Abstract

Abstract: The photonic lattice, a mesoscopic artificial structure, contributes to the optics and quantum fields. Here we fabricate octagon and dodecagon lattices with strontium barium niobate (SBN), a new kind of two-dimensional (2D) complicated period polygon photonic lattices. The photonic lattices are composed of two unequal sublattices corresponding to the valley freedom (pseudospin) of electrons, which are similar to a honeycomb lattice. We demonstrate the nonlinear transmission and pseudospin in the octagon lattice (OL) and dodecagon lattice (DL). The transmission beam is eventually localized in the lattice with a nonlinear effect. In addition, we explore the pseudospin in the lattice by the specially-designed probing beam, which supplies a new lattice for photonic research. We gain both in our simulation and experiment.

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

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2017 (3)

2016 (1)

2015 (4)

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. 6(1), 6272 (2015).
[Crossref] [PubMed]

L. H. Wu and X. Hu, “Scheme to achieve silicon topological photonics,” Phys. Rev. Lett. 114, 223901 (2015).
[Crossref] [PubMed]

F. Chen and J. Lv, “Three-dimensional femtosecond laser fabrication of waveguide beam splitters in LiNbO3 crystal,” Opt. Mater. Express 5(6), 1274 (2015).
[Crossref]

R. Márquez-Islas, B. Zenteno-Mateo, B. Flores-Desirena, A. Reyes-Coronado, and F. Pérez-Rodríguez, “Plasma-phonon polaritons in superlattices of semimetal bismuth and polaritonic material,” Opt. Mater. Express 5(12), 2820–2834 (2015).
[Crossref]

2014 (2)

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

2013 (5)

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, and M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111(10), 103901 (2013).
[Crossref] [PubMed]

Z. Cao, X. Qi, G. Zhang, and J. Bai, “Asymmetric light propagation in transverse separation modulated photonic lattices,” Opt. Lett. 38(17), 3212–3215 (2013).
[Crossref] [PubMed]

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, “Artificial honeycomb lattices for electrons, atoms and photons,” Nat. Nanotechnol. 8(9), 625–633 (2013).
[Crossref] [PubMed]

2012 (7)

C. Fefferman and M. Weinstein, “Honeycomb lattice potentials and Dirac points,” J. Am. Math. Soc. 25(4), 1169–1220 (2012).
[Crossref]

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

D. Leykam, B.-T. Omri, and A. S. Desyatnikov, “Pseudospin and nonlinear conical diffraction in Lieb lattices,” Phys. Rev. A 86(3), 031805 (2012).
[Crossref]

Z. Cao, X. Qi, X. Feng, Z. Ren, G. Zhang, and J. Bai, “Light controlling in transverse separation modulated photonic lattices,” Opt. Express 20(17), 19119–19124 (2012).
[Crossref] [PubMed]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483(7389), 302–305 (2012).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, A. Tünnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and Landau levels in photonic structures,” Nat. Photonics 7, 153–158 (2012).
[Crossref]

2011 (5)

A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M. I. Katsnelson, A. Pinczuk, L. N. Pfeiffer, K. W. West, and V. Pellegrini, “Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice,” Science 332(6034), 1176–1179 (2011).
[Crossref] [PubMed]

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, “Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light,” Phys. Rev. Lett. 107(16), 166803 (2011).
[Crossref] [PubMed]

M. Trushin and J. Schliemann, “Pseudospin in optical and transport properties of graphene,” Phys. Rev. Lett. 107(15), 156801 (2011).
[Crossref] [PubMed]

F. Laurell, K. Gallo, and M. Manzo,“Two-dimensional domain engineering in LiNbO3 via a hybrid patterning technique,” Adv. Opt. Mater 1(3), 365–371 (2011).

2009 (3)

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

C.-H. Park and S. G. Louie, “Making massless Dirac fermions from a patterned two-dimensional electron gas,” Nano Lett. 9(5), 1793–1797 (2009).
[Crossref] [PubMed]

M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L. N. Pfeiffer, and K. W. West, “A. Singha, V. Pellegrini, M. Polini, G. Vignale, and A. Pinczuk, “Engineering artificial graphene in a two-dimensional electron gas,” Phys. Rev. B 79(24), 241406 (2009).
[Crossref]

2007 (3)

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007).
[Crossref] [PubMed]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 497–500 (2007).
[Crossref]

2006 (1)

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

2002 (1)

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, “Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016609 (2002).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Abbarchi, M.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Amo, A.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Bai, J.

