Abstract

The properties of hybrid nonlinear surface-phonon-plasmon-polaritons (SP3) at the interface of nonlinear medium and graphene-covered hexagonal boron nitride (hBN) are investigated theoretically. It is demonstrated that the hybrid nonlinear SP3 can be tuned by controlling the chemical potential, layer number and relaxation time of graphene. The real and imaginary parts of the propagation constant increase by decreasing the Fermi energy or the layer number of the graphene in the frequency outside of the upper Reststrahlen band of hBN. Moreover, we show that the nonlinear dielectric permittivity has great effect on the propagation constant. The real part of the propagation constant increases with positive nonlinear dielectric permittivity at different frequency for low frequency mode; while the imaginary part of the propagation constant decreases in the upper Reststrahlen band of hBN, keeps nearly constant in the lower band, and increases outside the Reststrahlen band with positive nonlinear dielectric permittivity for low frequency mode.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Hybrid plasmon–phonon polariton bands in graphene–hexagonal boron nitride metamaterials [Invited]

Hodjat Hajian, Amir Ghobadi, Sina Abedini Dereshgi, Bayram Butun, and Ekmel Ozbay
J. Opt. Soc. Am. B 34(7) D29-D35 (2017)

Tunable, omnidirectional, and nearly perfect resonant absorptions by a graphene-hBN-based hole array metamaterial

Hodjat Hajian, Amir Ghobadi, Bayram Butun, and Ekmel Ozbay
Opt. Express 26(13) 16940-16954 (2018)

Modal properties of a cylindrical graphene-coated nanowire deposited on a hexagonal boron nitride substrate

Morteza Hajati and Yashar E. Monfared
Appl. Opt. 58(24) 6666-6671 (2019)

References

  • View by:
  • |
  • |
  • |

  1. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
    [Crossref]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
    [Crossref] [PubMed]
  4. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
    [Crossref]
  5. I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
    [Crossref] [PubMed]
  6. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  7. V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
    [Crossref]
  8. M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
    [Crossref]
  9. D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–823 (2010).
    [Crossref]
  10. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
    [Crossref]
  11. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, “Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface,” Opt. Lett. 12(3), 187–189 (1987).
    [Crossref] [PubMed]
  12. I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36(17), 3374–3376 (2011).
    [Crossref] [PubMed]
  13. I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
    [Crossref]
  14. G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
    [Crossref] [PubMed]
  15. L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
    [Crossref] [PubMed]
  16. Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
    [Crossref]
  17. X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
    [Crossref] [PubMed]
  18. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
    [Crossref] [PubMed]
  19. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
    [Crossref] [PubMed]
  20. N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
    [Crossref] [PubMed]
  21. 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. C. 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]
  22. C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
    [Crossref] [PubMed]
  23. R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
    [Crossref]
  24. 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]
  25. H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
    [Crossref] [PubMed]
  26. 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]
  27. Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
    [Crossref]
  28. Nagaraj and A. A. Krokhin, “Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates,” Phys. Rev. B 81(8), 085426 (2010).
    [Crossref]
  29. G. Borstel, H. Falge, and A. Otto, “Surface and bulk phonon-polaritons observed by attenuated total reflection,” in Solid-State Physics (Springer, 1974), 107–148.
  30. B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
    [Crossref]
  31. T. Dumelow and D. R. Tilley, “Optical properties of semiconductor superlattices in the far infrared,” J. Opt. Soc. Am. A 10(4), 633–645 (1993).
    [Crossref]

2015 (2)

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (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]

2014 (5)

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

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]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

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. C. 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]

2012 (5)

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

2011 (4)

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

I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36(17), 3374–3376 (2011).
[Crossref] [PubMed]

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
[Crossref]

2010 (4)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
[Crossref]

Nagaraj and A. A. Krokhin, “Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates,” Phys. Rev. B 81(8), 085426 (2010).
[Crossref]

D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–823 (2010).
[Crossref]

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

2006 (3)

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[Crossref]

2004 (1)

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

1993 (1)

1987 (1)

Agrawal, G. P.

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

Andersen, D. R.

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]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[Crossref]

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]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Basov, D. N.

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. C. 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]

Bludov, Y. V.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Boardman, A. D.

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 infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

Cai, W.

Carminati, R.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Chen, J.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Chen, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

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]

Crassee, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Dai, S.

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. C. 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, X.

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Davoyan, A. R.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

De Wilde, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Dean, C. R.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

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. C. 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]

Dumelow, T.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Engheta, N.

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

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

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]

Fei, Z.

