Abstract

We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of the lattice are obtained. By adopting the tight-binding approximation, we give an explanation of the asymmetry of Dirac cones. By utilizing the appropriate Bloch modes, linear and nonlinear asymmetric conical diffraction are demonstrated. We find that both the focusing and defocusing nonlinearities can enhance the asymmetry of the conical diffractions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

Corrections

Hua Zhong, Rong Wang, Milivoj R. Belić, Yanpeng Zhang, and Yiqi Zhang, "Asymmetric conical diffraction in dislocated edge-centered square lattices: erratum," Opt. Express 27, 24498-24498 (2019)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-27-17-24498

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References

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  32. X.-Y. Zhu, S. K. Gupta, X.-C. Sun, C. He, G.-X. Li, J.-H. Jiang, X.-P. Liu, M.-H. Lu, and Y.-F. Chen, “z2 topological edge state in honeycomb lattice of coupled resonant optical waveguides with a flat band,” Opt. Express 26, 24307–24317 (2018).
    [Crossref] [PubMed]
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    [Crossref]
  41. M. Trescher, B. Sbierski, P. W. Brouwer, and E. J. Bergholtz, “Quantum transport in Dirac materials: Signatures of tilted and anisotropic dirac and weyl cones,” Phys. Rev. B 91, 115135 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  46. 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, 57–62 (2014).
    [Crossref]
  47. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
    [Crossref] [PubMed]
  48. Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
    [Crossref]
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    [Crossref] [PubMed]

2018 (3)

C. Li, F. Ye, X. Chen, Y. V. Kartashov, A. Ferrando, L. Torner, and D. V. Skryabin, “Lieb polariton topological insulators,” Phys. Rev. B 97, 081103 (2018).
[Crossref]

X.-Y. Zhu, S. K. Gupta, X.-C. Sun, C. He, G.-X. Li, J.-H. Jiang, X.-P. Liu, M.-H. Lu, and Y.-F. Chen, “z2 topological edge state in honeycomb lattice of coupled resonant optical waveguides with a flat band,” Opt. Express 26, 24307–24317 (2018).
[Crossref] [PubMed]

C. R. Mann, T. J. Sturges, G. Weick, W. L. Barnes, and E. Mariani, “Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces,” Nat. Commun. 9, 2194 (2018).
[Crossref] [PubMed]

2017 (3)

G. G. Pyrialakos, N. S. Nye, N. V. Kantartzis, and D. N. Christodoulides, “Emergence of type-II Dirac points in graphynelike photonic lattices,” Phys. Rev. Lett. 119, 113901 (2017).
[Crossref] [PubMed]

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

D. R. Gulevich, D. Yudin, D. V. Skryabin, I. V. Iorsh, and I. A. Shelykh, “Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice,” Sci. Rep. 7, 1780 (2017).
[Crossref] [PubMed]

2016 (12)

M. Leder, C. Grossert, L. Sitta, M. Genske, A. Rosch, and M. Weitz, “Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice,” Nat. Commun. 7, 13112 (2016).
[Crossref] [PubMed]

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, 1435–1438 (2016).
[Crossref] [PubMed]

F. Diebel, D. Leykam, S. Kroesen, C. Denz, and A. S. Desyatnikov, “Conical diffraction and composite Lieb bosons in photonic lattices,” Phys. Rev. Lett. 116, 183902 (2016).
[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, 8877–8885 (2016).
[Crossref] [PubMed]

D. Leykam and Y. D. Chong, “Edge solitons in nonlinear-photonic topological insulators,” Phys. Rev. Lett. 117, 143901 (2016).
[Crossref] [PubMed]

Y. Lumer, M. C. Rechtsman, Y. Plotnik, and M. Segev, “Instability of bosonic topological edge states in the presence of interactions,” Phys. Rev. A 94, 021801 (2016).
[Crossref]

Y. V. Kartashov and D. V. Skryabin, “Modulational instability and solitary waves in polariton topological insulators,” Optica 3, 1228–1236 (2016).
[Crossref]

O. Bleu, D. D. Solnyshkov, and G. Malpuech, “Interacting quantum fluid in a polariton chern insulator,” Phys. Rev. B 93, 085438 (2016).
[Crossref]

C. He, X. Ni, H. Ge, X.-C. Sun, Y.-B. Chen, M.-H. Lu, X.-P. Liu, and Y.-F. Chen, “Acoustic topological insulator and robust one-way sound transport,” Nat. Phys. 12, 1124–1129 (2016).
[Crossref]

