Abstract

We theoretically investigate mid-infrared electromagnetic wave propagation in multilayered graphene–hexagonal boron nitride (hBN) metamaterials. Hexagonal boron nitride is a natural hyperbolic material that supports highly dispersive phonon polariton modes in two Reststrahlen bands with different types of hyperbolicity. Due to the hybridization of surface plasmon polaritons of graphene and hyperbolic phonon polaritons of hBN, each isolated unit cell of the graphene–hBN metamaterial supports hybrid plasmon–phonon polaritons (HPPs). Through the investigation of band structure of the metamaterial we find that, due to the coupling between the HPPs supported by each unit cell, the graphene–hBN metamaterial can support HPP bands. The dispersion of these bands can be noticeably modified for different thicknesses of hBN layers, leading to the appearance of bands with considerably flat dispersions. Moreover, analysis of light transmission through the metamaterial reveals that this system is capable of supporting high-k propagating HPPs. This characteristic makes graphene–hBN metamaterials very promising candidates for the modification of the spontaneous emission of a quantum emitter, hyperlensing, negative refraction, and waveguiding.

© 2017 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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, 722–726 (2010).
    [Crossref]
  2. A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
    [Crossref]
  3. M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
    [Crossref]
  4. 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, 3172–3180 (2015).
    [Crossref]
  5. 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, 682–686 (2015).
    [Crossref]
  6. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
    [Crossref]
  7. 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, 1125–1129 (2014).
    [Crossref]
  8. J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
    [Crossref]
  9. V. W. Brar, M. Seok 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, 3876–3880 (2014).
    [Crossref]
  10. F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
    [Crossref]
  11. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
    [Crossref]
  12. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
    [Crossref]
  13. T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
    [Crossref]
  14. W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
    [Crossref]
  15. W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
    [Crossref]
  16. I. D. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. P. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B. 84, 113409 (2011).
    [Crossref]
  17. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [Crossref]
  18. A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
    [Crossref]
  19. Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
    [Crossref]
  20. C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
    [Crossref]
  21. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
    [Crossref]
  22. L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
    [Crossref]
  23. S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21, 14982–14987 (2013).
    [Crossref]
  24. H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
    [Crossref]
  25. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
    [Crossref]
  26. I. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87, 075416 (2013).
    [Crossref]
  27. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21, 7614–7632 (2013).
    [Crossref]
  28. H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
    [Crossref]
  29. Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
    [Crossref]
  30. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).
  31. E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).
  32. W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).
  33. T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
    [Crossref]
  34. A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
    [Crossref]
  35. J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Tunable perfect absorption at infrared frequencies by a graphene–hBN hyper crystal,” Opt. Express 24, 17103–17114 (2016).
    [Crossref]
  36. H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
    [Crossref]
  37. H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
    [Crossref]
  38. K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
    [Crossref]
  39. K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
    [Crossref]
  40. G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallelplate waveguide,” J. Appl. Phys. 104, 084314 (2008).
    [Crossref]
  41. H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
    [Crossref]
  42. D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
    [Crossref]

2017 (1)

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[Crossref]

2016 (3)

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Tunable perfect absorption at infrared frequencies by a graphene–hBN hyper crystal,” Opt. Express 24, 17103–17114 (2016).
[Crossref]

2015 (5)

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

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, 3172–3180 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

2014 (6)

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, 1125–1129 (2014).
[Crossref]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

2013 (9)

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

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

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

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21, 14982–14987 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

2012 (4)

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

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

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
[Crossref]

2011 (4)

H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
[Crossref]

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

F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

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

2010 (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, 722–726 (2010).
[Crossref]

2008 (2)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallelplate waveguide,” J. Appl. Phys. 104, 084314 (2008).
[Crossref]

2007 (1)

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

2006 (1)

2004 (1)

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

2003 (2)

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

1958 (1)

W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).

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, 113409 (2011).
[Crossref]

Al Sayem, A.