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

Baumberg, J. J.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

Becker, C.

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Berloff, N. G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

Bian, G.

Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, “Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light,” Phys. Rev. Lett. 107(16), 166803 (2011).
[Crossref] [PubMed]

Bick, A.

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Bissbort, U.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

Bloch, J.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Blömer, D.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[Crossref]

Burghoff, J.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[Crossref]

Cao, Z.

Carusotto, I.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Castro Neto, A. H.

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

Chen, F.

Chen, J. J.

Chen, Z.

P. Zhang, D. Gallardo, S. Liu, Y. Gao, T. Li, Y. Wang, Z. Chen, and X. Zhang, “Vortex degeneracy lifting and Aharonov-Bohm-like interference in deformed photonic graphene,” Opt. Lett. 42(5), 915–918 (2017).
[Crossref] [PubMed]

Y. Zong, S. Xia, L. Tang, D. Song, Y. Hu, Y. Pei, J. Su, Y. Li, and Z. Chen, “Observation of localized flat-band states in Kagome photonic lattices,” Opt. Express 24(8), 8877–8885 (2016).
[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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, and M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111(10), 103901 (2013).
[Crossref] [PubMed]

Chiang, T.-C.

Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, “Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light,” Phys. Rev. Lett. 107(16), 166803 (2011).
[Crossref] [PubMed]

Christmann, G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007).
[Crossref] [PubMed]

Desyatnikov, A. S.

D. Leykam, B.-T. Omri, and A. S. Desyatnikov, “Pseudospin and nonlinear conical diffraction in Lieb lattices,” Phys. Rev. A 86(3), 031805 (2012).
[Crossref]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 497–500 (2007).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Esslinger, T.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483(7389), 302–305 (2012).
[Crossref] [PubMed]

Fefferman, C.

C. Fefferman and M. Weinstein, “Honeycomb lattice potentials and Dirac points,” J. Am. Math. Soc. 25(4), 1169–1220 (2012).
[Crossref]

Feng, X.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Flores-Desirena, B.

Freedman, B.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007).
[Crossref] [PubMed]

Gaididei, Y. B.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, “Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016609 (2002).
[Crossref] [PubMed]

Gallardo, D.

P. Zhang, D. Gallardo, S. Liu, Y. Gao, T. Li, Y. Wang, Z. Chen, and X. Zhang, “Vortex degeneracy lifting and Aharonov-Bohm-like interference in deformed photonic graphene,” Opt. Lett. 42(5), 915–918 (2017).
[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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Gallo, K.

F. Laurell, K. Gallo, and M. Manzo,“Two-dimensional domain engineering in LiNbO3 via a hybrid patterning technique,” Adv. Opt. Mater 1(3), 365–371 (2011).

Galopin, E.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Gao, T.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

Gao, Y.

Garanovich, I. L.

Geim, A. K.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Gibertini, M.

A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M. I. Katsnelson, A. Pinczuk, L. N. Pfeiffer, K. W. West, and V. Pellegrini, “Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice,” Science 332(6034), 1176–1179 (2011).
[Crossref] [PubMed]

M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L. N. Pfeiffer, and K. W. West, “A. Singha, V. Pellegrini, M. Polini, G. Vignale, and A. Pinczuk, “Engineering artificial graphene in a two-dimensional electron gas,” Phys. Rev. B 79(24), 241406 (2009).
[Crossref]

Gomes, K. K.

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

Greif, D.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483(7389), 302–305 (2012).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Guinea, F.

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, “Artificial honeycomb lattices for electrons, atoms and photons,” Nat. Nanotechnol. 8(9), 625–633 (2013).
[Crossref] [PubMed]

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

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

Hatzopoulos, Z.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3(1), 1243 (2012).
[Crossref] [PubMed]

Hauke, P.

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Heinrich, M.

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

Hofstetter, W.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

Hu, X.

L. H. Wu and X. Hu, “Scheme to achieve silicon topological photonics,” Phys. Rev. Lett. 114, 223901 (2015).
[Crossref] [PubMed]

Hu, Y.

