Abstract

The recent simulation of quantum behavior in condensed matter physics by well-designed photonic structures has opened unprecedented opportunities to steer the flow of light in novel manners. Here, we propose a design to simulate massless Dirac dynamics in evanescently coupled plasmonic ridge waveguide arrays with alternating positive and negative coupling coefficients. The coupling coefficients are carefully tailored by adjusting the geometric parameters of the waveguide in arrays, which are supposed to be feasible with advanced nanofabrication techniques. Further theoretical studies are also carried out based on the coupled mode theory to discuss the influence of excitation condition on beam propagation in this massless Dirac dynamics simulation case.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3(3), 243–261 (2009).
    [Crossref]
  2. S. Longhi, “Classical simulations of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104(3), 453–468 (2011).
    [Crossref]
  3. A. Trabesinger, “Quantum simulation,” Nat. Phys. 8(4), 263 (2012).
    [Crossref]
  4. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [Crossref] [PubMed]
  5. F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
    [Crossref]
  6. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
    [Crossref] [PubMed]
  7. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
    [Crossref]
  8. A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
    [Crossref] [PubMed]
  9. W. Zhang and S. E. Ulloa, “ac-field-controlled localization-delocalization transition in a one-dimensional disordered system,” Phys. Rev. B 74(11), 115304 (2006).
    [Crossref]
  10. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
    [Crossref] [PubMed]
  11. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
    [Crossref] [PubMed]
  12. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
    [Crossref]
  13. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
    [Crossref] [PubMed]
  14. 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]
  15. S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81(7), 075102 (2010).
    [Crossref]
  16. 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(14), 143902 (2010).
    [Crossref] [PubMed]
  17. S. L. Ding and G. P. Wang, “Plasmonic analogs of Zitterbewegung in nanoscale metal waveguide arrays,” J. Opt. Soc. Am. B 31(3), 603 (2014).
    [Crossref]
  18. S. H. Nam, J. Zhou, A. J. Taylor, and A. Efimov, “Dirac dynamics in one-dimensional graphene-like plasmonic crystals: pseudo-spin, chirality, and diffraction anomaly,” Opt. Express 18(24), 25329–25338 (2010).
    [Crossref] [PubMed]
  19. S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “General properties of surface modes in binary metal-dielectric metamaterials,” Opt. Express 18(25), 25627–25632 (2010).
    [Crossref] [PubMed]
  20. J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
    [Crossref] [PubMed]
  21. Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
    [Crossref]
  22. Y. M. Liu and X. Zhang, “Metasurface for manipulating surface plamons,” Appl. Phys. Lett. 103(14), 141101 (2013).
    [Crossref]
  23. A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
    [Crossref] [PubMed]
  24. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [Crossref]
  25. H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
    [Crossref] [PubMed]
  26. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
    [Crossref] [PubMed]
  27. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]

2015 (2)

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

2014 (2)

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

S. L. Ding and G. P. Wang, “Plasmonic analogs of Zitterbewegung in nanoscale metal waveguide arrays,” J. Opt. Soc. Am. B 31(3), 603 (2014).
[Crossref]

2013 (1)

Y. M. Liu and X. Zhang, “Metasurface for manipulating surface plamons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

2012 (2)

A. Trabesinger, “Quantum simulation,” Nat. Phys. 8(4), 263 (2012).
[Crossref]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

2011 (1)

S. Longhi, “Classical simulations of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104(3), 453–468 (2011).
[Crossref]

2010 (7)

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81(7), 075102 (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(14), 143902 (2010).
[Crossref] [PubMed]

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. H. Nam, J. Zhou, A. J. Taylor, and A. Efimov, “Dirac dynamics in one-dimensional graphene-like plasmonic crystals: pseudo-spin, chirality, and diffraction anomaly,” Opt. Express 18(24), 25329–25338 (2010).
[Crossref] [PubMed]

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “General properties of surface modes in binary metal-dielectric metamaterials,” Opt. Express 18(25), 25627–25632 (2010).
[Crossref] [PubMed]

2009 (2)

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

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

2008 (4)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

2006 (2)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

W. Zhang and S. E. Ulloa, “ac-field-controlled localization-delocalization transition in a one-dimensional disordered system,” Phys. Rev. B 74(11), 115304 (2006).
[Crossref]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

1999 (1)

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

Bartal, G.

Blatt, R.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

Bleckmann, F.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Block, A.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Brauer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Cheng, Q. Q.

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Christodoulides, D. N.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

de Leon, N. P.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Devlin, R. C.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Dibos, A.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Ding, S. L.

Dreisow, F.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Efimov, A.

Efremidis, N. K.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Etrich, C.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[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(7277), 68–71 (2010).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

High, A. A.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Ismail, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Keil, R.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

Kirchmair, G.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

Kivshar, Y. S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Lahini, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Li, T.

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Limboeck, T.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Linden, S.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Liu, Y. M.

Y. M. Liu and X. Zhang, “Metasurface for manipulating surface plamons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

Lobino, M.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, “Classical simulations of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104(3), 453–468 (2011).
[Crossref]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81(7), 075102 (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(14), 143902 (2010).
[Crossref] [PubMed]

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

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Lukin, M. D.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Matsuda, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Matthews, J. C. F.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Morandotti, R.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Nam, S. H.

Nolte, S.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

OBrien, J. L.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Pan, Y. M.

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Park, H.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Perczel, J.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Perets, H. B.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Peruzzo, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Politi, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Polking, M.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Poulios, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Pozzi, F.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

Rockstuhl, C.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

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(7277), 68–71 (2010).
[Crossref] [PubMed]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Silberberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Soergel, E.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Solano, E.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Sukhorukov, A. A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Szameit, A.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Taylor, A. J.