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

Alekseyev, L. V.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[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, 682–686 (2015).
[Crossref]

Atwater, H.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[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, 3172–3180 (2015).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Belov, P. A.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

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

Bienstman, P.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

Boyle, W. S.

W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).

Brailsford, A. D.

W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).

Brar, V. W.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

Buslaev, P.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

Caglayan, H.

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[Crossref]

Caldwell, J. D.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Capolino, F.

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[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, 1125–1129 (2014).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Chang, Y. C.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Chen, Y.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Choi, M.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

Chou, C. T.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Considine, C. R.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Cormode, D.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Cortes, C. L.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Dai, X.

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, 722–726 (2010).
[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, 1125–1129 (2014).
[Crossref]

Ellis, C. T.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Engheta, N.

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

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

Fan, S.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

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, 3172–3180 (2015).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Ferraria, L.

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (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. 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, 1125–1129 (2014).
[Crossref]

Francescato, Y.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Franz, K. J.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[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, 3172–3180 (2015).
[Crossref]

Galfsky, T.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Galt, J. K.

W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).

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, 1125–1129 (2014).
[Crossref]

Gao, Y.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Geim, A. K.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

Giannini, V.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Giles, A. J.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Gmachl, C.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

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, 682–686 (2015).
[Crossref]

Grigorenko, A. N.

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

Grigorieva, I. V.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

Guclu, C.

Guo, J.

Hajian, H.

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
[Crossref]

H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
[Crossref]

Hanson, G. W.

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallelplate waveguide,” J. Appl. Phys. 104, 084314 (2008).
[Crossref]

Hillenbrand, R.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Hoffman, A. J.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Hone, J.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

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, 722–726 (2010).
[Crossref]

Hong, M.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Howard, S. S.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Huang, K. C.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

Iorsh, I.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

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

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Jacob, Z.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

Jacquod, P.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Jahangir, I.

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Javier García de Abajo, F.

F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Jiang, L.

Jiang, X.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

Joannopoulos, J. D.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Kalafi, M.

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
[Crossref]

H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Kidwai, O.

Kim, L. B.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

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, 722–726 (2010).
[Crossref]

Kim, S.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Kivshar, Y. S.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

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

Ko, W. C.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Koppens, F. H. L.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Kretinin, A. V.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[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, 3172–3180 (2015).
[Crossref]

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, 722–726 (2010).
[Crossref]

Lee, Y. H.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Lepaged, D.

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

LeRoy, B. J.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Lidorikis, E.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

Liu, C. H.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Liu, Z.

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Lopez, J. J.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[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, 3172–3180 (2015).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

Lundeberg, M. B.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Mahdy, M. R. C.

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

Maier, S. A.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Marder, S. R.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[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. 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, 1125–1129 (2014).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Menon, V. M.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

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, 722–726 (2010).
[Crossref]

Molesky, S.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Mukhin, I. S.

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

Narimanov, E. E.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

Nelson, K. A.

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

Newman, W.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Norris, T. B.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Novoselov, K. S.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

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

Othman, M. A. K.

Ozbay, E.

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[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, 113409 (2011).
[Crossref]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Podolskiy, V. A.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Polini, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

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

Premaratne, M.

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

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

Principi, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Rahman, M. M.

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

Rahman, M. S.

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

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. 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, 1125–1129 (2014).
[Crossref]

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. 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, 1125–1129 (2014).
[Crossref]

Rukhlenko, I. D.

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

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

Sanchez-Yamagishi, J. D.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Seok Jang, M.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

Shadrivov, I. V.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

I. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87, 075416 (2013).
[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, 722–726 (2010).
[Crossref]

Sherrott, M.

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

Si, L.

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

Sipe, J. E.

Sivco, D. L.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Smirnova, D.

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

SoltaniVala, A.

H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
[Crossref]

Soltani-Vala, A.

