Abstract

We report the first experimental demonstration of localized flat-band states in optically induced Kagome photonic lattices. Such lattices exhibit a unique band structure with the lowest band being completely flat (diffractionless) in the tight-binding approximation. By taking the advantage of linear superposition of the flat-band eigenmodes of the Kagome lattices, we demonstrate a high-fidelity transmission of complex patterns in such two-dimensional pyrochlore-like photonic structures. Our numerical simulations find good agreement with experimental observations, upholding the belief that flat-band lattices can support distortion-free image transmission.

© 2016 Optical Society of America

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References

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  1. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).
  2. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
    [Crossref]
  3. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [Crossref]
  4. Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
    [Crossref] [PubMed]
  5. 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. 96243901 (2006).
    [Crossref] [PubMed]
  6. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
    [Crossref]
  7. A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
    [Crossref]
  8. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
    [Crossref] [PubMed]
  9. P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
    [Crossref] [PubMed]
  10. J. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36, 772 (2011).
    [Crossref] [PubMed]
  11. R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).
  12. H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
    [Crossref]
  13. R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
    [Crossref] [PubMed]
  14. S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
    [Crossref] [PubMed]
  15. S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, and Z. Chen, “Demonstration of flat-band image transmission in optically induced Lieb photonic lattices,” Opt. Lett. 41(7), 1435–1438 (2016).
    [Crossref]
  16. J. L. Atwood, “Kagome lattice: a molecular toolkit for magnetism,” Nat. Mater. 1, 91 (2002).
    [Crossref]
  17. D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
    [Crossref]
  18. B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
    [Crossref] [PubMed]
  19. Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
    [Crossref]
  20. S. Endo, T. Oka, and H. Aoki, “Tight-binding photonic bands in metallophotonic waveguide networks and flat bands in kagome lattices,” Phys. Rev. B 81, 113104 (2010).
    [Crossref]
  21. H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).
  22. M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98, 061111 (2011).
    [Crossref]
  23. Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
    [Crossref]
  24. R. A. Vicencio and C. Meja-Corts, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
    [Crossref]
  25. 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]
  26. D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
    [Crossref] [PubMed]
  27. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
    [Crossref] [PubMed]
  28. A. Kelberer, M. Boguslawski, P. Rose, and C. Denz, “Embedding defect sites into hexagonal nondiffracting wave fields,” Opt. Lett. 37, 5009–5011 (2012).
    [Crossref] [PubMed]
  29. R. A. Vicencio and M. Johansson, “Discrete flat-band solitons in the kagome lattice,” Phys. Rev. A 87, 061803(R) (2013).
    [Crossref]
  30. G. Chern and A. Saxena, “PT-symmetric phase in kagome photonic lattices,” Opt. Lett. 40(24), 5806–5809 (2015).
    [Crossref] [PubMed]
  31. S. Mukherjee and R. R. Thomson, “Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice,” Opt. Lett. 40, 5443–5446 (2015).
    [Crossref] [PubMed]

2016 (1)

2015 (5)

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

G. Chern and A. Saxena, “PT-symmetric phase in kagome photonic lattices,” Opt. Lett. 40(24), 5806–5809 (2015).
[Crossref] [PubMed]

S. Mukherjee and R. R. Thomson, “Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice,” Opt. Lett. 40, 5443–5446 (2015).
[Crossref] [PubMed]

2014 (2)

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[Crossref]

R. A. Vicencio and C. Meja-Corts, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
[Crossref]

2013 (1)

R. A. Vicencio and M. Johansson, “Discrete flat-band solitons in the kagome lattice,” Phys. Rev. A 87, 061803(R) (2013).
[Crossref]

2012 (4)

A. Kelberer, M. Boguslawski, P. Rose, and C. Denz, “Embedding defect sites into hexagonal nondiffracting wave fields,” Opt. Lett. 37, 5009–5011 (2012).
[Crossref] [PubMed]

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (1)

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

2008 (3)

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

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

D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
[Crossref]

2007 (2)

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]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
[Crossref]

2006 (1)

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. 96243901 (2006).
[Crossref] [PubMed]

2004 (2)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

2002 (3)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

J. L. Atwood, “Kagome lattice: a molecular toolkit for magnetism,” Nat. Mater. 1, 91 (2002).
[Crossref]

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

1996 (1)

H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
[Crossref]

Ablowitz, M.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Andersson, E.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Ando, M.

H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
[Crossref]

Aoki, H.

S. Endo, T. Oka, and H. Aoki, “Tight-binding photonic bands in metallophotonic waveguide networks and flat bands in kagome lattices,” Phys. Rev. B 81, 113104 (2010).
[Crossref]

H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
[Crossref]

Assanto, G.

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

Atwood, J. L.

J. L. Atwood, “Kagome lattice: a molecular toolkit for magnetism,” Nat. Mater. 1, 91 (2002).
[Crossref]

Balents, L.