S. D. Huber, “Topological mechanics,” Nat. Phys. 12, 621–623 (2016).
[Crossref]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: fundamentals and applications,” Laser Photon. Rev. 10, 750–771 (2016).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

2015 (5)

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

M. Trescher, B. Sbierski, P. W. Brouwer, and E. J. Bergholtz, “Quantum transport in Dirac materials: Signatures of tilted and anisotropic dirac and weyl cones,” Phys. Rev. B 91, 115135 (2015).
[Crossref]

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, 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. Öhberg, 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]

Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, “Topological acoustics,” Phys. Rev. Lett. 114, 114301 (2015).
[Crossref] [PubMed]

2014 (5)

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realisation of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref] [PubMed]

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

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photon. 8, 821–829 (2014).
[Crossref]

M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma, “Linear and nonlinear traveling edge waves in optical honeycomb lattices,” Phys. Rev. A 90, 023813 (2014).
[Crossref]

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, 57–62 (2014).
[Crossref]

2013 (5)

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (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, 196–200 (2013).
[Crossref] [PubMed]

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin Hall effect in a quantum gas,” Nature 498, 201–204 (2013).
[Crossref] [PubMed]

C. J. Kennedy, G. A. Siviloglou, H. Miyake, W. C. Burton, and W. Ketterle, “Spin-orbit coupling and quantum spin Hall effect for neutral atoms without spin flips,” Phys. Rev. Lett. 111, 225301 (2013).
[Crossref] [PubMed]

Z. Liu, J. Wang, and J. Li, “Dirac cones in two-dimensional systems: from hexagonal to square lattices,” Phys. Chem. Chem. Phys. 15, 18855–18862 (2013).
[Crossref] [PubMed]

2012 (4)

Z. Lan, N. Goldman, and P. Öhberg, “Coexistence of spin-12 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice,” Phys. Rev. B 85, 155451 (2012).
[Crossref]

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

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

H. Ramezani, T. Kottos, V. Kovanis, and D. N. Christodoulides, “Exceptional-point dynamics in photonic honeycomb lattices with 𝒫𝒯 symmetry,” Phys. Rev. A 85, 013818 (2012).
[Crossref]

2011 (2)

M. J. Ablowitz and Y. Zhu, “Nonlinear diffraction in photonic graphene,” Opt. Lett. 36, 3762–3764 (2011).
[Crossref] [PubMed]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

2010 (1)

M. J. Ablowitz and Y. Zhu, “Evolution of Bloch-mode envelopes in two-dimensional generalized honeycomb lattices,” Phys. Rev. A 82, 013840 (2010).
[Crossref]

2009 (2)

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

M. J. Ablowitz, S. D. Nixon, and Y. Zhu, “Conical diffraction in honeycomb lattices,” Phys. Rev. A 79, 053830 (2009).
[Crossref]

2008 (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]

2007 (1)

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]

2005 (1)

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

2001 (1)

A. Ferrando and J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
[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. 6, 6272 (2015).
[Crossref] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma, “Linear and nonlinear traveling edge waves in optical honeycomb lattices,” Phys. Rev. A 90, 023813 (2014).
[Crossref]

M. J. Ablowitz and Y. Zhu, “Nonlinear diffraction in photonic graphene,” Opt. Lett. 36, 3762–3764 (2011).
[Crossref] [PubMed]

M. J. Ablowitz and Y. Zhu, “Evolution of Bloch-mode envelopes in two-dimensional generalized honeycomb lattices,” Phys. Rev. A 82, 013840 (2010).
[Crossref]

M. J. Ablowitz, S. D. Nixon, and Y. Zhu, “Conical diffraction in honeycomb lattices,” Phys. Rev. A 79, 053830 (2009).
[Crossref]

Amo, A.

M. Milićević, G. Montambaux, T. Ozawa, I. Sagnes, A. Lemaítre, L. Le Gratiet, A. Harouri, J. Bloch, and A. Amo, “Tilted and type-III Dirac cones emerging from flat bands in photonic orbital graphene,” arXiv1807.08650 (2018).

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” arXiv1802.04173 (2018).

Andersson, E.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, 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]

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]

Bahat-Treidel, O.

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

Barnes, W. L.

C. R. Mann, T. J. Sturges, G. Weick, W. L. Barnes, and E. Mariani, “Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces,” Nat. Commun. 9, 2194 (2018).
[Crossref] [PubMed]

Bartal, G.

