Abstract

Valley-dependent propagation of light in an artificial photonic hexagonal lattice, akin to electrons in graphene, is investigated in microwave regime. Both numerical and experimental results show that the valley degeneracy in the photonic graphene is broken when the frequency is away from the Dirac point. The peculiar anisotropic wave transport property due to distinct valleys is analyzed using the equifrequency contours. More interestingly, the valley-dependent self-collimation and beam splitting phenomena are experimentally demonstrated with the armchair and zigzag interfaces, respectively. Our results confirm that there are two inequivalent Dirac points that lead to two distinct valleys in photonic graphene, which could be used to control the flow of light and might be used to carry information in valley polarized beam splitter, collimator or guiding device.

© 2014 Optical Society of America

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References

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  1. S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
    [Crossref] [PubMed]
  2. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  3. A. H. Castro Neto, 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]
  4. A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
    [Crossref]
  5. D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
    [Crossref] [PubMed]
  6. J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
    [Crossref] [PubMed]
  7. Z. Wang and F. Liu, “Manipulation of electron beam propagation by hetero-dimensional graphene junctions,” ACS Nano 4(4), 2459–2465 (2010).
    [Crossref] [PubMed]
  8. F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
    [Crossref]
  9. Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
    [Crossref] [PubMed]
  10. D. Gunlycke and C. T. White, “Graphene valley filter using a line defect,” Phys. Rev. Lett. 106(13), 136806 (2011).
    [Crossref] [PubMed]
  11. F. Zhai and K. Chang, “Valley filtering in graphene with a Dirac gap,” Phys. Rev. B 85(15), 155415 (2012).
    [Crossref]
  12. K. Behnia, “Condensed-matter physics: polarized light boosts valleytronics,” Nat. Nanotechnol. 7(8), 488–489 (2012).
    [Crossref] [PubMed]
  13. H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
    [Crossref] [PubMed]
  14. K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
    [Crossref] [PubMed]
  15. X. Zhang, “Demonstration of a new transport regime of photon in two-dimensional photonic crystal,” Phys. Lett. A 372(19), 3512–3516 (2008).
    [Crossref]
  16. R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
    [Crossref]
  17. M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
    [Crossref]
  18. S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
    [Crossref] [PubMed]
  19. S. Raghu and F. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).
  20. S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
    [Crossref]
  21. 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 (2013).
    [Crossref] [PubMed]
  22. 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]
  23. J. M. Zeuner, M. C. Rechtsman, S. Nolte, and A. Szameit, “Edge states in disordered photonic graphene,” Opt. Lett. 39(3), 602–605 (2014).
    [Crossref] [PubMed]
  24. X. Zhang, “Observing zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
    [Crossref] [PubMed]
  25. Q. Liang, Y. Yan, and J. Dong, “Zitterbewegung in the honeycomb photonic lattice,” Opt. Lett. 36(13), 2513–2515 (2011).
    [Crossref] [PubMed]
  26. O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
    [Crossref] [PubMed]
  27. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y. S. Kivshar, “Polychromatic dynamic localization in curved photonic lattices,” Nat. Phys. 5(4), 271–275 (2009).
    [Crossref]
  28. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
    [Crossref] [PubMed]
  29. A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
    [Crossref]
  30. R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
    [Crossref]
  31. X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
    [Crossref]
  32. J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
    [Crossref]
  33. X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
    [Crossref] [PubMed]
  34. Y. Luo, W. Zhang, Y. Huang, J. Zhao, and J. Peng, “Wide-angle beam splitting by use of positive-negative refraction in photonic crystals,” Opt. Lett. 29(24), 2920–2922 (2004).
    [Crossref] [PubMed]
  35. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
    [Crossref] [PubMed]
  36. X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
    [Crossref]

2014 (1)

2013 (4)

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[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(1), 57–62 (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]

2012 (6)

F. Zhai and K. Chang, “Valley filtering in graphene with a Dirac gap,” Phys. Rev. B 85(15), 155415 (2012).
[Crossref]

K. Behnia, “Condensed-matter physics: polarized light boosts valleytronics,” Nat. Nanotechnol. 7(8), 488–489 (2012).
[Crossref] [PubMed]

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
[Crossref] [PubMed]

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

2011 (5)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Q. Liang, Y. Yan, and J. Dong, “Zitterbewegung in the honeycomb photonic lattice,” Opt. Lett. 36(13), 2513–2515 (2011).
[Crossref] [PubMed]

F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
[Crossref]

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

D. Gunlycke and C. T. White, “Graphene valley filter using a line defect,” Phys. Rev. Lett. 106(13), 136806 (2011).
[Crossref] [PubMed]

