Abstract

Dirac cones discovered in classical periodic systems such as photonic and phononic crystals have exhibited many interesting properties, particularly conical dispersion at the Brillouin zone center can be related to a zero-refractive-index. Here, we theoretically and numerically explore the conical dispersion in plasmonic crystal of graphene nanodisks arranged in triangular lattice. We show that the plasmonic crystal of Dirac-like cone resulted from three-fold accidental degeneracy can be mapped to a zero-refractive-index medium around the Dirac-like point frequency of 65.5 THz. The isotropic behavior of Dirac-like point formed by a monopole and two dipoles is observed by calculating isofrequency contours. Furthermore, numerical simulations including cloaking, focusing and unidirectional transmission are implemented to demonstrate the zero-index characteristics of the graphene plasmonic crystal.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  26. H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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    [Crossref] [PubMed]
  29. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (5)

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

2016 (6)

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
[Crossref] [PubMed]

2015 (4)

L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref] [PubMed]

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Y. Li and J. Mei, “Double Dirac cones in two-dimensional dielectric photonic crystals,” Opt. Express 23(9), 12089–12099 (2015).
[Crossref] [PubMed]

2014 (2)

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

2013 (1)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

2012 (3)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

2011 (5)

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

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

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

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Q. Liang, Y. Yan, and J. Dong, “Zitterbewegung in the honeycomb photonic lattice,” Opt. Lett. 36(13), 2513–2515 (2011).
[Crossref] [PubMed]

2010 (2)

S. R. Zandbergen and M. J. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

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

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

2008 (1)

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[Crossref] [PubMed]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Alù, A.

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

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Bechtel, H. A.

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

Briggs, D. P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Cai, W.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

Camara, N.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Centeno, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Chan, C. T.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Chang, M. L.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Chen, H.

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

Chen, J.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Chen, P. Y.

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

Chen, X. D.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

Christensen, T.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

de Dood, M. J.

S. R. Zandbergen and M. J. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

Deng, S. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Dominguez, G.

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Dong, J.

Dong, J. W.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

Dubois, M.

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

Efetov, D. K.

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

Elorza, A. Z.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

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Fang, N. X.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
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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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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Fogler, M. 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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (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, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
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He, X. T.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
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X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
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Huang, Z. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
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P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
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J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
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J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
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Keilmann, F.

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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Koppens, F. H. L.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
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X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

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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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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Y. Li and J. Mei, “Double Dirac cones in two-dimensional dielectric photonic crystals,” Opt. Express 23(9), 12089–12099 (2015).
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Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
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Liang, Q.

Liang, R.

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

Liu, X.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
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Liu, Z.

J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
[Crossref] [PubMed]

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

Loncar, M.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Lu, H.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Lu, J.

J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
[Crossref] [PubMed]

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

Lu, L.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

Ma, T.

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

Ma, Y.

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

Martin, M.

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

Mazur, E.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

McLeod, 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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Mei, J.

Moitra, P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Muñoz, P.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
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Osmond, J.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Pan, J.

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

Pan, J. Q.

Pan, J.-Q.

Pesquera, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Qiang, K.

Qiu, C.

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
[Crossref] [PubMed]

Qiu, P.

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

Qiu, W.

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

Reineck, P.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Ren, J.

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

Ren, M.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

Reshef, O.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

She, J. C.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Shen, Y. R.

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

Shi, B.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
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Shi, C.

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
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Shvets, G.

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

Soljacic, M.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Thongrattanasiri, S.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Vakil, A.

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

Valentine, J.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Vulis, D. I.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Wang, F.

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

Wang, J. R.

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

Wang, J. X.

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

Wang, J.-X.

P. Qiu, R. Liang, W. Qiu, H. Chen, J. Ren, Z. Lin, J.-X. Wang, Q. Kan, and J.-Q. Pan, “Topologically protected edge states in graphene plasmonic crystals,” Opt. Express 25(19), 22587–22594 (2017).
[Crossref] [PubMed]

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

Wang, Y.

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Wu, L.-H.

L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref] [PubMed]

Xiang, Y.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

Xu, J.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

Xu, S. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Yan, Y.

Yang, Y.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Ye, L.

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

Yin, M.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Zandbergen, S. R.

S. R. Zandbergen and M. J. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

Zeng, C.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Zettl, A.

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

Zhan, Y.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

Zhang, F.

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Zhang, Q.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Zhang, X.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[Crossref] [PubMed]

Zhao, F. L.

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Zhao, J.

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Zhao, X. Liu, W. Qiu, Y. Ma, Y. Huang, J. X. Wang, K. Qiang, and J. Q. Pan, “Surface-plasmon-polariton whispering-gallery mode analysis of the graphene monolayer coated InGaAs nanowire cavity,” Opt. Express 22(5), 5754–5761 (2014).
[Crossref] [PubMed]

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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Zhu, H.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Zhu, X.