Huo, S. Y.

Jacqmin, T.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Jotzu, G.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483(7389), 302–305 (2012).
[Crossref] [PubMed]

Karmakar, B.

A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M. I. Katsnelson, A. Pinczuk, L. N. Pfeiffer, K. W. West, and V. Pellegrini, “Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice,” Science 332(6034), 1176–1179 (2011).
[Crossref] [PubMed]

Katsnelson, M. I.

A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M. I. Katsnelson, A. Pinczuk, L. N. Pfeiffer, K. W. West, and V. Pellegrini, “Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice,” Science 332(6034), 1176–1179 (2011).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Kevrekidis, P. G.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, “Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016609 (2002).
[Crossref] [PubMed]

Kivshar, Y. S.

Ko, W.

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

Krolikowski, W.

Laurell, F.

F. Laurell, K. Gallo, and M. Manzo,“Two-dimensional domain engineering in LiNbO3 via a hybrid patterning technique,” Adv. Opt. Mater 1(3), 365–371 (2011).

Lederer, F.

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 497–500 (2007).
[Crossref]

Lemaître, A.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

Lewenstein, M.

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, “Artificial honeycomb lattices for electrons, atoms and photons,” Nat. Nanotechnol. 8(9), 625–633 (2013).
[Crossref] [PubMed]

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Leykam, D.

D. Leykam, B.-T. Omri, and A. S. Desyatnikov, “Pseudospin and nonlinear conical diffraction in Lieb lattices,” Phys. Rev. A 86(3), 031805 (2012).
[Crossref]

Li, T.

Li, Y.

Liu, S.

P. Zhang, D. Gallardo, S. Liu, Y. Gao, T. Li, Y. Wang, Z. Chen, and X. Zhang, “Vortex degeneracy lifting and Aharonov-Bohm-like interference in deformed photonic graphene,” Opt. Lett. 42(5), 915–918 (2017).
[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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, “Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light,” Phys. Rev. Lett. 107(16), 166803 (2011).
[Crossref] [PubMed]

Louie, S. G.

C.-H. Park and S. G. Louie, “Making massless Dirac fermions from a patterned two-dimensional electron gas,” Nano Lett. 9(5), 1793–1797 (2009).
[Crossref] [PubMed]

Lumer, Y.

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

Lv, J.

Malkova, N.

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

Malomed, B. A.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, “Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 016609 (2002).
[Crossref] [PubMed]

Malpuech, G.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[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(10), 103901 (2007).
[Crossref] [PubMed]

Manoharan, H. C.

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, “Artificial honeycomb lattices for electrons, atoms and photons,” Nat. Nanotechnol. 8(9), 625–633 (2013).
[Crossref] [PubMed]

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

Manzo, M.

F. Laurell, K. Gallo, and M. Manzo,“Two-dimensional domain engineering in LiNbO3 via a hybrid patterning technique,” Adv. Opt. Mater 1(3), 365–371 (2011).

Mar, W.

K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, “Designer Dirac fermions and topological phases in molecular graphene,” Nature 483(7389), 306–310 (2012).
[Crossref] [PubMed]

Márquez-Islas, R.

Meineke, G.

P. Soltanpanahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nat. Phys. 7(5), 434–440 (2011).
[Crossref]

Messer, M.

T. Uehlinger, G. Jotzu, M. Messer, D. Greif, W. Hofstetter, U. Bissbort, and T. Esslinger, “Artificial graphene with tunable interactions,” Phys. Rev. Lett. 111(18), 185307 (2013).
[Crossref] [PubMed]

Miller, T.

Y. Liu, G. Bian, T. Miller, and T.-C. Chiang, “Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light,” Phys. Rev. Lett. 107(16), 166803 (2011).
[Crossref] [PubMed]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Neshev, D.

Nolte, S.

Y. Plotnik, M. C. Rechtsman, D. Song, M. Heinrich, J. M. Zeuner, S. Nolte, Y. Lumer, N. Malkova, J. Xu, A. Szameit, Z. Chen, and M. Segev, “Observation of unconventional edge states in ‘photonic graphene’,” Nat. Mater. 13(1), 57–62 (2014).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, A. Tünnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and Landau levels in photonic structures,” Nat. Photonics 7, 153–158 (2012).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 497–500 (2007).
[Crossref]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
[Crossref]

Novoselov, K. S.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).

