Abstract

Both plasmon-phonon-polariton (SPP-PHP) modes and phonon-polariton (PHP) modes supported in graphene-coated hexagon boron nitride (h-BN) single nanowire are presented. The field distributions of the lowest 5 order modes of SPP-PHP modes supported in graphene-coated hexagon boron nitride nanowire pairs (SPP-PHP-GHNP) and the lowest 5 order modes of PHP modes supported in graphene-coated hexagon boron nitride nanowire pairs (GHNP) are also demonstrated and analyzed, respectively. The results of numerical calculation show that SPP-PHP-GHNP mode 0 owns the strongest confinement and lowest loss among the lowest 5 order modes of SPP-PHP-GHNP. Furthermore, the field enhancement of SPP-PHP-GHNP mode 0 can reach over 105 by controlling the geometry parameters of GHNP. Meanwhile, the influence of tuning the Fermi level of graphene on the field enhancement is also presented in the paper. The proposed structure may improve the development of graphene-h-BN-based optoelectronic devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

2017 (4)

2016 (12)

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

B. Zhu, G. Ren, B. Wu, Y. Gao, H. Li, and S. Jian, “Nanofocusing of hybrid plasmons-phonons-polaritons in a graphene-hexagonal boron nitride heterostructure,” Opt. Lett. 41(19), 4578–4581 (2016).
[Crossref] [PubMed]

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016).
[Crossref] [PubMed]

J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Turnable perfect absorption at infrared frequencies by a Graphene-hBN Hyper Crystal,” Opt. Express 24(15), 17103–17114 (2016).
[Crossref] [PubMed]

A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
[Crossref]

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “An ultra-high sensitivity surface plasmon resonance sensor based on graphene-aluminum-graphene sandwich-like structure,” J. Appl. Phys. 120(5), 053101 (2016).
[Crossref]

Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
[Crossref] [PubMed]

W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
[Crossref] [PubMed]

Z.-W. Zhao, H.-W. Wu, and Y. Zhou, “Surface-confined edge phonon polaritons in hexagonal boron nitride thin films and nanoribbons,” Opt. Express 24(20), 22930–22942 (2016).
[Crossref] [PubMed]

R. Xing and S. Jian, “Numerical analysis on the multilayer nanoring waveguide pair,” IEEE Photonics Technol. Lett. 28(24), 2779–2782 (2016).
[Crossref]

2015 (10)

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]

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

B. Zhu, G. Ren, M. J. Cryan, Y. Gao, Y. Yang, B. Wu, Y. Lian, and S. Jian, “Magnetically tunable non-reciprocal plasmons resonator based on graphene-coated nanowire,” Opt. Mater. Express 5(10), 2174–2183 (2015).
[Crossref]

V. Dmitriev and C. Monte do Nascimento, “Planar THz electromagnetic graphene pass-band filter with low polarization and angle of incidence dependencies,” Appl. Opt. 54(6), 1515–1520 (2015).
[Crossref] [PubMed]

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015).
[Crossref]

2014 (5)

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
[Crossref] [PubMed]

2013 (1)

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

2012 (2)

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

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

2011 (1)

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

2009 (1)

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

Aharonovich, I.

A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
[Crossref]

Alighanbari, A.

Alonso-Gonzalez, P.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Andersen, T.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Atwater, H.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Avouris, P.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Barnard, H. R.

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Basov, D. N.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Buljan, H.

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

Caldwell, J. D.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Casanova, F.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Castro Neto, A. H.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Chen, D.

Chen, H.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Chen, H.-S.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Chen, J.-H.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Chen, Z.-X.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Choi, M.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Christensen, T.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Cryan, M. J.

Dai, S.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Dai, T.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Dai, X.

Dmitriev, V.

Dolado, I.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Dominguez, G.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Fan, D.

Fang, N. X.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Fang, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Farmani, A.

Fei, Z.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Fogler, M. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Forati, E.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Fung, K. H.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Gannett, W.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Gao, H.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Gao, W.

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

Gao, Y.

Gaussmann, F.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Goldflam, M. D.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Gu, M.

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]

Guinea, F.

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Guo, J.

Guo, Z.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Han, X.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

Han, Y.

