Abstract

We numerically observed plasmonic Zitterbewegung (ZB) in nanoscale binary metal waveguide arrays constructed by alternately filling two different dielectrics into adjacent guides. The positive- and negative-energy states of a relativistic electron, whose interference causes the ZB, are mimicked by surface plasmon polariton modes of the two bands of the guide array, respectively. Different from photonic ZB appearing in dielectric systems, we also found that SPP wave packets satisfy a negative-coupled Dirac equation; hence the beam center of SPP shows a shift direction opposite to photonic ZB.

© 2014 Optical Society of America

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  1. E. Schrödinger, “Ueber die kraeftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 24, 418–428 (1930).
  2. W. Zawadzki and T. M. Rusin, “Zitterbewegung (trembling motion) of electrons in semiconductors: a review,” J. Phys. Condens. Matter 23, 143201 (2011).
    [CrossRef]
  3. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
    [CrossRef]
  4. J. Y. Vaishnav and C. W. Clark, “Observing Zitterbewegung with ultracold atoms,” Phys. Rev. Lett. 100, 153002 (2008).
    [CrossRef]
  5. X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101, 264303 (2008).
    [CrossRef]
  6. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
    [CrossRef]
  7. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef]
  8. B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992–1994 (2004).
    [CrossRef]
  9. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
    [CrossRef]
  10. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
    [CrossRef]
  11. E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
    [CrossRef]
  12. Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, and S. Liu, “Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays,” Opt. Lett. 35, 685–687 (2010).
    [CrossRef]
  13. W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
    [CrossRef]
  14. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
    [CrossRef]
  15. R. Shiu and Y. Lan, “Plasmonic Zener tunneling in metal-dielectric waveguide arrays,” Opt. Lett. 36, 4179–4181 (2011).
    [CrossRef]
  16. X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
    [CrossRef]
  17. S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
    [CrossRef]
  18. F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
    [CrossRef]
  19. S. Longhi, “Klein tunneling in binary photonics superlattices,” Phys. Rev. B 81, 075102 (2010).
    [CrossRef]
  20. F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
    [CrossRef]
  21. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [CrossRef]
  22. E. D. Palik, ed. Handbook of Optical Constants of Solids (Academic, 1985).
  23. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
    [CrossRef]

2012 (1)

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

2011 (2)

W. Zawadzki and T. M. Rusin, “Zitterbewegung (trembling motion) of electrons in semiconductors: a review,” J. Phys. Condens. Matter 23, 143201 (2011).
[CrossRef]

R. Shiu and Y. Lan, “Plasmonic Zener tunneling in metal-dielectric waveguide arrays,” Opt. Lett. 36, 4179–4181 (2011).
[CrossRef]

2010 (6)

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonics superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, and S. Liu, “Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays,” Opt. Lett. 35, 685–687 (2010).
[CrossRef]

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

2009 (3)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

2008 (3)

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

J. Y. Vaishnav and C. W. Clark, “Observing Zitterbewegung with ultracold atoms,” Phys. Rev. Lett. 100, 153002 (2008).
[CrossRef]

X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101, 264303 (2008).
[CrossRef]

2007 (2)

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

2006 (2)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

2004 (1)

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

1930 (1)

E. Schrödinger, “Ueber die kraeftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 24, 418–428 (1930).

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Blatt, R.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Chan, C. T.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Clark, C. W.

J. Y. Vaishnav and C. W. Clark, “Observing Zitterbewegung with ultracold atoms,” Phys. Rev. Lett. 100, 153002 (2008).
[CrossRef]

Davoyan, R.

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

de Waele, R.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Dreisow, F.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Gerritsma, R.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Heinrich, M.

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Keil, R.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Kirchmair, G.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Kivshar, Y. S.

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Kuipers, L.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Lan, Y.

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Lin, W.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Liu, S.

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Liu, Z.

X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101, 264303 (2008).
[CrossRef]

Longhi, S.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonics superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Nolte, S.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Polman, A.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Roos, C. F.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Rusin, T. M.