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
[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, 722–726 (2010).
[Crossref]

Sun, Z.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

Taniguchi, T.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

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, 722–726 (2010).
[Crossref]

Thiemens, 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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Tischler, J. G.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Vakil, A.

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

Vignale, G.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Wagner, 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, 682–686 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

Wang, 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, 722–726 (2010).
[Crossref]

Wasserman, D.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Watanabe, 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, 682–686 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[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. 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, 1125–1129 (2014).
[Crossref]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

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, 722–726 (2010).
[Crossref]

Wen, S.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Woessner, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Woods, C. R.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Wu, J.

Wub, C.

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Xiang, Y.

Xue, J.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Yankowitz, M.

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

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, 722–726 (2010).
[Crossref]

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, 1125–1129 (2014).
[Crossref]

Zhang, S.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Zhang, X.

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Zhong, Z.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

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, 682–686 (2015).
[Crossref]

Zhu, W.

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

Zhukovsky, S. V.

ACS Nano (1)

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

Appl. Phys. Lett. (2)

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

W. Zhu, I. D. Rukhlenko, L. Si, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

J. Appl. Phys. (3)

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene–dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[Crossref]

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallelplate waveguide,” J. Appl. Phys. 104, 084314 (2008).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

J. Opt. (1)

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

J. Phys. Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

Nano Lett. (4)

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16, 4940–4945 (2016).
[Crossref]

V. W. Brar, M. Seok 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, 3876–3880 (2014).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. Javier García de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

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, 3172–3180 (2015).
[Crossref]

Nat. Commun. (2)

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref]

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Nat. Mater. (2)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Nat. Nanotechnol. (2)

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, 682–686 (2015).
[Crossref]

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, 722–726 (2010).
[Crossref]

Nat. Photonics (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

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

Nat. Phys. (1)

M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382–386 (2012).
[Crossref]

Nature (1)

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

Opt. Commun. (1)

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene–dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

Opt. Express (4)

Phys. Rev. (1)

W. S. Boyle, A. D. Brailsford, and J. K. Galt, “Dielectric anomalies and cyclotron absorption in the Infrared: observations on bismuth,” Phys. Rev. 109, 1396–1398 (1958).

Phys. Rev. B (4)

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

D. Smirnova, P. Buslaev, I. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Deeply subwavelength electromagnetic Tamm states in graphene metamaterials,” Phys. Rev. B 89, 245414 (2014).
[Crossref]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B 68, 075209 (2003).
[Crossref]

K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).
[Crossref]

Phys. Rev. B. (1)

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

Phys. Rev. Lett. (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Phys. Rev. X (1)

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).

Phys. Status Solidi C (1)

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Tunable far-IR bandgaps in a one-dimensional graphene–dielectric photonic crystal,” Phys. Status Solidi C 9, 2614–2617 (2012).
[Crossref]

Physica B (1)

H. Hajian, A. SoltaniVala, and M. Kalafi, “Effect of uniaxial anisotropy of left-handed layers on created surface waves in a one dimensional photonic crystal,” Physica B 406, 4094–4099 (2011).
[Crossref]

Prog. Quantum Electron. (1)

L. Ferraria, C. Wub, D. Lepaged, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Sci. Rep. (1)

A. Al Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene–hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2015).
[Crossref]

Science (2)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[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. 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, 1125–1129 (2014).
[Crossref]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

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 (6)

Fig. 1.
Fig. 1.

Panels (a) and (b) respectively illustrate an isolated unit cell of the GhMM, which is referred to as hGhGh and the GhMM under our consideration in this paper. Panels (c) and (d) show the real and imaginary values of εx and εz of hBN, respectively. The vertical dashed lines in these panels illustrate the boundary of the Reststrahlen bands noted as RH1 and RH2 in these panels.

Fig. 2.
Fig. 2.