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C. Li, F. Ye, X. Chen, Y. V. Kartashov, A. Ferrando, L. Torner, and D. V. Skryabin, “Lieb polariton topological insulators,” Phys. Rev. B 97, 081103 (2018).
[Crossref]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Trescher, M.

M. Trescher, B. Sbierski, P. W. Brouwer, and E. J. Bergholtz, “Quantum transport in Dirac materials: Signatures of tilted and anisotropic dirac and weyl cones,” Phys. Rev. B 91, 115135 (2015).
[Crossref]

Turpin, A.

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: fundamentals and applications,” Laser Photon. Rev. 10, 750–771 (2016).
[Crossref]

Uehlinger, T.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realisation of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref] [PubMed]

Vicencio, R. A.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, 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. Mejía-Cortés, “Diffraction-free image transmission in kagome photonic lattices,” J. Opt. 16, 015706 (2014).
[Crossref]

Wang, J.

Z. Liu, J. Wang, and J. Li, “Dirac cones in two-dimensional systems: from hexagonal to square lattices,” Phys. Chem. Chem. Phys. 15, 18855–18862 (2013).
[Crossref] [PubMed]

Weick, G.

C. R. Mann, T. J. Sturges, G. Weick, W. L. Barnes, and E. Mariani, “Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces,” Nat. Commun. 9, 2194 (2018).
[Crossref] [PubMed]

Weimann, S.

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

Weitz, M.

M. Leder, C. Grossert, L. Sitta, M. Genske, A. Rosch, and M. Weitz, “Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice,” Nat. Commun. 7, 13112 (2016).
[Crossref] [PubMed]

Williams, R. A.

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin Hall effect in a quantum gas,” Nature 498, 201–204 (2013).
[Crossref] [PubMed]

Windpassinger, P.

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
[Crossref] [PubMed]

Xia, S.

Xiao, M.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

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. 6, 6272 (2015).
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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, 57–62 (2014).
[Crossref]

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Xu, N. K. Efremidis, and Z. Chen, “Asymmetric conical diffraction and generation of non-integer phase singularities in photonic graphene,” in CLEO: 2015 (Optical Society of America, 2015), p. FTh3D.6.

Yang, Z.

Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, “Topological acoustics,” Phys. Rev. Lett. 114, 114301 (2015).
[Crossref] [PubMed]

Ye, F.

C. Li, F. Ye, X. Chen, Y. V. Kartashov, A. Ferrando, L. Torner, and D. V. Skryabin, “Lieb polariton topological insulators,” Phys. Rev. B 97, 081103 (2018).
[Crossref]

Yudin, D.

D. R. Gulevich, D. Yudin, D. V. Skryabin, I. V. Iorsh, and I. A. Shelykh, “Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice,” Sci. Rep. 7, 1780 (2017).
[Crossref] [PubMed]

Zeuner, J. 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, 57–62 (2014).
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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, 196–200 (2013).
[Crossref] [PubMed]

Zhang, B.

Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, “Topological acoustics,” Phys. Rev. Lett. 114, 114301 (2015).
[Crossref] [PubMed]

Zhang, D.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Zhang, Y. P.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

Zhang, Y. Q.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

Zhong, H.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

Zhong, W. P.

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

Zhu, X.-Y.

Zhu, Y.

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
[Crossref]

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (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. 6, 6272 (2015).
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M. J. Ablowitz and Y. Zhu, “Nonlinear diffraction in photonic graphene,” Opt. Lett. 36, 3762–3764 (2011).
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M. J. Ablowitz and Y. Zhu, “Evolution of Bloch-mode envelopes in two-dimensional generalized honeycomb lattices,” Phys. Rev. A 82, 013840 (2010).
[Crossref]

M. J. Ablowitz, S. D. Nixon, and Y. Zhu, “Conical diffraction in honeycomb lattices,” Phys. Rev. A 79, 053830 (2009).
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Zilberberg, O.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” arXiv1802.04173 (2018).

Zong, Y.

