time-reversal invariance violation,” Phys. Rev. Lett. 106(15), 150403 (2011).
[Crossref] [PubMed]

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

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

2010 (2)

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

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

2008 (1)

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

2007 (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

2001 (1)

C. Dembowski, H. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001).
[Crossref] [PubMed]

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1996 (1)

Almeida, V. R.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012).
[Crossref] [PubMed]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Alù, A.

P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
[Crossref]

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

Amin, M.

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

Askarpour, A. N.

P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
[Crossref]

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]

Azad, A. K.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Bagci, H.

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

Bliokh, K. Y.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

Bolotin, K. I.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

Brida, D.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4(3), 1987–1995 (2013).
[PubMed]

Brodbeck, S.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

Cacho, C.

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X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
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M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
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P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
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B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
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J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
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M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
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Cui, H. X.

Dall, R. G.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
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P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
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M. Amin, M. Farhat, and H. Baǧcı, “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
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A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
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B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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C. Dembowski, H. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
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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).
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Guo, T. J.

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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Han, J.

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
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Han, X.

X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
[Crossref]

Harney, H. L.

B. Dietz, H. L. Harney, O. N. Kirillov, M. Miski-Oglu, A. Richter, and F. Schäfer, “Exceptional points in a microwave billiard with time-reversal invariance violation,” Phys. Rev. Lett. 106(15), 150403 (2011).
[Crossref] [PubMed]

C. Dembowski, H. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001).
[Crossref] [PubMed]

Heine, A.

C. Dembowski, H. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001).
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Heiss, W. D.

C. Dembowski, H. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86(5), 787–790 (2001).
[Crossref] [PubMed]

Hillenbrand, R.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Höfling, S.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

Hofmann, P.

J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
[Crossref] [PubMed]

Hone, J.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

Hu, H.

X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
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Huang, H.

Huang, X.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
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Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

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K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
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Johannsen, J. C.

J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
[Crossref] [PubMed]

Kamp, M.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

Kang, M.

M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
[Crossref]

H. X. Cui, X. W. Cao, M. Kang, T. F. Li, M. Yang, T. J. Guo, Q. H. Guo, and J. Chen, “Exceptional points in extraordinary optical transmission through dual subwavelength metallic gratings,” Opt. Express 21(11), 13368–13379 (2013).
[Crossref] [PubMed]

Ke, S.

Kim, P.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

Kim, Y. J.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4(3), 1987–1995 (2013).
[PubMed]

Kirillov, O. N.

B. Dietz, H. L. Harney, O. N. Kirillov, M. Miski-Oglu, A. Richter, and F. Schäfer, “Exceptional points in a microwave billiard with time-reversal invariance violation,” Phys. Rev. Lett. 106(15), 150403 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
[Crossref] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
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A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Wang, B.

H. Huang, S. Ke, B. Wang, H. Long, K. Wang, and P. Lu, “Numerical study on plasmonic absorption enhancement by a rippled graphene sheet,” J. Lightwave Technol. 35(2), 320–324 (2017).
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F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 125–129 (2017).
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C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Nonreciprocal phase shift and mode modulation in dynamic graphene waveguides,” J. Lightwave Technol. 34(16), 3877–3883 (2016).

X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
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Z. Wang, B. Wang, K. Wang, H. Long, and P. Lu, “Vector plasmonic lattice solitons in nonlinear graphene-pair arrays,” Opt. Lett. 41(15), 3619–3622 (2016).
[Crossref] [PubMed]

S. Ke, B. Wang, C. Qin, H. Long, K. Wang, and P. Lu, “Exceptional points and asymmetric mode switching in plasmonic waveguides,” J. Lightwave Technol. 34(22), 5258–5262 (2016).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Wang, D.

Wang, F.

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 125–129 (2017).
[Crossref]

Wang, K.

Wang, Y.

M. Pan, Z. Liang, Y. Wang, and Y. Chen, “Tunable angle-independent refractive index sensor based on Fano resonance in integrated metal and graphene nanoribbons,” Sci. Rep. 6(1), 29984 (2016).
[Crossref] [PubMed]

H. Ramezani, Y. Wang, E. Yablonovitch, and X. Zhang, “Unidirectional perfect absorber,” IEEE J. Sel. Top. Quantum Electron. 22(5), 115–120 (2016).
[Crossref]

L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22(2), 1760–1767 (2014).
[Crossref] [PubMed]

Wang, Z.

Watanabe, K.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Woessner, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (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]

Xu, N.

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
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Xu, Y. L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012).
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Yablonovitch, E.

H. Ramezani, Y. Wang, E. Yablonovitch, and X. Zhang, “Unidirectional perfect absorber,” IEEE J. Sel. Top. Quantum Electron. 22(5), 115–120 (2016).
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[Crossref] [PubMed]

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]

Yang, M.

Yang, S.

Yin, X.

Yu, R.

R. Yu, V. Pruneri, and F. J. García de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

Yuan, X.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Zacchigna, M.

J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
[Crossref] [PubMed]

Zeng, B.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Zhang, H.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Zhang, P.

Zhang, Q.

Zhang, S.

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
[Crossref] [PubMed]

Zhang, W.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
[Crossref] [PubMed]

Zhang, X.