Omri, B.-T.

D. Leykam, B.-T. Omri, and A. S. Desyatnikov, “Pseudospin and nonlinear conical diffraction in Lieb lattices,” Phys. Rev. A 86(3), 031805 (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. 6(1), 6272 (2015).
[Crossref] [PubMed]

Park, C.-H.

C.-H. Park and S. G. Louie, “Making massless Dirac fermions from a patterned two-dimensional electron gas,” Nano Lett. 9(5), 1793–1797 (2009).
[Crossref] [PubMed]

Pei, Y.

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

Pellegrini, V.

M. Polini, F. Guinea, M. Lewenstein, H. C. Manoharan, and V. Pellegrini, “Artificial honeycomb lattices for electrons, atoms and photons,” Nat. Nanotechnol. 8(9), 625–633 (2013).
[Crossref] [PubMed]

A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M. I. Katsnelson, A. Pinczuk, L. N. Pfeiffer, K. W. West, and V. Pellegrini, “Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice,” Science 332(6034), 1176–1179 (2011).
[Crossref] [PubMed]

M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L. N. Pfeiffer, and K. W. West, “A. Singha, V. Pellegrini, M. Polini, G. Vignale, and A. Pinczuk, “Engineering artificial graphene in a two-dimensional electron gas,” Phys. Rev. B 79(24), 241406 (2009).
[Crossref]

Peres, N. M. R.

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

Pérez-Rodríguez, F.

Pertsch, T.

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, “Light evolution in arbitrary two-dimensional waveguide arrays,” Phys. Rev. A 75(5), 497–500 (2007).
[Crossref]

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82(4), 507–512 (2006).
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Nature (4)

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Figures (7)

Fig. 1
Fig. 1 The experiment to measure the transmission and pseudospin in the OL and DL. L1-L8: convex lens; PBS: polarizing beam splitter; λ/2: half -wave plate; SLM: Spatial Light Modulator; M: Mask 1 and Mask 2; A1and A2: apertures.
Fig. 2
Fig. 2 The simulation results of structure images of photonic lattice OL and DL. (a)-(d) are the lattice light field distribution, phase image, light intensity distribution in three dimension (3D) and the lattice light field in frequency domain corresponding to the Dirac points in K-space for OL respectively. (e)-(f) are the similar simulation results for DL.
Fig. 3
Fig. 3 The experiment result of OL and DL induced in SBN.(a) and (c) are the photonic lattices, OL and DL, captured by CCD. (b) and (d) are the far-field diffraction patterns of OL and DL.
Fig. 4
Fig. 4 The numerical simulation of nonlinear light transmission in OL and DL. (a)-(c) and (d)-(f) are transmission results in OL and DL respectively.
Fig. 5
Fig. 5 The experimental nonlinear phenomena and the power spectrum corresponding to the transmission image. (a)-(c) are transmission results of OL. (d)-(f) are the similar results in DL.
Fig. 6
Fig. 6 The simulation results of speudospin in OL and DL. Fig (a)-(c) are probe beam, transmission image and interference pattern of lattice light and plane wave in OL. (d)-(f) are the simulations of DL.
Fig. 7
Fig. 7 The experiment results of pseudospin in OL and DL. (a)-(c) are probe beam, transmission image and interference pattern of lattice light and plane wave in OL. (d)-(f) are the simulations of DL.

Equations (5)

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i ψ z + ψ x 2 + ψ y 2 +Δn(x,y)ψ=0
ψ A = 0 n-1 e i( K A r+ ϕ A ) ψ B = 0 n-1 e i( K B r+ ϕ B )
K A =[cos( 2jπ n + π n )sinθ,sin( 2jπ n + π n )sinθ,cosθ] K B =[cos( 2jπ n π n )sinθ,sin( 2jπ n π n )sinθ,cosθ]
i z ψ A +( x iμ y ) ψ B =0 i z ψ B ( x +iμ y ) ψ A =0
J = L + S = R 2 [ i ψ A * φ ψ A i ψ B * φ ψ B + μ 2 ( | ψ A | 2 | ψ B | 2 ) ] dxdy

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