Abstract

We introduce a new class of plasmonic crystals possessing graphene-like internal symmetries and Dirac-type spectrum in k-space. We study dynamics of surface plasmon polaritons supported in the plasmonic crystals by employing the formalism of Dirac dynamics for relativistic quantum particles. Through an analogy with graphene, we introduce a concept of pseudo-spin and chirality to indicate built-in symmetry of the plasmonic crystals near Dirac point. The surface plasmon polaritons with different pseudo-spin states are shown to split in the crystals into two beams, analogous to spin Hall effect.

© 2010 OSA

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  1. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
    [CrossRef] [PubMed]
  2. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [CrossRef] [PubMed]
  3. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
    [CrossRef]
  4. T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
    [CrossRef]
  5. X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
    [CrossRef] [PubMed]
  6. 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(10), 103901 (2007).
    [CrossRef] [PubMed]
  7. O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
    [CrossRef] [PubMed]
  8. S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
    [CrossRef] [PubMed]
  9. S. Hyun Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
    [CrossRef] [PubMed]
  10. A. A. Sukhorukov and Y. S. Kivshar, “Discrete gap solitons in modulated waveguide arrays,” Opt. Lett. 27(23), 2112–2114 (2002).
    [CrossRef] [PubMed]
  11. A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [CrossRef]
  12. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
    [CrossRef]
  13. T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
    [CrossRef]
  14. Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
    [CrossRef] [PubMed]
  15. F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
    [CrossRef]
  16. A. K. Geim and A. H. MacDonald, “Graphene: Exploring carbon flatland,” Phys. Today 60(8), 35–41 (2007).
    [CrossRef]
  17. J. K. Furdyna, “Split light,” Physics 3, 56 (2010).
    [CrossRef]
  18. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [CrossRef] [PubMed]
  19. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  20. B. Thaller, Advanced visual quantum mechanics, (Springer, 2005).

2010

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
[CrossRef]

J. K. Furdyna, “Split light,” Physics 3, 56 (2010).
[CrossRef]

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[CrossRef] [PubMed]

S. Hyun Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef] [PubMed]

2009

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[CrossRef]

2008

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[CrossRef] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

2007

A. K. Geim and A. H. MacDonald, “Graphene: Exploring carbon flatland,” Phys. Today 60(8), 35–41 (2007).
[CrossRef]

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(10), 103901 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

2006

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
[CrossRef]

2004

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

2002

1998

T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
[CrossRef]

Ando, T.

T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
[CrossRef]

Bahat-Treidel, O.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

Bartal, G.

S. Hyun Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[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(10), 103901 (2007).
[CrossRef] [PubMed]

Castro Neto, A. H.

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (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(10), 103901 (2007).
[CrossRef] [PubMed]

Efimov, A.

Feng, Y. P.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[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(10), 103901 (2007).
[CrossRef] [PubMed]

Furdyna, J. K.

J. K. Furdyna, “Split light,” Physics 3, 56 (2010).
[CrossRef]

Geim, A. K.

F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
[CrossRef]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

A. K. Geim and A. H. MacDonald, “Graphene: Exploring carbon flatland,” Phys. Today 60(8), 35–41 (2007).
[CrossRef]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
[CrossRef]

Grobman, M.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

Guinea, F.

F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
[CrossRef]

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Hyun Nam, S.

Katsnelson, M. I.

F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
[CrossRef]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
[CrossRef]

Kivshar, Y. S.

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Lu, Y. H.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

MacDonald, A. H.

A. K. Geim and A. H. MacDonald, “Graphene: Exploring carbon flatland,” Phys. Today 60(8), 35–41 (2007).
[CrossRef]

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(10), 103901 (2007).
[CrossRef] [PubMed]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Nakanishi, T.

T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
[CrossRef]

Nam, S. H.

Ni, Z. H.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

Novoselov, K. S.

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
[CrossRef]

Ochiai, T.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[CrossRef]

Onoda, M.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[CrossRef]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Peleg, O.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[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(10), 103901 (2007).
[CrossRef] [PubMed]

Pereg-Barnea, T.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Raghu, S.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Saito, R.

T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
[CrossRef]

Segev, M.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[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(10), 103901 (2007).
[CrossRef] [PubMed]

Shapira, N.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

Shen, Z. X.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Taylor, A. J.

Ulin-Avila, E.

Wang, Y. Y.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

Yu, T.

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

Zhang, X.

S. Hyun Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “Deep subwavelength surface modes in metal-dielectric metamaterials,” Opt. Lett. 35(11), 1847–1849 (2010).
[CrossRef] [PubMed]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[CrossRef] [PubMed]

ACS Nano

Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS Nano 2(11), 2301–2305 (2008).
[CrossRef] [PubMed]

J. Phys. Soc. Jpn.

T. Ando, T. Nakanishi, and R. Saito, “Berry's phase and absence of back scattering in carbon nanotubes,” J. Phys. Soc. Jpn. 67(8), 2857–2862 (1998).
[CrossRef]

Nat. Mater.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Nat. Phys.

F. Guinea, M. I. Katsnelson, and A. K. Geim, “Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering,” Nat. Phys. 6(1), 30–33 (2010).
[CrossRef]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2(9), 620–625 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Phys. Rev. B

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[CrossRef]

Phys. Rev. Lett.

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (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(10), 103901 (2007).
[CrossRef] [PubMed]

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[CrossRef] [PubMed]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Phys. Today

A. K. Geim and A. H. MacDonald, “Graphene: Exploring carbon flatland,” Phys. Today 60(8), 35–41 (2007).
[CrossRef]

Physics

J. K. Furdyna, “Split light,” Physics 3, 56 (2010).
[CrossRef]

Rev. Mod. Phys.

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Science

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

Other

B. Thaller, Advanced visual quantum mechanics, (Springer, 2005).

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