D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
[Crossref]

Bartal, G.

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

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
[Crossref]

Barthélémy, A.

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Bergman, D. L.

D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
[Crossref]

Boguslawski, M.

Cantillano, C.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Chen, Z.

S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, and Z. Chen, “Demonstration of flat-band image transmission in optically induced Lieb photonic lattices,” Opt. Lett. 41(7), 1435–1438 (2016).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[Crossref]

Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

J. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36, 772 (2011).
[Crossref] [PubMed]

P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Chern, G.

Choudhury, D.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[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, 103901 (2007).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

Christodoulides, D.N.

Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

Chu, S.

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[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. 96243901 (2006).
[Crossref] [PubMed]

Denz, C.

Dreisow, F.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Efremidis, N. K.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

Endo, S.

S. Endo, T. Oka, and H. Aoki, “Tight-binding photonic bands in metallophotonic waveguide networks and flat bands in kagome lattices,” Phys. Rev. B 81, 113104 (2010).
[Crossref]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
[Crossref]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

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. 96243901 (2006).
[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]

Gallardo, D.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Gao, Y.

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[Crossref]

Goldman, N.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Hajndl, R.

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

Hariharan, S.

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

Heinrich, M.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Hu, Y.

Johansson, M.

R. A. Vicencio and M. Johansson, “Discrete flat-band solitons in the kagome lattice,” Phys. Rev. A 87, 061803(R) (2013).
[Crossref]

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

Keil, R.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

Kelberer, A.

Kitano, M.

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

Lahini, Y.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

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. 96243901 (2006).
[Crossref] [PubMed]

Lederer, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

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

Liu, S.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Lobino, 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. 96243901 (2006).
[Crossref] [PubMed]

Longhi, S.

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[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. 96243901 (2006).
[Crossref] [PubMed]

Louradour, F.

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Lu, J.

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[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]

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. 96243901 (2006).
[Crossref] [PubMed]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Matsumura, H.

H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
[Crossref]

Meja-Corts, C.

R. A. Vicencio and C. Meja-Corts, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
[Crossref]

Mejia-Cortes, C.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Miller, A.

Molina, M. I.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Morales-Inostroza, L.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Moulton, B.

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

Mukherjee, S.

S. Mukherjee and R. R. Thomson, “Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice,” Opt. Lett. 40, 5443–5446 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Nakanishi, T.

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

Nakata, Y.

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

Nolte, S.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Ohberg, P.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Oka, T.

S. Endo, T. Oka, and H. Aoki, “Tight-binding photonic bands in metallophotonic waveguide networks and flat bands in kagome lattices,” Phys. Rev. B 81, 113104 (2010).
[Crossref]

Okada, T.

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

Paltoglou, V.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[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]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Pugatch, R.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

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. 96243901 (2006).
[Crossref] [PubMed]

Real, B.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Rose, P.

Saxena, A.

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
[Crossref]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

Segev, M.

Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

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

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (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, 103901 (2007).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

Shechtman, Y.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

Silberberg, Y.

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

Song, D.

S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, and Z. Chen, “Demonstration of flat-band image transmission in optically induced Lieb photonic lattices,” Opt. Lett. 41(7), 1435–1438 (2016).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[Crossref]

Spracklen, A.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Stegeman, G. I.

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

Suran, E.

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Szameit, A.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Takashima, T.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).

Takeda, H.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).

Tang, L.

S. Xia, Y. Hu, D. Song, Y. Zong, L. Tang, and Z. Chen, “Demonstration of flat-band image transmission in optically induced Lieb photonic lattices,” Opt. Lett. 41(7), 1435–1438 (2016).
[Crossref]

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Thomson, R. R.

S. Mukherjee and R. R. Thomson, “Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice,” Opt. Lett. 40, 5443–5446 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[Crossref] [PubMed]

Torner, L.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

Tünnermann, A.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Vicencio, R. A.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

R. A. Vicencio and C. Meja-Corts, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
[Crossref]

R. A. Vicencio and M. Johansson, “Discrete flat-band solitons in the kagome lattice,” Phys. Rev. A 87, 061803(R) (2013).
[Crossref]

Vysloukh, V. A.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

Weimann, S.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

Wu, C.

D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
[Crossref]

Xia, S.

Xu, J.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Yang, J.

Yoshihara, M.

Yoshino, K.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).

Zaworotko, M. J.

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

Zhang, P.

Zhu, Y.

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Zong, Y.

Angew. Chem. Int. Ed. Engl. (1)

B. Moulton, J. Lu, R. Hajndl, S. Hariharan, and M. J. Zaworotko, “Crystal engineering of a nanoscale kagome lattice,” Angew. Chem. Int. Ed. Engl. 41, 2821–2824 (2002).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98, 061111 (2011).
[Crossref]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Appl. Phys. Lett. 37, 809 (2012).

