Abstract

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), we make theoretical investigations of the guided modes in the NZPIM waveguide near the DP by using the graphical method. Due to the linear Dirac dispersion, the fundamental mode is absent when the angular frequency is smaller than the DP, while the behaviors of NZPIM waveguide are similar to the conventional dielectric waveguide when the angular frequency is larger than the DP. The unique properties of the guided modes are analogous to the propagation of electron waves in graphene waveguide [Appl. Phys. Lett., 94, 212105 (2009)], corresponding to the classical motion and the Klein tunneling. These results suggest that many exotic phenomena in graphene can be simulated by the relatively simple optical NZPIM.

©2010 Optical Society of America

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    [Crossref] [PubMed]
  4. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature (London)  438, 201 (2005).
    [Crossref] [PubMed]
  5. K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
    [Crossref] [PubMed]
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    [Crossref]
  7. V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
    [Crossref] [PubMed]
  8. C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
    [Crossref] [PubMed]
  9. P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
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  10. S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys.: Condens. Matter,  21, 292204 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  14. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
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    [Crossref] [PubMed]
  16. R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
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    [Crossref]
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    [Crossref]
  22. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
    [Crossref]
  23. I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
    [Crossref] [PubMed]
  24. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
    [Crossref]
  25. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
    [Crossref] [PubMed]
  26. T. Jiang, J.-M. Zhao, and Y.-J. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17, 170 (2008).
    [Crossref]
  27. D. Ö. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79, 063834 (2009).
    [Crossref]

2010 (1)

L. Zhao and S. F. Yelin, “Proposal for graphene-based coherent buffers and memories,” Phys. Rev. B,  81, 115441 (2010).
[Crossref]

2009 (9)

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

F.-M. Zhang, Y. He, and X. Chen, “Guided modes in graphene waveguides,” Appl. Phys. Lett. 94, 212105 (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,” EPL 86, 47008 (2009).
[Crossref]

X. Chen, L.-G. Wang, and C.-F. Li, “Transmssion gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A 80, 043839 (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 (2009).
[Crossref]

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
[Crossref] [PubMed]

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys.: Condens. Matter,  21, 292204 (2009).
[Crossref]

D. Ö. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79, 063834 (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 (2009).
[Crossref] [PubMed]

2008 (6)

T. Jiang, J.-M. Zhao, and Y.-J. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17, 170 (2008).
[Crossref]

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

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

C. W. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80, 1337 (2008).
[Crossref]

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (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]

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
[Crossref]

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
[Crossref] [PubMed]

2006 (1)

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
[Crossref]

2005 (4)

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[Crossref] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

2003 (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

Akhmerov, A. R.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

Altshuler, B. L.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
[Crossref] [PubMed]

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, Y. B.

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
[Crossref]

Beenakker, C. W.

C. W. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80, 1337 (2008).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
[Crossref]

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
[Crossref] [PubMed]

Chaubet, M.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Cheianov, V. V.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
[Crossref] [PubMed]

Chen, X.

X. Chen, L.-G. Wang, and C.-F. Li, “Transmssion gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A 80, 043839 (2009).
[Crossref]

F.-M. Zhang, Y. He, and X. Chen, “Guided modes in graphene waveguides,” Appl. Phys. Lett. 94, 212105 (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]

Cohen, M. L.

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

Darancet, P.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Fal’ko, V.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
[Crossref] [PubMed]

Feng, Y.-J.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

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]

Geim, A. K.

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 (2009).
[Crossref]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Ghosh, S.

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys.: Condens. Matter,  21, 292204 (2009).
[Crossref]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Guinea, F.

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 (2009).
[Crossref]

Güney, D. Ö.

D. Ö. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79, 063834 (2009).
[Crossref]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref] [PubMed]

He, Y.

F.-M. Zhang, Y. He, and X. Chen, “Guided modes in graphene waveguides,” Appl. Phys. Lett. 94, 212105 (2009).
[Crossref]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
[Crossref] [PubMed]

Houzet, G.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Jiang, T.

Katsnelson, M. I.

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
[Crossref]

Kim, P.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

Kivshar, Yuri S.