2010 (5)

Z. Wang and F. Liu, “Manipulation of electron beam propagation by hetero-dimensional graphene junctions,” ACS Nano 4(4), 2459–2465 (2010).
[Crossref] [PubMed]

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[Crossref]

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

2009 (3)

R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
[Crossref]

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

A. H. Castro Neto, 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]

2008 (4)

J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
[Crossref] [PubMed]

X. Zhang, “Demonstration of a new transport regime of photon in two-dimensional photonic crystal,” Phys. Lett. A 372(19), 3512–3516 (2008).
[Crossref]

S. Raghu and F. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

X. Zhang, “Observing zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[Crossref] [PubMed]

2007 (4)

R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[Crossref]

A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
[Crossref]

D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

2006 (1)

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

2004 (2)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Y. Luo, W. Zhang, Y. Huang, J. Zhao, and J. Peng, “Wide-angle beam splitting by use of positive-negative refraction in photonic crystals,” Opt. Lett. 29(24), 2920–2922 (2004).
[Crossref] [PubMed]

2003 (1)

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[Crossref]

Bahat-Treidel, O.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Bazaliy, Y.

R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[Crossref]

Beenakker, C.

R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[Crossref]

Beenakker, C. W. J.

R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
[Crossref]

A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
[Crossref]

Behnia, K.

K. Behnia, “Condensed-matter physics: polarized light boosts valleytronics,” Nat. Nanotechnol. 7(8), 488–489 (2012).
[Crossref] [PubMed]

Bittner, S.

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

Castro Neto, A. H.

A. H. Castro Neto, 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]

Chan, C. T.

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Chang, K.

F. Zhai and K. Chang, “Valley filtering in graphene with a Dirac gap,” Phys. Rev. B 85(15), 155415 (2012).
[Crossref]

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
[Crossref]

Chen, H.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Chen, Z.

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 (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]

Corrielli, G.

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

Cortijo, A.

J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
[Crossref] [PubMed]

Crespi, A.

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

Cui, X.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
[Crossref] [PubMed]

Dai, J.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
[Crossref] [PubMed]

de Dood, M. J. A.

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
[Crossref] [PubMed]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Diem, M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[Crossref]

Dietz, B.

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

Dikin, D. A.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Dommett, G. H.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Dong, J.

Dreisow, F.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Fan, S.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[Crossref]

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Garcia-Pomar, J. L.

J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
[Crossref] [PubMed]

Geim, A. K.

A. H. Castro Neto, 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]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Grobman, M.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Gunlycke, D.

D. Gunlycke and C. T. White, “Graphene valley filter using a line defect,” Phys. Rev. Lett. 106(13), 136806 (2011).
[Crossref] [PubMed]

Haldane, F.

S. Raghu and F. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

He, K.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

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 (2013).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Heinz, T. F.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Huang, Y.

Jiang, H. T.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Kivshar, Y. S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Kohlhaas, K. M.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Koschny, T.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[Crossref]

Lai, Y.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref] [PubMed]

Li, Y. H.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Liang, Q.

Liu, F.

Z. Wang and F. Liu, “Manipulation of electron beam propagation by hetero-dimensional graphene junctions,” ACS Nano 4(4), 2459–2465 (2010).
[Crossref] [PubMed]

Longhi, S.

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[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 (2013).
[Crossref] [PubMed]

Luo, Y.

Ma, Y.

F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
[Crossref]

Mak, K. F.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

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 (2013).
[Crossref] [PubMed]

Mei, J.

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Miski-Oglu, M.

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

Nguyen, S. T.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
[Crossref] [PubMed]

Niu, Q.

D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
[Crossref] [PubMed]

Nolte, S.

J. M. Zeuner, M. C. Rechtsman, S. Nolte, and A. Szameit, “Edge states in disordered photonic graphene,” Opt. Lett. 39(3), 602–605 (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 (2013).
[Crossref] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Novoselov, K. S.

A. H. Castro Neto, 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]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Osellame, R.

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

Ossipov, A.

R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
[Crossref]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Peeters, F. M.

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

Peleg, O.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Peng, J.

Pereg-Barnea, T.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, 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]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Piner, R. D.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Plotnik, Y.

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]

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 (2013).
[Crossref] [PubMed]

Raghu, S.

S. Raghu and F. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

Rechtsman, M. C.

J. M. Zeuner, M. C. Rechtsman, S. Nolte, and A. Szameit, “Edge states in disordered photonic graphene,” Opt. Lett. 39(3), 602–605 (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 (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]

Richter, A.