X. Zhang, X. Zhu, X. Liu, D. Wang, Q. Zhang, P. Lan, and P. Lu, “Ellipticity-tunable attosecond XUV pulse generation with a rotating bichromatic circularly polarized laser field,” Opt. Lett. 42(6), 1027–1030 (2017).
[Crossref] [PubMed]

H. Ramezani, Y. Wang, E. Yablonovitch, and X. Zhang, “Unidirectional perfect absorber,” IEEE J. Sel. Top. Quantum Electron. 22(5), 115–120 (2016).
[Crossref]

L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22(2), 1760–1767 (2014).
[Crossref] [PubMed]

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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Zhu, H.

Zhu, W.

M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
[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]

Zhu, X.

ACS Nano (2)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
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ACS Photonics (2)

X. Han, K. Wang, H. Long, H. Hu, J. Chen, B. Wang, and P. Lu, “Highly sensitive detection of the lattice distortion in single bent ZnO nanowires by second-harmonic generation microscopy,” ACS Photonics 3(7), 1308–1314 (2016).
[Crossref]

R. Yu, V. Pruneri, and F. J. García de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 125–129 (2017).
[Crossref]

H. Ramezani, Y. Wang, E. Yablonovitch, and X. Zhang, “Unidirectional perfect absorber,” IEEE J. Sel. Top. Quantum Electron. 22(5), 115–120 (2016).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. (1)

P. Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
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J. Opt. Soc. Am. A (1)

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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Nanoscale (1)

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Nat. Commun. (2)

P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(4), 8969 (2015).
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D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4(3), 1987–1995 (2013).
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Nat. Mater. (4)

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

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]

Nature (1)

T. Gao, E. Estrecho, K. Y. Bliokh, T. C. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526(7574), 554–558 (2015).
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Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

M. Kang, H. Cui, T. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89(6), 065801 (2014).
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Phys. Rev. Lett. (7)

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113(9), 093901 (2014).
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Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011).
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B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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J. C. Johannsen, S. Ulstrup, F. Cilento, A. Crepaldi, M. Zacchigna, C. Cacho, I. C. E. Turcu, E. Springate, F. Fromm, C. Raidel, T. Seyller, F. Parmigiani, M. Grioni, and P. Hofmann, “Direct view of hot carrier dynamics in graphene,” Phys. Rev. Lett. 111(2), 027403 (2013).
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Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
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Sci. Rep. (2)

M. Pan, Z. Liang, Y. Wang, and Y. Chen, “Tunable angle-independent refractive index sensor based on Fano resonance in integrated metal and graphene nanoribbons,” Sci. Rep. 6(1), 29984 (2016).
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M. Amin, M. Farhat, and H. Baǧcı, “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013).
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Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
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Solid State Commun. (1)

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
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Figures (7)

Fig. 1
Fig. 1 Schematic of the Ag-graphene hybrid structure. The graphene nanoribbons are deposited on the slits of the upper Ag strips. The structural parameters are: h1 = 220 nm, h0 = 350 nm, h2 = 155 nm, wg = 75 nm, wm1 = 600 nm, wm2 = 525 nm and d = 675 nm. Inset is the cross section of the design. The structure is excited by TM-polarized incident light with the magnetic field parallel to the grating.

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Fig. 2
Fig. 2 (a) Transmission for the graphene ribbon arrays suspended in air (the red curve), metallic structure without graphene (the blue curve), and the hybrid structure (the green curve). All parameters are the same as they presented in the hybrid structure. (b) Reflection spectra of the hybrid structure. The chemical potential of graphene is 0.479 eV.

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Fig. 3
Fig. 3 (a) Reflection spectra R1 and (c) reflection spectra R2 as a function of the incident wavelength λ and chemical potential of graphene μc. (b) and (d) show the reflection phase φ1 and φ2. The black arrows point to the positions of EPs.

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Fig. 4
Fig. 4 Eigenvalues s1,2 as a function of incident wavelength λ and chemical potential of graphene μc. Re(s) indicates the real parts of s1,2, and Im(s) indicates the imaginary parts of s1,2. The red curves indicate the intersection of two surfaces. The black arrows point to the positions of EP1 and EP2.

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Fig. 5
Fig. 5 The topological property while encircling the EPs. (a) Two loops in the parameter space of wavelength λ and chemical potential μc. The two black stars indicate the location of EP1 and EP2, respectively. The two black dots present the starting position of the two loops, denoted by capital A (λ = 5.396 μm, μc = 0.428 eV) and B (λ = 5.58 μm, μc = 0.4535 eV). (b), (c) The trajectories of real and imaginary parts of eigenvalues along the clockwise orientation of the blue loop in (a). (d), (e) The trajectories of real and imaginary parts of eigenvalues along the clockwise orientation for the red loop in (a). The red and blue curves in (b), (c), (d) and (e) mean two eigenvalues s1,2 but not refer to the red and blue curves in (a).

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Fig. 6
Fig. 6 Normalized electric field intensity (|E|2) distribution when normal incident light illuminates to the metamaterials at EPs while (a), (d) the structure is illuminated from the top and (b), (c) from the bottom. The wavelength of incident light and the chemical potential of graphene at (a), (b) are μc = μc1 and λ = λ1 and at (c), (d) are μc = μc2 and λ = λ2. The white arrows imply the incident direction.

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Fig. 7
Fig. 7 (a) Reflection spectra R1 for different refractive index of the surrounding environment as μc = 0.428 eV. (b) Reflection spectra R1 for different chemical potential of graphene as n = 1. (c) Resonance wavelength as a function of the refractive index for different chemical potential. (d) Resonance wavelength as a function of the chemical potential for different refractive index.

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Equations (1)

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( b 1 b 2 ) = S ( a 2 a 1 ) = ( t r 1 r 2 t ) ( a 2 a 1 ) ,

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