I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[Crossref] [PubMed]

Lheurette, E.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Li, C.-F.

X. Chen, L.-G. Wang, and C.-F. Li, “Transmssion gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A 80, 043839 (2009).
[Crossref]

Lippens, D.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Louie, S. G.

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

Manela, O.

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]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

Mayou, D.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
[Crossref] [PubMed]

Meyer, D. A.

D. Ö. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79, 063834 (2009).
[Crossref]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Neto, A. H. Castro

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 (2009).
[Crossref]

Novoselov, K. S.

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 (2009).
[Crossref]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Olevano, V.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
[Crossref] [PubMed]

Park, C. H.

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

Peleg, O.

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]

Peres, N. M. R.

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 (2009).
[Crossref]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref] [PubMed]

Scalora, M.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

Segev, M.

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]

Sepkhanov, R. A.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
[Crossref]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

Sharma, M.

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys.: Condens. Matter,  21, 292204 (2009).
[Crossref]

Son, Y. W.

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

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,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[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,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
[Crossref] [PubMed]

Tworzydlo, J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

Wang, L.-G.

X. Chen, L.-G. Wang, and C.-F. Li, “Transmssion gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A 80, 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,” EPL 86, 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 (2009).
[Crossref] [PubMed]

Wang, Z.-G.

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 (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,” EPL 86, 47008 (2009).
[Crossref]

Yang, L.

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

Yelin, S. F.

L. Zhao and S. F. Yelin, “Proposal for graphene-based coherent buffers and memories,” Phys. Rev. B,  81, 115441 (2010).
[Crossref]

Zhang, F.-M.

F.-M. Zhang, Y. He, and X. Chen, “Guided modes in graphene waveguides,” Appl. Phys. Lett. 94, 212105 (2009).
[Crossref]

Zhang, J.-X.

Zhang, L.-F.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Zhang, X.

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

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,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

Zhao, J.-M.

Zhao, L.

L. Zhao and S. F. Yelin, “Proposal for graphene-based coherent buffers and memories,” Phys. Rev. B,  81, 115441 (2010).
[Crossref]

Zhao, X.-P.

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Zhu, S.-Y.

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 (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,” EPL 86, 47008 (2009).
[Crossref]

Appl. Phys. Lett. (1)

F.-M. Zhang, Y. He, and X. Chen, “Guided modes in graphene waveguides,” Appl. Phys. Lett. 94, 212105 (2009).
[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,” EPL 86, 47008 (2009).
[Crossref]

J. Appl. Phys. (1)

L.-F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X.-P. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

J. Phys.: Condens. Matter (1)

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys.: Condens. Matter,  21, 292204 (2009).
[Crossref]

Nano Lett. (1)

C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron beam supercollimation in graphene superlattices,” Nano Lett. 8, 2920 (2008).
[Crossref] [PubMed]

Nat. Phys. (1)

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
[Crossref]

Nature (3)

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature (London)  438, 201 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature (London)  438, 197 (2005).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’storage of light in metamaterials,” Nature (London)  450, 397 (2007).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

D. Ö. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79, 063834 (2009).
[Crossref]

X. Chen, L.-G. Wang, and C.-F. Li, “Transmssion gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab,” Phys. Rev. A 80, 043839 (2009).
[Crossref]

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75, 063813 (2007).
[Crossref]

Phys. Rev. B (1)

L. Zhao and S. F. Yelin, “Proposal for graphene-based coherent buffers and memories,” Phys. Rev. B,  81, 115441 (2010).
[Crossref]

Phys. Rev. E (2)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71, 046603 (2005).
[Crossref]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

Phys. Rev. Lett. (6)

I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[Crossref] [PubMed]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[Crossref] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref] [PubMed]

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]

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

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constrictions: Sub-wavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803 (2009).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

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 (2009).
[Crossref]

C. W. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80, 1337 (2008).
[Crossref]

Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666 (2004).
[Crossref] [PubMed]