W. Zawadzki and T. M. Rusin, “Zitterbewegung (trembling motion) of electrons in semiconductors: a review,” J. Phys. Condens. Matter 23, 143201 (2011).
[CrossRef]

Schrödinger, E.

E. Schrödinger, “Ueber die kraeftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 24, 418–428 (1930).

Shadrivov, I. V.

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Shiu, R.

Solano, E.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Song, Y.

Sukhorukov, A. A.

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Szameit, A.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Tünnermann, A.

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

Vaishnav, J. Y.

J. Y. Vaishnav and C. W. Clark, “Observing Zitterbewegung with ultracold atoms,” Phys. Rev. Lett. 100, 153002 (2008).
[CrossRef]

Verhagen, E.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Wang, B.

Wang, G. P.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992–1994 (2004).
[CrossRef]

Wang, Y.

Yang, K.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Zähringer, F.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Zawadzki, W.

W. Zawadzki and T. M. Rusin, “Zitterbewegung (trembling motion) of electrons in semiconductors: a review,” J. Phys. Condens. Matter 23, 143201 (2011).
[CrossRef]

Zhang, X.

Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, and S. Liu, “Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays,” Opt. Lett. 35, 685–687 (2010).
[CrossRef]

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

X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101, 264303 (2008).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Zhou, K.

Zhou, X.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Europhys. Lett. (1)

F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Klein tunneling of light in waveguide superlattices,” Europhys. Lett. 97, 10008 (2012).
[CrossRef]

J. Phys. Condens. Matter (1)

W. Zawadzki and T. M. Rusin, “Zitterbewegung (trembling motion) of electrons in semiconductors: a review,” J. Phys. Condens. Matter 23, 143201 (2011).
[CrossRef]

Laser Photon. Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Nature (1)

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Phys. Rev. B (1)

S. Longhi, “Klein tunneling in binary photonics superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

Phys. Rev. Lett. (8)

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[CrossRef]

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

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

J. Y. Vaishnav and C. W. Clark, “Observing Zitterbewegung with ultracold atoms,” Phys. Rev. Lett. 100, 153002 (2008).
[CrossRef]

X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett. 101, 264303 (2008).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. (1)

E. Schrödinger, “Ueber die kraeftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 24, 418–428 (1930).

Other (1)

E. D. Palik, ed. Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic diagram of binary NMWAs. Gray, green, and red regions are the metal Ag (εm), dielectric ε1, and dielectric ε2, respectively, l is the period of the structure. (b) Dispersion relation of a NMWA (black lines with two symmetric bands). Red dotted lines correspond to the dispersion relations of the analog of freely moving relativistic electron in vacuum.

Fig. 2.
Fig. 2.

(a) Amplitude RZ (dashed line) and period PZ (solid line) of plasmonic ZB versus the permittivity of dielectric ε2 when the incident light is at λ=633nm. Inset shows the calculated propagation constant mismatch ν (solid line) and coupling coefficient κ (dashed line) between the two adjacent guides versus dielectric ε2. (b) Relation curves of RZ (dashed line) and PZ (solid line) versus wavelength when dielectric ε2=1.5 is fixed.

Fig. 3.
Fig. 3.

Electric field intensity |E|2 distributions of plasmonic ZB (a)–(c) and corresponding centric positions of SPP beams (d) and (e) versus propagation distance in NMWA excited by the incident light with λ=633nm as the permittivity of dielectric ε2= [(a), (d)] 1.2, [(b), (e)] 1.5, and [(c), (f)] 1.8, respectively.

Fig. 4.
Fig. 4.

Electric field intensity |E|2 distributions of plasmonic ZB [(a), (b)] and corresponding centric positions of SPP beams [(c), (d)] versus propagation distance in NMWA excited by the incident light with [(a), (c)] λ=550nm and [(b), (d)] λ=700nm as the permittivity of dielectric ε2=1.5.

Equations (4)

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idAndz|κ|(Bn1+Bn)ν2An=0idBndz|κ|(An+An+1)+ν2Bn=0,
iϕzi|κ|αϕην2βϕ=0,
RZ=|κ|l/2νPZ=2π/ν,
Hy(x)=exp[(x2/w2)+iπx/l)],

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