Panels (a) and (b) respectively represent the band structure of graphene–hBN metamaterial for lossless and lossy cases with t=10  nm. In accordance with panels (a) and (b), panels (c), (d) and (e), (f) show similar results for t=50  nm and t=100  nm GhMMs, respectively.

Fig. 3.
Fig. 3.

Panels (a) and (b) respectively illustrate the projected band structure of GhMM with t=10  nm and the transmission of light passing through this system considering N=10 for both TE and TM polarizations; N shows the number of hBN layers taken in the calculations. The solid-blue curves in panel (a) show SP3 and HP3 modes supported by an isolated hGhGh unit cell, for which the graphene layers are separated by a 10 nm thin film of hBN. Similar to panel (b), TM light transmission for fictitious metamaterials with εf=εz and εf=εx are represented in panels (c) and (d), respectively. Notice that the boundaries of the RH bands, in which hBN has a hyperbolic optical response, are determined with the dashed horizontal lines.

Fig. 4.
Fig. 4.

Panels (a) and (b) respectively show the projected band structure of GhMM with t=50  nm and light transmission through this system for both TE and TM polarizations for N=10. Solid-blue curves in panel (a) represent SP3 and HP3 modes of an isolated HGHGH unit cell with t=50  nm. Moreover, horizontal dashed-black lines in panels (a) and (b) highlight the boundaries of the RH bands of hBN.

Fig. 5.
Fig. 5.

Similar to Fig. 4, but panels (a) and (b) of this figure are illustrated for t=100  nm.

Fig. 6.
Fig. 6.

Panels (a), (b), (c), and (d) represent TM light transmission through the GhMM with t=100  nm for μ=0.1  eV, μ=0.3  eV, μ=0.4  eV, and μ=0.5  eV, respectively. Notice that the case of μ=0.2  eV is already presented in Fig. 5(b). It should be noted that these results are obtained for N=10.

Equations (21)

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

Ex|z=0+=Ex|z=0,
εtkh,TM2dExdz|z=0+εAkA2dExdz|z=0=αEx|z=0,
Ey|z=0+=Ey|z=0,
dEydz|z=0+dEydz|z=0=β02αEy|z=0,
εm=ε,m×[1+ωLO,m2ωTO,m2ωTO,m2ω2iωΓm],m=t,z.
cos(KBt)=cos(kh,TMt)+αkh,TM2εtsin(kh,TMt),
cos(KBt)=cos(kh,TEt)+αβ022kh,TEsin(kh,TEt),
Hy(z)={H1eikh,TM(zt/2)z>t/2H2sin(ikh,TMz)[odd]t/2zt/2H2cos(ikh,TMz)[even]t/2zt/2H3eikh,TM(z+t/2)z<t/2}.
tan(kh,TMt/2)={η,Hyodd1/η,Hyeven},
Hy(z)={HieikAz+HreikAz,z<0Hn1eikh,TM[z(n1)t]+Hn2eikh,TM[z(n1)t],(n1)t<z<ntHteikA(znt),z>nt},
T=|Ht/Hi|2=|1/M11|2,
M=[M11M12]=mA11(m1m21)NmA2.
mA1=[ikA/εAikA/εA1iαkA/εA1+iαkA/εA],
mA2=[ikA/εA1],
m1=[ikh,TM/εtikh,TM/εt11],
m2=[ikh,TMeikh,TMt/εtikh,TMeikh,TMt/εt(1iαkh,TM/εt)eikh,TMt(1+iαkh,TM/εt)eikh,TMt].
Ey(z)={EieikAz+EreikAz,z<0En1eikh,TE[z(n1)t]+En2eikh,TE[z(n1)t],(n1)t<z<ntEteikA(znt),z>nt},
mA1=[11ikA+αβ02ikA+αβ02],
mA2=[1ikA],
m1=[11ikh,TEikh,TE],
m2=[eikh,TEteikh,TEt(ikh,TE+αβ02)eikh,TEt(ikh,TE+αβ02)eikh,TEt].

Metrics