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252 (2007).
[Crossref] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1. Schematic structure of NZPIM waveguide, where the core is the air with the thickness is d and the cladding is the so-called NZPIM.
Fig. 2.
Fig. 2. (Color online) Graphical determination of κxd for fast wave guided modes when ω < ωD. The solid and dashed curves correspond to tan (κxd) and F(κxd), respectively. The initial parameters are ωD = 2π × 10GHz, ω = 0.8ωD which means the total reflection angle is θc = 30°, the thickness of the core are (a) d = 10cm and (b) d = 1cm.
Fig. 3.
Fig. 3. (Color online) The electric field distribution of guided modes as a function of distance in the NZPIM waveguide corresponding to the intersection in Fig. (2) when ω < ωD. (a) TE2: κxd = 3.41; (b) TE3: κxd = 6.87; (c) TE4: κxd = 10.49; (d) TE1: κxd = 1.03.
Fig. 4.
Fig. 4. (Color online) Graphical determination of κxd for fast wave guided modes when ω > ωD. The solid and dashed curves correspond to tan (κxd) and F(κxd), respectively. The initial parameters are ωD = 2π × 10GHz, ω = 4ωD/3 which means the total reflection angle is θc = 30°, the thickness of the core is d = 10cm.
Fig. 5.
Fig. 5. (Color online) The electric field distribution of guided modes as a function of distance in the NZPIM waveguide corresponding to the intersection in Fig. (4) when ω > ωD. (a) TE0: κxd = 3.03; (b) TE1: κxd = 6.06; (c) TE2: κxd = 9.07; (d) TE3: κxd = 12.07.
Fig. 6.
Fig. 6. (Color online) The propagation constant β versus the incident frequency ω near the DP in the NZPIM waveguide.
Fig. 7.
Fig. 7. (Color online) The wave function of guided modes as a function of distance of NZPIM waveguide. The initial parameters are ωD = 2π × 10GHz, ω = 0.69ωD, and the thickness of the core is d = 10cm.(a) TE0: κxd = 13.8109; (b) TE1: κxd = 13.8112.

Equations (14)

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

k ( ω ) = ( ω ω D ) v D ,
[ 0 i ( x i y ) i ( x + i y ) 0 ] Ψ = ( ω ω D ν D ) Ψ ,
ε 2 ( ω ) = 1 ω ep 2 ( ω 2 + i γ e ω ) ,
μ 2 ( ω ) = 1 ω mp 2 ( ω 2 + i γ m ω ) ,
ψ A ( x ) = { Ae α x e i β y , x < 0 , [ B cos ( κ x x ) + C sin ( κ x x ) ] e i β y , 0 < x < d , De α ( x d ) e i β y , x > d ,
tan ( κ x d ) = 2 μ 1 μ 2 α κ x μ 2 2 κ x 2 μ 1 2 α 2 .
F ( κ x d ) = 2 μ 1 μ 2 ( κ x d ) ( κ 1 d ) 2 ( κ x d ) 2 ( κ 2 d ) 2 μ 2 2 ( κ x d ) 2 μ 1 2 [ ( κ 1 d ) 2 ( κ x d ) 2 ( κ 2 d ) 2 ] .
θ c = sin 1 [ 2 ( ω D ω 1 ) ]
κ x d = m π + 2 ϕ , m = 0 , 1 , 2 , . . .
ϕ = arctan ( μ 1 α μ 2 κ x ) ,
θ c = sin 1 [ 2 ( 1 ω D ω ) ]
ψ A ( x ) = { Ae α x e i β y , x < 0 , [ B cosh ( κ x x ) + C sinh ( κ x x ) ] e i β y , 0 < x < d , De α ( x d ) e i β y , x > d ,
tanh ( κ x d ) = 2 μ 1 μ 2 α κ x μ 2 2 κ x 2 + μ 1 2 α 2 .
F ( κ x d ) = 2 μ 1 μ 2 ( κ x d ) ( κ 1 d ) 2 + ( κ x d ) 2 ( κ 2 d ) 2 μ 2 2 ( κ x d ) 2 + μ 1 2 [ ( κ 1 d ) 2 + ( κ x d ) 2 ( κ 2 d ) 2 ] .

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