Ann. Phys. (Berlin) (1)

H. Zhong, Y. Q. Zhang, Y. Zhu, D. Zhang, C. B. Li, Y. P. Zhang, F. L. Li, M. R. Belić, and M. Xiao, “Transport properties in the photonic super-honeycomb lattice – a hybrid fermionic and bosonic system,” Ann. Phys. (Berlin) 529, 1600258 (2017).
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Appl. Phys. Lett. (1)

A. Ferrando and J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
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J. Opt. (1)

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

Laser Photon. Rev. (3)

Y. Q. Zhang, H. Zhong, M. R. Belić, Y. Zhu, W. P. Zhong, Y. P. Zhang, D. N. Christodoulides, and M. Xiao, “𝒫𝒯 symmetry in a fractional Schrödinger equation,” Laser Photon. Rev. 10, 526–531 (2016).
[Crossref]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: fundamentals and applications,” Laser Photon. Rev. 10, 750–771 (2016).
[Crossref]

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

M. Leder, C. Grossert, L. Sitta, M. Genske, A. Rosch, and M. Weitz, “Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice,” Nat. Commun. 7, 13112 (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, 6272 (2015).
[Crossref] [PubMed]

C. R. Mann, T. J. Sturges, G. Weick, W. L. Barnes, and E. Mariani, “Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces,” Nat. Commun. 9, 2194 (2018).
[Crossref] [PubMed]

Nat. Mater. (1)

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, 57–62 (2014).
[Crossref]

Nat. Photon. (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photon. 8, 821–829 (2014).
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Nat. Phys. (2)

C. He, X. Ni, H. Ge, X.-C. Sun, Y.-B. Chen, M.-H. Lu, X.-P. Liu, and Y.-F. Chen, “Acoustic topological insulator and robust one-way sound transport,” Nat. Phys. 12, 1124–1129 (2016).
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S. D. Huber, “Topological mechanics,” Nat. Phys. 12, 621–623 (2016).
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Nature (3)

M. C. Beeler, R. A. Williams, K. Jiménez-García, L. J. LeBlanc, A. R. Perry, and I. B. Spielman, “The spin Hall effect in a quantum gas,” Nature 498, 201–204 (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, 196–200 (2013).
[Crossref] [PubMed]

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realisation of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Optica (1)

Phys. Chem. Chem. Phys. (1)

Z. Liu, J. Wang, and J. Li, “Dirac cones in two-dimensional systems: from hexagonal to square lattices,” Phys. Chem. Chem. Phys. 15, 18855–18862 (2013).
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Phys. Rep. (2)

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).
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Phys. Rev. A (6)

M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma, “Linear and nonlinear traveling edge waves in optical honeycomb lattices,” Phys. Rev. A 90, 023813 (2014).
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Y. Lumer, M. C. Rechtsman, Y. Plotnik, and M. Segev, “Instability of bosonic topological edge states in the presence of interactions,” Phys. Rev. A 94, 021801 (2016).
[Crossref]

M. J. Ablowitz, S. D. Nixon, and Y. Zhu, “Conical diffraction in honeycomb lattices,” Phys. Rev. A 79, 053830 (2009).
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H. Ramezani, T. Kottos, V. Kovanis, and D. N. Christodoulides, “Exceptional-point dynamics in photonic honeycomb lattices with 𝒫𝒯 symmetry,” Phys. Rev. A 85, 013818 (2012).
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M. J. Ablowitz and Y. Zhu, “Evolution of Bloch-mode envelopes in two-dimensional generalized honeycomb lattices,” Phys. Rev. A 82, 013840 (2010).
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D. Leykam, O. Bahat-Treidel, and A. S. Desyatnikov, “Pseudospin and nonlinear conical diffraction in Lieb lattices,” Phys. Rev. A 86, 031805 (2012).
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Phys. Rev. B (4)

Z. Lan, N. Goldman, and P. Öhberg, “Coexistence of spin-12 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice,” Phys. Rev. B 85, 155451 (2012).
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C. Li, F. Ye, X. Chen, Y. V. Kartashov, A. Ferrando, L. Torner, and D. V. Skryabin, “Lieb polariton topological insulators,” Phys. Rev. B 97, 081103 (2018).
[Crossref]

M. Trescher, B. Sbierski, P. W. Brouwer, and E. J. Bergholtz, “Quantum transport in Dirac materials: Signatures of tilted and anisotropic dirac and weyl cones,” Phys. Rev. B 91, 115135 (2015).
[Crossref]

O. Bleu, D. D. Solnyshkov, and G. Malpuech, “Interacting quantum fluid in a polariton chern insulator,” Phys. Rev. B 93, 085438 (2016).
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Phys. Rev. Lett. (9)

D. Leykam and Y. D. Chong, “Edge solitons in nonlinear-photonic topological insulators,” Phys. Rev. Lett. 117, 143901 (2016).
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Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, “Topological acoustics,” Phys. Rev. Lett. 114, 114301 (2015).
[Crossref] [PubMed]

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
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D. R. Gulevich, D. Yudin, D. V. Skryabin, I. V. Iorsh, and I. A. Shelykh, “Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice,” Sci. Rep. 7, 1780 (2017).
[Crossref] [PubMed]

Other (3)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” arXiv1802.04173 (2018).

