Abstract

The giant optical nonlocality near the Dirac point in lossless metal-dielectric multilayer metamaterials is revealed and investigated through the analysis of the band structure of the multilayer stack in the three-dimensional ω-k space, according to the transfer-matrix method with the optical nonlocal effect. The position of the Dirac point is analytically located in the ω-k space. It is revealed that the emergence of the Dirac point is due to the degeneracy of the symmetric and the asymmetric eigenmodes of the coupled surface plasmon polaritons. The optical nonlocality induced epsilon-near-zero frequency shift for the multilayer stack compared to the effective medium is studied. Furthermore, the giant optical nonlocality around the Dirac point is explored with the iso-frequency contour analysis, while the beam splitting phenomenon at the Dirac point due to the optical nonlocal effect is also demonstrated.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
    [CrossRef]
  5. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B44, 8565–8571 (1991).
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  6. R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75, 063813 (2007).
    [CrossRef]
  7. T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B80, 155103 (2009).
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  8. M. Diema, T. Koschnya, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405, 2990–2995 (2010).
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    [CrossRef] [PubMed]
  11. O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
    [CrossRef] [PubMed]
  12. X. Chen, L.-G. Wang, and C.-F. Li, “Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A80, 043839 (2009).
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    [CrossRef]
  26. E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
    [CrossRef]
  27. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
    [CrossRef]
  28. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
    [CrossRef]
  29. S. S. Kruk, D. A. Powell, A. Minovich, D. N. Neshev, and Y. S. Kivshar, “Spatial dispersion of multilayer fishnet metamaterials,” Opt. Express20, 15100–15105 (2012).
    [CrossRef] [PubMed]
  30. A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
    [CrossRef]
  31. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
    [CrossRef] [PubMed]
  32. R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
    [CrossRef] [PubMed]
  33. G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
    [CrossRef] [PubMed]

2013 (2)

L. Sun, J. Gao, and X. Yang, “Broadband epsilon-near-zero metamaterials with steplike metal-dielectric multilayer structures,” Phys. Rev. B87, 165134 (2013).
[CrossRef]

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
[CrossRef]

2012 (7)

G. Subramania, A. J. Fischer, and T. S. Luk, “Optical properties of metal-dielectric based epsilon near zero metamaterials,” Appl. Phys. Lett.101, 241107 (2012).
[CrossRef]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
[CrossRef]

G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
[CrossRef] [PubMed]

K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express20, 3898–3917 (2012).
[CrossRef] [PubMed]

S. S. Kruk, D. A. Powell, A. Minovich, D. N. Neshev, and Y. S. Kivshar, “Spatial dispersion of multilayer fishnet metamaterials,” Opt. Express20, 15100–15105 (2012).
[CrossRef] [PubMed]

K. Sakoda, “Proof of the universality of mode symmetries in creating photonic Dirac cones,” Opt. Express20, 25181–25194 (2012).
[CrossRef] [PubMed]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.101, 241101 (2012).
[CrossRef]

2011 (5)

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

V. Yannopapas and A. Vanakaras, “Dirac point in the photon dispersion relation of a negative/zero/positive-index plasmonic metamaterial,” Phys. Rev. B84, 045128 (2011).
[CrossRef]

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

2010 (3)

M. J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophotonics4, 043511 (2010).
[CrossRef]

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
[CrossRef]

M. Diema, T. Koschnya, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405, 2990–2995 (2010).
[CrossRef]

2009 (6)

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B80, 155103 (2009).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
[CrossRef]

X. Chen, L.-G. Wang, and C.-F. Li, “Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A80, 043839 (2009).
[CrossRef]

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL86, 47008 (2009).
[CrossRef]

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
[CrossRef] [PubMed]

L.-G. Wang, Z.-G. Wang, J.-X. Zhang, and S.-Y. Zhu, “Realization of Dirac point with double cones in optics,” Opt. Lett.34, 1510–1512 (2009).
[CrossRef] [PubMed]

2008 (1)

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

2007 (4)

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75, 155410 (2007).
[CrossRef]

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75, 063813 (2007).
[CrossRef]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
[CrossRef]

2005 (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
[CrossRef] [PubMed]

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
[CrossRef] [PubMed]

1991 (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B44, 8565–8571 (1991).
[CrossRef]

1947 (1)

P. R. Wallace, “The band theory of graphite,” Phys. Rev.71, 622–634 (1947).
[CrossRef]

Abanin, D. A.