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

Ruoff, R. S.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Rycerz, A.

A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
[Crossref]

Segev, M.

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]

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 (2013).
[Crossref] [PubMed]

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Sepkhanov, R.

R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[Crossref]

Sepkhanov, R. A.

R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
[Crossref]

Shan, J.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

Shapira, N.

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
[Crossref] [PubMed]

Shi, Y. L.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Song, D.

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 (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]

Soukoulis, C. M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[Crossref]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Stach, E. A.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Stankovich, S.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Sukhorukov, A. A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Sun, Y.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Szameit, A.

J. M. Zeuner, M. C. Rechtsman, S. Nolte, and A. Szameit, “Edge states in disordered photonic graphene,” Opt. Lett. 39(3), 602–605 (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 (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]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Tünnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

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

Tworzydlo, J.

A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
[Crossref]

Valle, G. D.

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Wang, X.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Wang, Z.

Z. Wang and F. Liu, “Manipulation of electron beam propagation by hetero-dimensional graphene junctions,” ACS Nano 4(4), 2459–2465 (2010).
[Crossref] [PubMed]

White, C. T.

D. Gunlycke and C. T. White, “Graphene valley filter using a line defect,” Phys. Rev. Lett. 106(13), 136806 (2011).
[Crossref] [PubMed]

Wu, Y.

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Wu, Z.

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

Xiao, D.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
[Crossref] [PubMed]

D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
[Crossref] [PubMed]

Xu, H. Q.

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

Xu, J.

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Yan, C.

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
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Yan, Y.

Yao, W.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
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D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
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Yu, X.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
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S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
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Zeng, H.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
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Zeuner, J. M.

J. M. Zeuner, M. C. Rechtsman, S. Nolte, and A. Szameit, “Edge states in disordered photonic graphene,” Opt. Lett. 39(3), 602–605 (2014).
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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(1), 57–62 (2013).
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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]

Zhai, F.

F. Zhai and K. Chang, “Valley filtering in graphene with a Dirac gap,” Phys. Rev. B 85(15), 155415 (2012).
[Crossref]

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
[Crossref]

Zhang, W.

Zhang, X.

X. Zhang, “Demonstration of a new transport regime of photon in two-dimensional photonic crystal,” Phys. Lett. A 372(19), 3512–3516 (2008).
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X. Zhang, “Observing zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[Crossref] [PubMed]

Zhang, Z.-Q.

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
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Zhao, J.

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
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Zimney, E. J.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
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ACS Nano (1)

Z. Wang and F. Liu, “Manipulation of electron beam propagation by hetero-dimensional graphene junctions,” ACS Nano 4(4), 2459–2465 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83(16), 3251–3253 (2003).
[Crossref]

Europhys. Lett. (2)

R. A. Sepkhanov, A. Ossipov, and C. W. J. Beenakker, “Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum,” Europhys. Lett. 85(1), 14005 (2009).
[Crossref]

X. Wang, H. T. Jiang, C. Yan, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Anomalous transmission of disordered photonic graphenes at the Dirac point,” Europhys. Lett. 103(1), 17003 (2013).
[Crossref]

Nat. Mater. (3)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[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 (2013).
[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nat. Nanotechnol. (3)

K. Behnia, “Condensed-matter physics: polarized light boosts valleytronics,” Nat. Nanotechnol. 7(8), 488–489 (2012).
[Crossref] [PubMed]

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7(8), 490–493 (2012).
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K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7(8), 494–498 (2012).
[Crossref] [PubMed]

Nat. Phys. (2)

A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nat. Phys. 3(3), 172–175 (2007).
[Crossref]

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

Nature (1)

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

New J. Phys. (2)

F. Zhai, Y. Ma, and K. Chang, “Valley beam splitter based on strained graphene,” New J. Phys. 13(8), 083029 (2011).
[Crossref]

A. Crespi, G. Corrielli, G. D. Valle, R. Osellame, and S. Longhi, “Dynamic band collapse in photonic graphene,” New J. Phys. 15(1), 013012 (2013).
[Crossref]

Opt. Lett. (3)

Phys. Lett. A (1)

X. Zhang, “Demonstration of a new transport regime of photon in two-dimensional photonic crystal,” Phys. Lett. A 372(19), 3512–3516 (2008).
[Crossref]

Phys. Rev. A (2)

R. Sepkhanov, Y. Bazaliy, and C. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[Crossref]

S. Raghu and F. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

Phys. Rev. B (3)

S. Bittner, B. Dietz, M. Miski-Oglu, and A. Richter, “Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard,” Phys. Rev. B 85(6), 064301 (2012).
[Crossref]