M. Milićević, G. Montambaux, T. Ozawa, I. Sagnes, A. Lemaítre, L. Le Gratiet, A. Harouri, J. Bloch, and A. Amo, “Tilted and type-III Dirac cones emerging from flat bands in photonic orbital graphene,” arXiv1807.08650 (2018).

D. Song, S. Liu, V. Paltoglou, D. Gallardo, L. Tang, J. Xu, N. K. Efremidis, and Z. Chen, “Asymmetric conical diffraction and generation of non-integer phase singularities in photonic graphene,” in CLEO: 2015 (Optical Society of America, 2015), p. FTh3D.6.

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Figures (7)

Fig. 1
Fig. 1 (a) Dislocated edge-centered square lattice. (b) Far-field diffraction pattern of the lattice. The dashed hexagon is the first Brillouin zone. (c) Band structure of the lattice. The right four panels are the top-views of the four bands.
Fig. 2
Fig. 2 (a) Band structure of the lattice strained with flat boundaries along x direction and periodic along y direction. (b) and (c) Same as (a) but with short-bearded boundaries and long-bearded boundaries along x direction. The corresponding lattices are shown above the band structure. The states below the band structures correspond to the edge and cone states marked with different labels in (c). The lattices and states are shown in the window −38 ≤ x ≤ 38 and −4dy ≤ 4d.
Fig. 3
Fig. 3 (a) Conical diffraction of the state marked with a blue dot in Fig. 2(c) superposed by a Gaussian, at selected propagation distances. (b) Same as (a), but the state is that below the blue dot in Fig. 2(c). (c) Same as (a), but with both the states used in (a) and (b) being excited. (d) Conical diffraction of the state above the green dot in Fig. 2(c). (e) Same as (d), but the state is marked by the green dot in in Fig. 2(c). (f) Same as (d), but with both states used in (d) and (e) being excited. The panels are shown in the window −90 ≤ x ≤ 90 and −90 ≤ y ≤ 90.
Fig. 4
Fig. 4 Figure setup is as Fig. 3, but for the states marked with triangles in Fig. 2.
Fig. 5
Fig. 5 Figure setup is as Fig. 3, but for the states marked with squares in Fig. 2.
Fig. 6
Fig. 6 Three-dimensional formation process of the asymmetric conical diffraction. (a1) and (a2) correspond to Figs. 3(c3) and 3(f3); (b1) and (b2) correspond to Figs. 4(c3) and 4(f3); (c1) and (c2) correspond to Figs. 5(c3) and 5(f3). The visual angles for these panels are the same.
Fig. 7
Fig. 7 Nonlinear conical diffraction. (a1), (c1), (e1) The focusing case g = 1, corresponding to Figs. 3(c3), 4(c3), and 5(c3). (b1), (d1), (f1) The defocusing case g = −1, corresponding to Figs. 3(f3), 4(f3), and 5(f3). The input beam power in (a1) and (b1) is 8.9, in (c1) and (d1) the beam power is 10.7, in (e1) the beam power is 10.0, and in (f1) the beam power is 13.3. (a2)–(f2) The three-dimensional picture of the nonlinear asymmetric conical diffraction, corresponding to (a1)–(f1).

Equations (4)

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i ψ ( x , y , z ) z = 1 2 ( 2 x 2 + 2 y 2 ) ψ ( x , y , z ) + R ( x , y ) ψ ( x , y , z ) + g | ψ ( x , y , z ) | 2 ψ ( x , y , z ) ,
i ψ ( X , Y , Z ) Z = 5 18 ( 5 2 X 2 + 5 2 Y 2 8 2 X Y ) ψ ( X , Y , Z ) + R ( X , Y ) ψ ( X , Y , Z ) .
= [ 0 exp ( i k e 1 ) 0 2 cos ( i k e 2 ) exp ( i k e 1 ) 0 exp ( i k e 1 ) 0 0 exp ( i k e 1 ) 0 exp ( i k e 1 ) 2 cos ( i k e 2 ) 0 exp ( i k e 1 ) 0 ] ,
β = 2 + 6 4 a p y + 2 4 a 9 p x 2 + 6 p y 2 ,

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