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

Alekseyev, L. V.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
[CrossRef]

Alù, A.

G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75, 155410 (2007).
[CrossRef]

Atkinson, R.

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
[CrossRef] [PubMed]

Avrutsky, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
[CrossRef]

Barnakov, Yu. A.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
[CrossRef]

Bartal, G.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
[CrossRef] [PubMed]

Bazaliy, Ya. B.

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75, 063813 (2007).
[CrossRef]

Beenakker, C. W. J.

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75, 063813 (2007).
[CrossRef]

Belov, P. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
[CrossRef]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
[CrossRef]

Bliokh, Y.

Y. Bliokh, V. Freilikher, and F. Nori, “Charge transport in graphene and light propagation in periodic dielectric structures with metamaterials: a comparative study,” arXiv:1302.5533v2 [physics.optics].

Caglayan, H.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
[CrossRef]

Castaldi, G.

G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
[CrossRef] [PubMed]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
[CrossRef]

Chan, C. T.

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

Chebykin, A. V.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
[CrossRef]

Chen, X.

X. Chen, L.-G. Wang, and C.-F. Li, “Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A80, 043839 (2009).
[CrossRef]

Christodoulides, D. N.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
[CrossRef] [PubMed]

Coenen, T.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
[CrossRef]

Diema, M.

M. Diema, T. Koschnya, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405, 2990–2995 (2010).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
[CrossRef] [PubMed]

Elser, J.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
[CrossRef]

Engheta, N.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
[CrossRef]

G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75, 155410 (2007).
[CrossRef]

Evans, P. R.

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
[CrossRef] [PubMed]

Feng, S.

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.101, 241101 (2012).
[CrossRef]

M. J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophotonics4, 043511 (2010).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
[CrossRef] [PubMed]

Fischer, A. J.

G. Subramania, A. J. Fischer, and T. S. Luk, “Optical properties of metal-dielectric based epsilon near zero metamaterials,” Appl. Phys. Lett.101, 241107 (2012).
[CrossRef]

Freedman, B.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
[CrossRef] [PubMed]

Freilikher, V.

Y. Bliokh, V. Freilikher, and F. Nori, “Charge transport in graphene and light propagation in periodic dielectric structures with metamaterials: a comparative study,” arXiv:1302.5533v2 [physics.optics].

Galdi, V.

G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Nonlocal transformation optics,” Phys. Rev. Lett.108, 063902 (2012).
[CrossRef] [PubMed]

Gao, J.

L. Sun, J. Gao, and X. Yang, “Broadband epsilon-near-zero metamaterials with steplike metal-dielectric multilayer structures,” Phys. Rev. B87, 165134 (2013).
[CrossRef]

Geim, A. K.

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
[CrossRef] [PubMed]

Gorbachev, R. V.

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

Gosztola, D. J.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

Grigorieva, I. V.

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G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
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R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
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Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
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A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
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A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
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M. Diema, T. Koschnya, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405, 2990–2995 (2010).
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Lai, Y.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater.10, 582–586 (2011).
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D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
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X. Chen, L.-G. Wang, and C.-F. Li, “Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A80, 043839 (2009).
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L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
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G. Subramania, A. J. Fischer, and T. S. Luk, “Optical properties of metal-dielectric based epsilon near zero metamaterials,” Appl. Phys. Lett.101, 241107 (2012).
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D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
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D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
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R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
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L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
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Noginov, M. A.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
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D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
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T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B80, 155103 (2009).
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T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B80, 155103 (2009).
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A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
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A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
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O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
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A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81, 109–162 (2009).
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M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B44, 8565–8571 (1991).
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G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
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R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
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J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
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G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
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Pollard, R. J.

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
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E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
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D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
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Roberts, M. J.

M. J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophotonics4, 043511 (2010).
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Salakhutdinov, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
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O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett.98, 103901 (2007).
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R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75, 063813 (2007).
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A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75, 155410 (2007).
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A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
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Soukoulis, C. M.

M. Diema, T. Koschnya, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405, 2990–2995 (2010).
[CrossRef]

Stormer, H. L.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
[CrossRef] [PubMed]

Subramania, G.