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

ACS Nano (1)

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

ACS Photonics (1)

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of zero-refractive-index lens with ultralow spherical aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Appl. Phys. Lett. (1)

W. Qiu, X. Liu, J. Zhao, S. He, Y. Ma, J. X. Wang, and J. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 641 (2014).
[Crossref]

J. Phys. D Appl. Phys. (1)

P. Qiu, W. Qiu, Z. Lin, H. Chen, J. Ren, J.-X. Wang, Q. Kan, and J. Pan, “Double Dirac point in photonic graphene,” J. Phys. D Appl. Phys. 50(33), 335101 (2017).
[Crossref]

Nat. Commun. (1)

M. Dubois, C. Shi, X. Zhu, Y. Wang, and X. Zhang, “Observation of acoustic Dirac-like cone and double zero refractive index,” Nat. Commun. 8, 14871 (2017).
[Crossref] [PubMed]

Nat. Mater. (2)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

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

Nat. Photonics (2)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Nat. Phys. (1)

J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, “Observation of topological valley transport of sound in sonic crystals,” Nat. Phys. 13(4), 369–374 (2016).
[Crossref]

Nature (2)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[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, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

New J. Phys. (1)

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Phys. Rev. Lett. (7)

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

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

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref] [PubMed]

S. R. Zandbergen and M. J. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[Crossref] [PubMed]

J. Lu, C. Qiu, M. Ke, and Z. Liu, “Valley vortex states in sonic crystals,” Phys. Rev. Lett. 116(9), 093901 (2016).
[Crossref] [PubMed]

Sci. Rep. (3)

J. R. Wang, X. D. Chen, F. L. Zhao, and J. W. Dong, “Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals,” Sci. Rep. 6(1), 22739 (2016).
[Crossref] [PubMed]

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6(1), 26796 (2016).
[Crossref] [PubMed]

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Science (1)

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

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the GPC. (a) Schematic illustration of the GPC. A silica layer with periodic thickness is utilized to periodically modify the chemical potential of graphene. Graphene regions with silica thicknesses d1 and d2 have different chemical potentials under an external gate voltage, the chemical potential ratio is μc1c2 = (d2/d1)1/2. (b) Unit cell of the GPC. a and r are the lattice constant and radii of the graphene nanodisks respectively. (c) BZ with the irreducible zone ��-M-K-��.
Fig. 2
Fig. 2 The band structures of the GPC consisting of a triangular lattice of graphene nanodisks. (a) The band structure of GPC for r = 0.2256a. The inset is the enlarged view around the Dirac-like point D. (b) Three-dimensional dispersion surfaces near the Dirac-like frequency of the band structure exhibited in Fig. 2(a). (c) and (d) The band structure around the BZ center with r = 0.23a and r = 0.22a respectively. (e)-(g) The electric field distributions of the three degenerate eigenstates at point D, which exhibits the dipole and monopole field profiles. Throughout this paper, we set a = 40 nm, μc1 = 0.3 eV and μc2 = 0.6 eV.
Fig. 3
Fig. 3 (a) Retrieved effective permittivity and permeability of the GPC acquired using field-averaging. (b) and (c) Calculated isofrequency contours of the GPC: (b) TM2 band. (c) TM4 band.
Fig. 4
Fig. 4 Cloaking effect of the GPC near the Dirac-like point frequency. (a) The transmittance/reflectance spectrums of the GPC with a dielectric obstacle of refractive index from 0 to 20 embedded. The inset illustrates the schematic structure with W = 12a, L = 18.2a. (b)-(d) Electric field distributions of GPC with a dielectric obstacle embedded for nd = 0, 10, 20 respectively. (e)-(g) Electric field distributions of GPC: (e) without defect; (f) with a rectangular PMC object; (g) with a circular PMC object.
Fig. 5
Fig. 5 (a) Focusing lens. (b) Plane wave generator. (c) Norm field intensity distribution of the focusing lens. The inset shows the schematic diagram of the focusing lens with W = 12.1a.
Fig. 6
Fig. 6 Electric field distribution of the unidirectional transmission. (a) A plane wave with the Dirac-like point frequency incidents from the left-side, then transmits through the trapezoid lens constructed by GPCs. (b) A plane wave with the Dirac-like point frequency incidents from the right side, then almost totally reflected back.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ε Air β 2 k 0 2 ε Air + ε Si O 2 β 2 k 0 2 ε Si O 2 = σ g iω ε 0 ,
σ g = σ intra + σ inter
σ intra = i e 2 k B T π 2 (ω+i/τ) [ μ c k B T +2ln( 1+exp( μ c k B T ) ) ],
σ inter = i e 2 4π ln[ 2| μ c |(ω+i/τ) 2| μ c |+(ω+i/τ) ].
β= ε 0 ε Air + ε Si O 2 2 2iω σ g .

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