Hanson, G. W.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Hao, R.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Hillenbrand, R.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Hossain, M. M.

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]

Hu, W.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Hu, Z.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Hu, Z.-D.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Huang, J.

Hueso, L. E.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Jablan, M.

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

Jang, M. S.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Janssen, G. C. A. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Jarillo-Herrero, P.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Jauho, A.-P.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Jian, S.

Jiang, J.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Jiang, L.

Jiang, X.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Jin, J.-M.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Ke, S.

Keilmann, F.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Kim, L. B.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Kim, S.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Kretinin, A. V.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Kumar, A.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Lail, B. A.

Lawton, L. M.

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Lewin, M.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Li, E.-P.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Li, H.

Li, P.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Li, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Li, X.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Li, Y.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Lian, Y.

Lin, X.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Liu, C.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Liu, H.

Liu, M. K.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Liu, W.

W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
[Crossref] [PubMed]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

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]

Liu, Y.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

Long, H.

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Lou, J.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Low, T.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

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, P.

Lu, Y.-Q.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Luxmoore, I. J.

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Ma, Q.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

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T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
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H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
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R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
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Qi, D.-X.

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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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Wang, G.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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Wang, T.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
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Watanabe, K.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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Wu, Z.-J.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
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T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
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X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
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Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
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R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Yan, X.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Yang, J.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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Yoxall, E.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Yu, B.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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Yu, H.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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Yuan, L.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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Yuan, Y.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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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.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Zhang, F.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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Zhang, J.

Zhang, Q.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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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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Zhang, X.-J.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Zhang, X.-M.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
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Zhang, Z.

Zhang, Z. M.

Zhao, B.

Zhao, Z.-W.

Zhou, Y.

Zhu, B.

Zhu, S.-E.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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Figures (10)

Fig. 1
Fig. 1 (a) Schematics of the GHNP structure. (b) The out-of-plane dielectric permittivity and in-plane dielectric permittivity of h-BN versus wavenumber.
Fig. 2
Fig. 2 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of SPP-PHP-GHN. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of PHP-GHN.
Fig. 3
Fig. 3 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 3 order modes of SPP-PHP-GHN versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 3 order modes of PHP-GHN versus wavenumber.
Fig. 4
Fig. 4 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of SPP-PHP-GHNP. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of PHP-GHNP.
Fig. 5
Fig. 5 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP versus wavenumber.
Fig. 6
Fig. 6 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the Fermi level of graphene. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the Fermi level of graphene.
Fig. 7
Fig. 7 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the radius of substrate. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the radius of substrate.
Fig. 8
Fig. 8 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the distance between the two GHN waveguides. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the distance between the two GHN waveguides.
Fig. 9
Fig. 9 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm.
Fig. 10
Fig. 10 Dependencies of field enhancement of the SPP-PHP-GHNP mode 0 on (a) the Fermi level of graphene. (b) the radius of substrate. (c) the distance between the two GHN waveguides. (d) the thickness of h-BN (Here R is fixed at 90 nm).

Equations (5)

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ε a ( r ) = ε , a ( r ) + ε , a ( r ) ( ω L O , a ( r ) ) 2 ( ω T O , a ( r ) ) 2 ( ω T O , a ( r ) ) 2 ω 2 i ω Γ a ( r ) ,
{ σ inter = e 2 4 { 0.5 + arc tan ( ω 2 E f 2 k B T ) π i 2 π ln [ ( ω + 2 E f ) 2 ( ω 2 E f ) 2 + ( 2 k B T ) 2 ] } , σ intra = 2 i e 2 k B T π 2 ( ω + i τ ) ln [ 2 cos h ( E f 2 k B T ) ] ,
β = Ψ t h B N { arc tan [ ε a i r + i ( β / k 0 ) Z 0 σ g ε r Ψ ] + arc tan ( ε s i ε r Ψ ) + π L } ,
β Z 2 = β 2 ( M / R 0 ) 2 ,
ε 1 μ 1 I 1 ( μ 1 R 0 ) I 0 ( μ 1 R 0 ) + ε 2 μ 2 K 1 ( μ 2 R 0 ) K 0 ( μ 2 R 0 ) = σ g j ω ,

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