IEEE Photonics J. (1)

Y. Gao, D. Song, S. Chu, and Z. Chen, “Artificial graphene and related photonic lattices generated with a simple method,” IEEE Photonics J.,  6, 2201806 (2014).
[Crossref]

J. Opt. (1)

R. A. Vicencio and C. Meja-Corts, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
[Crossref]

J. Phys.: Condens. Matter (1)

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys.: Condens. Matter 16, 6317 (2004).

Nat. Commun. (1)

D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. K. Efremidis, and Z. Chen, “Unveiling pseudospin and angular momentum in photonic graphene,” Nat. Commun. 66272 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

J. L. Atwood, “Kagome lattice: a molecular toolkit for magnetism,” Nat. Mater. 1, 91 (2002).
[Crossref]

Nature (London) (3)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Nature (London) 66, 046602 (2002).

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[Crossref]

Opt. Lett. (6)

Phys. Rep. (1)

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

Phys. Rev. A (1)

R. A. Vicencio and M. Johansson, “Discrete flat-band solitons in the kagome lattice,” Phys. Rev. A 87, 061803(R) (2013).
[Crossref]

Phys. Rev. B (4)

Y. Nakata, T. Okada, T. Nakanishi, and M. Kitano, “Observation of flat band for terahertz spoof plasmon in metallic kagome lattice,” Phys. Rev. B 85, 205128 (2012).
[Crossref]

S. Endo, T. Oka, and H. Aoki, “Tight-binding photonic bands in metallophotonic waveguide networks and flat bands in kagome lattices,” Phys. Rev. B 81, 113104 (2010).
[Crossref]

D. L. Bergman, C. Wu, and L. Balents, “Band touching from real-space topology in frustrated hopping models,” Phys. Rev. B 78, 125104 (2008).
[Crossref]

H. Aoki, M. Ando, and H. Matsumura, “Hofstadter butterflies for flat bands,” Phys. Rev. B 54, R17296 (1996).
[Crossref]

Phys. Rev. Lett. (6)

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejia-Cortes, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Ohberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114, 245504 (2015).
[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. 96243901 (2006).
[Crossref] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[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]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D.N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) A schematic diagram of 2D Kagome lattice structure with each unit cell consisting of three lattice sites marked as A, B, C. (b) Numerically calculated band structure under the tight-binding approximation, showing the first three bands with the flat band at the bottom. (c) A fundamental (ring) mode as the flat-band localized degenerate eignstate is denoted by black and white circles, all possessing equal intensity but alternating opposite phases.
Fig. 2
Fig. 2 (a) Experimental setup: (P)BS: (polarizing) beam splitter; ID: iris diaphragm; M: mirror; SBN: strontium barium niobate; SLM: phase-only spatial light modulator; AM: amplitude mask; PM1 (phase mask 1): phase modulation to lattice-forming beam at Fourier plane; PM2 (phase mask 2): phase modulation to probe beam encoded onto SLM. Red arrows 1, 2, 3 show, respectively, the lattice-forming beam, the probe beam, and the interfering beam for measuring the output phase structure. (b) Experimentally established Kagome lattice with lattice spacing of 28 μm. (c) Output of the guided intensity pattern of a quasi-plane wave by the corresponding Kagome structured waveguide arrays.
Fig. 3
Fig. 3 Experimental demonstration of localized flat-band states and their superposition propagating through the Kagome lattice. From left to right, shown are for probing with a single Gaussian beam, six-spot (necklace) beam with equal phase, six-spot beam with opposite phase (as a flat-band state), and an elongated necklace beam (as superposition of ring modes). (a)–(d) Input beam patterns, (e)–(h) linear output patterns without the Kagome lattice, and (i)–(l) linear output patterns exiting the lattice. Upper insets show the combined input intensity patterns when the probe beam is launched into the lattice, and lower insets (zoomed in) show the interferograms of (b) and (c) with a tilted quasi-plane wave to show the input phase structure.
Fig. 4
Fig. 4 Numerical simulation of localized flat-band states and their superposition through the Kagome lattices corresponding to Fig. 3. Other description is the same as for Fig. 3. λ = 532 nm, the lattice spacing D = 28μm, the index change associated with the induced Kagome lattices Δn = 1.8×10−4, and the propagation length L = 10 mm corresponding to the experimental results.
Fig. 5
Fig. 5 Numerical simulation of long distance propagation (L=60mm) of localized flat-band states in Kagome lattices under random-noise perturbations. (a) random-noise perturbations d = 0%; (b) d = 4%; (c) d = 6%; (d) d = 10%. Upper row shows the output profiles of a single flat-band mode. Lower row shows the “sideview” evolution for mode profiles taken along the dashed line in top panels.

Equations (1)

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i ψ ( x , y , z ) z = 1 2 k 1 2 ψ ( x , y , z ) k 0 Δ n ( x , y ) ψ ( x , y , z )

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