G. Subramania, A. J. Fischer, and T. S. Luk, “Optical properties of metal-dielectric based epsilon near zero metamaterials,” Appl. Phys. Lett.101, 241107 (2012).
[CrossRef]

Sun, L.

L. Sun, J. Gao, and X. Yang, “Broadband epsilon-near-zero metamaterials with steplike metal-dielectric multilayer structures,” Phys. Rev. B87, 165134 (2013).
[CrossRef]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.101, 241101 (2012).
[CrossRef]

Tan, Y.-W.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
[CrossRef] [PubMed]

Taniguchi, T.

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

Tumkur, T.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
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V. Yannopapas and A. Vanakaras, “Dirac point in the photon dispersion relation of a negative/zero/positive-index plasmonic metamaterial,” Phys. Rev. B84, 045128 (2011).
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Vesseur, E. J. R.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n= 0 structures for visible light,” Phys. Rev. Lett.110, 013902 (2013).
[CrossRef]

Voroshilov, P. M.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011).
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P. R. Wallace, “The band theory of graphite,” Phys. Rev.71, 622–634 (1947).
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X. Chen, L.-G. Wang, and C.-F. Li, “Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A80, 043839 (2009).
[CrossRef]

L.-G. Wang, Z.-G. Wang, J.-X. Zhang, and S.-Y. Zhu, “Realization of Dirac point with double cones in optics,” Opt. Lett.34, 1510–1512 (2009).
[CrossRef] [PubMed]

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL86, 47008 (2009).
[CrossRef]

Wang, Z.-G.

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL86, 47008 (2009).
[CrossRef]

L.-G. Wang, Z.-G. Wang, J.-X. Zhang, and S.-Y. Zhu, “Realization of Dirac point with double cones in optics,” Opt. Lett.34, 1510–1512 (2009).
[CrossRef] [PubMed]

Watanabe, K.

D. A. Abanin, S. V. Morozov, L. A. Ponomarenko, R. V. Gorbachev, A. S. Mayorov, M. I. Katsnelson, K. Watanabe, T. Taniguchi, K. S. Novoselov, L. S. Levitov, and A. K. Geim, “Giant nonlocality near the Dirac point in graphene,” Science332, 328–330 (2011).
[CrossRef] [PubMed]

Wiederrecht, G. P.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

Wurtz, G. A.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
[CrossRef] [PubMed]

Yang, X.

L. Sun, J. Gao, and X. Yang, “Broadband epsilon-near-zero metamaterials with steplike metal-dielectric multilayer structures,” Phys. Rev. B87, 165134 (2013).
[CrossRef]

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.101, 241101 (2012).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Vanakaras, “Dirac point in the photon dispersion relation of a negative/zero/positive-index plasmonic metamaterial,” Phys. Rev. B84, 045128 (2011).
[CrossRef]

Zayats, A. V.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009).
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Zhang, X.

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

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
[CrossRef] [PubMed]

Zheng, H.

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

Zhu, S.-Y.

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL86, 47008 (2009).
[CrossRef]

L.-G. Wang, Z.-G. Wang, J.-X. Zhang, and S.-Y. Zhu, “Realization of Dirac point with double cones in optics,” Opt. Lett.34, 1510–1512 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

L. Sun, S. Feng, and X. Yang, “Loss enhanced transmission and collimation in anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.101, 241101 (2012).
[CrossRef]

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97, 131107 (2010).
[CrossRef]

G. Subramania, A. J. Fischer, and T. S. Luk, “Optical properties of metal-dielectric based epsilon near zero metamaterials,” Appl. Phys. Lett.101, 241107 (2012).
[CrossRef]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007).
[CrossRef]

EPL (1)

L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL86, 47008 (2009).
[CrossRef]

J. Nanophotonics (1)

M. J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophotonics4, 043511 (2010).
[CrossRef]

Nat. Mater. (1)

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

Nat. Nanotechnol. (1)

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6, 107–111 (2011).
[CrossRef] [PubMed]

Nature (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438, 197–200 (2005).
[CrossRef] [PubMed]

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438, 201–204 (2005).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phy. Rev. B (1)

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phy. Rev. B86, 115420 (2012).
[CrossRef]

Phys. Rev. (1)

P. R. Wallace, “The band theory of graphite,” Phys. Rev.71, 622–634 (1947).
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Phys. Rev. A (2)

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