F. Zhai and K. Chang, “Valley filtering in graphene with a Dirac gap,” Phys. Rev. B 85(15), 155415 (2012).
[Crossref]

J. Mei, Y. Wu, C. T. Chan, and Z.-Q. Zhang, “First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Phys. Rev. Lett. (10)

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104(4), 043903 (2010).
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P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

X. Zhang, “Observing zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[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]

O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, “Klein tunneling in deformed honeycomb lattices,” Phys. Rev. Lett. 104(6), 063901 (2010).
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A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, and Y. S. Kivshar, “Observation of two-dimensional dynamic localization of light,” Phys. Rev. Lett. 104(22), 223903 (2010).
[Crossref] [PubMed]

Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, “Valley-dependent brewster angles and goos-hänchen effect in strained graphene,” Phys. Rev. Lett. 106(17), 176802 (2011).
[Crossref] [PubMed]

D. Gunlycke and C. T. White, “Graphene valley filter using a line defect,” Phys. Rev. Lett. 106(13), 136806 (2011).
[Crossref] [PubMed]

D. Xiao, W. Yao, and Q. Niu, “Valley-contrasting physics in graphene: magnetic moment and topological transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
[Crossref] [PubMed]

J. L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, “Fully valley-polarized electron beams in graphene,” Phys. Rev. Lett. 100(23), 236801 (2008).
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Physica B (1)

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
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Rev. Mod. Phys. (1)

A. H. Castro Neto, 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]

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Figures (6)

Fig. 1
Fig. 1 (a) Band structures for TE modes in PG with honeycomb lattace. Inset: Brillouin zone and the EFCs at normalized frequency of 0.36 (labeled with the horizontal dashed line). (b) Scheme of valley-dependent wave transport behavior: the blue triangles are the EFCs for the PG at normalized frequency of 0.36. These triangles encircles K or K' points. The blue semicircles are parts of the EFCs for free space at same frequency. The thin gray lines represent the conservation of the parallel wave vector, and the green and the red arrows in the triangles represent the directions of energy flow coming from the K and K' valley, respectively. For the zigzag interface, the refractions in the two valleys have different orientations. For the armchair interface, the beam associated to one of the valleys is fully self-collimated and the beam belonging to the other valley splits into three beams. The energy flows are also indicated with the arrows with different thickness and color in PG structure.
Fig. 2
Fig. 2 (a) Photograph of one PG sample in waveguide chamber. The width of incident beam is controlled by absorbing material. The cylindrical metal defects act as scatterers to monitor valley-dependent beam indirectly. Inset is the enlarged view of part of the honeycomb lattice structure where metal defects are inserted. (b) Waveguide chamber and field probe used in experiments.
Fig. 3
Fig. 3 Beam self-collimation in PG without metal defects. (a)Simulated electric field distribution of PG with armchair interface. Outgoing region is encircled by the red dashed lines; (b) Top: Measured electric field distribution in the outgoing region; Bottom: Comparation of simulated and experimental normalized profiles of electric field distribution along waveguide edge.
Fig. 4
Fig. 4 Beam splitting in PG without metal defects. (a) Simulated electric field distribution of PG with zigzag interface; (b) Top: Measured electric field distribution in the outgoing region, which is encircled by the red dashed lines in Fig. 4(a); Bottom: Comparation of simulated and experimental normalized profiles of electric field distribution along waveguide edge. Inset is the PG model with zigzag interface, in which the middle one of the first row of alumina rods is removed, as indicated by the black arrow).
Fig. 5
Fig. 5 Measured profiles of electric field distribution along waveguide edge (top) and simulated electric field distributions in PGs with armchair interface, with metal defects embedded in three different positions (bottom). The waveguide edge is indicated by the red dashed line. (a) Metal defects are embedded into positions accurately on the path of beam; (b) Metal defects are embedded into positions away from the beam path; (c) Metal defects are embedded into positions a little offset from the beam path.
Fig. 6
Fig. 6 Measured profiles of electric field distribution along waveguide edge (top) and simulated electric field distributions in PG with zigzag interface. The waveguide edge is indicated by the red dashed line. Six different defects are applied, respectively. (a) Metal defects are inserted in the right path of the splitting beams in close to the top edge of PG; (b) Metal defects are inserted in the right path of the splitting beams in close to the middle of PG; (c) Metal defects are inserted in the left path of the splitting beams in close to the bottom edge of PG; (d) Metal defects are inserted in a position outside of the paths of splitting beams at the left part of PG; (e) Metal defects are inserted in a position between the paths of the splitting beams; (f) Most of the alumina rods between the splitting beams are removed.

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