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. C. 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, 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. C. 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]

Formanek, F.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

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. C. 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]

Gaponenko, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Gomez-Diaz, J.

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

Gralak, B.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Greffet, J.-J.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Guinea, F.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Guo, J.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

Hone, J.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (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]

Jarillo-Herrero, P.

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. C. 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]

Jiang, L.

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

Joulain, K.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Keilmann, F.

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. C. 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, P.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[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]

Kivshar, Y. S.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Koch, R.

R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
[Crossref]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Krokhin, A. A.

Nagaraj and A. A. Krokhin, “Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates,” Phys. Rev. B 81(8), 085426 (2010).
[Crossref]

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]

Kuzmenko, A. B.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Lee, C.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Lemoine, P.-A.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Liu, B.-C.

B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
[Crossref]

Liu, M. K.

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. C. 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]

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]

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]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Lu, Z.-X.

B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
[Crossref]

Ma, Q.

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. C. 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]

Maier, S. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[Crossref]

McLeod, A. S.

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. C. 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]

Meric, I.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Mihalache, D.

Mosig, J. R.

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

Mulet, J.-P.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Nagaraj,

Nagaraj and A. A. Krokhin, “Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates,” Phys. Rev. B 81(8), 085426 (2010).
[Crossref]

Neto, A. H. C.

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. C. 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]

Ocelic, N.

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

Orlita, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Ostler, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Otsuji, T.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

Pannipitiya, A.

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36(17), 3374–3376 (2011).
[Crossref] [PubMed]

Peres, N.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Perruisseau-Carrier, J.

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

Polischuk, O. V.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

Pollard, R.

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

Popov, V. V.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

Potemski, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Premaratne, M.

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36(17), 3374–3376 (2011).
[Crossref] [PubMed]

Regan, 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. C. 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]

Rodin, A. S.

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. C. 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]

Rukhlenko, I. D.

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36(17), 3374–3376 (2011).
[Crossref] [PubMed]

Ryzhii, V.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

Schaefer, J.

R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
[Crossref]

Seaton, C. T.

Seyller, T.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
[Crossref]

Shepard, K. L.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Sherrott, 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]

Shur, M. S.

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Smirnova, D. A.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

Sorgenfrei, S.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Stegeman, G. I.

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Tamagnone, M.

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

Tang, D.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Taniguchi, T.

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. C. 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]

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Thiemens, M.

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. C. 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]

Tilley, D. R.

Twardowski, T.

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Vakil, A.

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

Vasilevskiy, M. I.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Wagner, M.

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. C. 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]

Walter, A. L.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Wang, L.

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Watanabe, K.

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. C. 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]

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Wen, S.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Wright, E. M.

Wurtz, G. A.

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

Xia, F.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Xiang, Y.

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Xu, J.

Yan, H.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref] [PubMed]

Young, A. F.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Yu, L.

B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
[Crossref]

Zanoni, R.

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[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. C. 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, X.

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

M. Tamagnone, J. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

Chin. Phys. B (1)

B.-C. Liu, L. Yu, and Z.-X. Lu, “The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity,” Chin. Phys. B 20(3), 037302 (2011).
[Crossref]

J. Appl. Phys. (1)

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nano Lett. (4)

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[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]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[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]

Nat. Mater. (1)

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. B (6)

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B 86(19), 80–82 (2012).
[Crossref]

I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84(11), 113409 (2011).
[Crossref]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infra-red frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

Nagaraj and A. A. Krokhin, “Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates,” Phys. Rev. B 81(8), 085426 (2010).
[Crossref]

R. Koch, T. Seyller, and J. Schaefer, “Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem,” Phys. Rev. B 82(20), 201413 (2010).
[Crossref]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. Peres, and M. I. Vasilevskiy, “Nonlinear TE-polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Phys. Rev. Lett. (1)

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

Sci. Rep. (1)

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

Science (4)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[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. C. 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]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

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

Other (1)