Thompson, M. G.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Trabesinger, A.

A. Trabesinger, “Quantum simulation,” Nat. Phys. 8(4), 263 (2012).
[Crossref]

Tünnermann, A.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

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(14), 143902 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

Ulin-Avila, E.

Ulloa, S. E.

W. Zhang and S. E. Ulloa, “ac-field-controlled localization-delocalization transition in a one-dimensional disordered system,” Phys. Rev. B 74(11), 115304 (2006).
[Crossref]

Wang, G. P.

Wang, Q. J.

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Wild, D. S.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Wörhoff, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Zähringer, F.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

Zeuner, J. M.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett. 109(2), 023602 (2012).
[Crossref] [PubMed]

Zhang, W.

W. Zhang and S. E. Ulloa, “ac-field-controlled localization-delocalization transition in a one-dimensional disordered system,” Phys. Rev. B 74(11), 115304 (2006).
[Crossref]

Zhang, X.

Y. M. Liu and X. Zhang, “Metasurface for manipulating surface plamons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

S. H. Nam, E. Ulin-Avila, G. Bartal, and X. Zhang, “General properties of surface modes in binary metal-dielectric metamaterials,” Opt. Express 18(25), 25627–25632 (2010).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Zhou, J.

Zhou, X. Q.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Zhu, S. N.

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Appl. Phys. B (1)

S. Longhi, “Classical simulations of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104(3), 453–468 (2011).
[Crossref]

Appl. Phys. Lett. (1)

Y. M. Liu and X. Zhang, “Metasurface for manipulating surface plamons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (2)

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

Q. Q. Cheng, Y. M. Pan, Q. J. Wang, T. Li, and S. N. Zhu, “Topologically protected interface mode in plasmonic waveguide arrays,” Laser Photonics Rev. 9(4), 392–398 (2015).
[Crossref]

Nat. Commun. (1)

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5, 3843 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Nat. Phys. (2)

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
[Crossref]

A. Trabesinger, “Quantum simulation,” Nat. Phys. 8(4), 263 (2012).
[Crossref]

Nature (3)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463(7277), 68–71 (2010).
[Crossref] [PubMed]

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

Opt. Express (3)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, M. Segev, G. Assanto, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Phys. Rev. B (3)

W. Zhang and S. E. Ulloa, “ac-field-controlled localization-delocalization transition in a one-dimensional disordered system,” Phys. Rev. B 74(11), 115304 (2006).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81(7), 075102 (2010).
[Crossref]

Phys. Rev. Lett. (7)

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(14), 143902 (2010).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96(24), 243901 (2006).
[Crossref] [PubMed]

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Science (1)

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[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of binary waveguide array, where red and blue arrows denote positive and negative coupling coefficients, respectively. (b) Dispersion relation of a binary waveguide array with balanced positive and negative coupling coefficients with the coupling strength is set as κ = 0.03k0. (c) CMT calculation results of beam evolution in a binary waveguide array.
Fig. 2
Fig. 2 (a) Schematic diagram of two closely placed rectangle ridge waveguides. (b) Electric field intensity distributions of symmetric mode and antisymmetric mode (w = 60 nm, h = 120 nm and g = 30 nm) and their corresponding vectorial field distributions. (c) Phase graph of coupling coefficients respect to structure parameters g and h for two coupled rectangle ridge waveguides shown as (a) with w = 60 nm and (d) for two coupled trapezoid ridge waveguides with w = 60 nm and w’ = 20 nm shown as the inset. The dashed line notes the zero coupling coefficient and the two white points on the dot-dashed line represent the selected parameters in the following simulation.
Fig. 3
Fig. 3 (a) Schematics of a binary rectangle PRWA with balanced positive and negative coupling by alternating the gaps. (b) Excitation field distributions on 7 waveguides corresponding to the blue box in (c). (c) COMSOL simulation result of the SPP propagation along z-axis in rectangle PRWA of (a). The propagation distance here is 30 μm. (d) Schematics of a binary trapezoid PRWA. (e) Excitation field distributions on 7 waveguides corresponding to the blue box in (f). (f) SPP propagation along z-axis in trapezoid PRWA of (d).
Fig. 4
Fig. 4 Excited band structures of binary waveguide array with balanced coupling coefficients of −0.03 and 0.03 for (a) single-site excitation, (b) 3-sites excitation and (c) 7-sites excitation. (d-f) are the corresponding beam propagation patterns (left panel) and end-face intensity distributions (right panel) for (a-c).
Fig. 5
Fig. 5 Simulation results of (a) lossless system and (b) lossy system with output intensity distributions shown on the right. Here the propagation distance is 50 μm with 9 waveguide sites excited in both cases. (c) Summation of electric field intensity in all waveguides along propagating length in lossy system. The fitting curve shows an obvious exponential attenuation during propagation.

Equations (5)

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{ ( i z + β 0 ) E 2n + κ 1 E 2n1 + κ 2 E 2n+1 =0 ( i z + β 0 ) E 2n+1 + κ 2 E 2n + κ 1 E 2n+2 =0 ,
Hψ=(β β 0 )ψ, H=( 0 κ( e ik 1) κ( e ik 1) 0 ),
H= ( κ + κ + β 0 κ κ β 0 κ + κ + β 0 κ κ ) 79×79
p= ψ in Ψ E =( p 1 , p 2 ,, p i ,, p 78 , p 79 ).
ψ E i (k)= p i n ψ E i (n)exp(ink) ,

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