G. Borstel, H. Falge, and A. Otto, “Surface and bulk phonon-polaritons observed by attenuated total reflection,” in Solid-State Physics (Springer, 1974), 107–148.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1 The system of a graphene separating semi-infinite nonlienear material and hBN crystal.
Fig. 2
Fig. 2 Dispersion relations in the upper Reststrahlen band of hBN without graphene (a) and with graphene (b). The green line is the light line in air β = ω / c , and the blue line is the light line in hBN β = ( ε ) 1 / 2 ω / c .
Fig. 3
Fig. 3 (a) Dispersion with two methods: red line obtained from Eq. (14), blue line obtained from Eq. (17). (b) Normalized magnetic field of low frequency mode. (c) Normalized magnetic field of high frequency mode. (d) is the enlarged view of position D in (c).
Fig. 4
Fig. 4 The dependence of β on wavenumber and Δ ε .
Fig. 5
Fig. 5 The dependence of β on Δ ε and wavenumber. (a), (c) and (e) represent Re ( β ) , and (b), (d) and (f) represent Im ( β ) . (c) and (d) represent low frequency mode, (e) and (f) represent high frequency mode.
Fig. 6
Fig. 6 The dependence of β on Δ ε with the different EF: (a) and (b) are at 1200 c m 1 , (c) and (d) are at 1500 c m 1 , and (e) and (f) are at 1800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.
Fig. 7
Fig. 7 The dependence of β on Δ ε with the different layer number: (a) and (b) are at 1200 c m 1 , (c) and (d) are at 1500 c m 1 , (e) and (f) are at 1800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.
Fig. 8
Fig. 8 The dependence of β on Δ ε with the different relaxation time: (a) and (b) are at 1200 c m 1 , (c) and (d) are at 1500 c m 1 , (e) and (f) are at 1800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.
Fig. 9
Fig. 9 The dependence of β on wavenumber and Δ ε .
Fig. 10
Fig. 10 The dependence of β on Δ ε and wavenumber for low frequency mode, (a) represents Re ( β ) , and (b) represents Im ( β ) .
Fig. 11
Fig. 11 The dependence of β on Δ ε with the different EF: (a) and (b) are at 700 c m 1 , and (c) and (d) are at 800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.
Fig. 12
Fig. 12 The dependence of β on Δ ε with the different layer number: (a) and (b) are at 700 c m 1 , and (c) and (d) are at 800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.
Fig. 13
Fig. 13 The dependence of β on Δ ε with the different relaxation time: (a) and (b) are at 700 c m 1 , and (c) and (d) are at 800 c m 1 . Solid lines are low frequency modes, dashed lines are high frequency modes.

Equations (18)

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

ε c = ε l + α | E 1 | 2 ,
σ t o t a l ( ω ) = σ i n t r a ( ω ) + σ i n t e r ( ω ) .
σ i n t r a ( ω ) = i e 2 k B T π 2 ( ω + i τ 1 ) [ E F / k B T + 2 ln ( e E F / k B T + 1 ) ] ,
σ i n t e r ( ω ) = i e 2 4 π ln ( 2 | E F | ( ω + i τ 1 ) 2 | E F | + ( ω + i τ 1 ) ) ,
ε u = ε , u ( 1 + ω L O , u 2 ω T O , u 2 ω T O , u 2 ω 2 i ω Γ u ) ,
β H y = ω ε ε 0 E z , d H y d z = i ω ε ε 0 E x , d E x d z i β E z = i ω μ 0 H y ,
( H 1 y k 0 2 ε c ) = ( β 2 k 0 2 ε c 1 ) H 1 y ,
( H 1 y ω ε 0 ε c ) 2 = ε c ε l α ( β H 1 y ω ε 0 ε c ) 2 .
H 1 y 2 = ( ω ε 0 ) 2 ε c 2 β 2 k 0 2 ε c ε c 2 ε l 2 2 α .
H 2 y = H 2 y ( 0 ) e γ 2 z ,
γ 2 = ε ε | | β 2 k 0 2 ε .
H 2 y ( 0 ) H 1 y ( 0 ) = σ E 2 x ( 0 ) , E 1 x = E 2 x .
β 2 = 1 4 ( 2 k 0 2 ε c + γ 2 2 k 0 2 ε c ( ε c + ε l ) ( k 0 ε + i γ 2 σ ( ω ) / ε 0 c ) 2 + β 2 ε c ( ε c + ε l ) ε c 2 ) ,
β 2 = ( 2 ε ε | | ε c 2 ( ε c + ε l ) ε c 2 ε | | ) k 0 2 4 ε ε | | ε c ε c 3 ε l ε c 2 ε ε | | ( ε c + ε l ) .
ε c = ε l + α | H 1 y | 2 ,
H 1 y = 2 α γ 1 k 0 cos h [ γ 1 ( z z 0 ) ] ,
s γ 1 ε c 1 Δ ε k 0 2 2 γ 1 2 = γ 2 ε σ γ 2 / ( i ω ε 0 ) ,
ε c β 2 ε c k 0 2 + ε ( ε / ε ) β 2 ε k 0 2 + i σ ω ε 0 = 0.

Metrics