Abstract

At the Dirac-like point at the Brillouin zone center, the photonic crystals (PhCs) can mimic a zero-index medium. In the band structure, an additional flat band of longitudinal mode will intersect the Dirac cone. This longitudinal mode can be excited in PhCs with finite sizes at the Dirac-like point. By introducing positional shift in the PhCs, we study the dependence of the longitudinal mode on the disorder. At the Dirac-like point, the transmission peak induced by the longitudinal mode decreases as the random degree increases. However, at a frequency slightly above the Dirac-like point, in which the longitudinal mode is absent, the transmission is insensitive to the disorder because the effective index is still near zero and the effective wavelength in the PhC is very large.

© 2015 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
    [Crossref] [PubMed]
  4. 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]
  5. S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
    [Crossref]
  6. U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
    [Crossref]
  7. S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
    [Crossref]
  8. C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (2012).
    [Crossref]
  9. P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
    [Crossref]
  10. F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).
  11. F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).
  12. X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
    [Crossref]
  13. R. Zoli, M. Gnan, D. Castaldini, G. Bellanca, and P. Bassi, “Reformulation of the plane wave method to model photonic crystals,” Opt. Express 11(22), 2905–2910 (2003).
    [Crossref] [PubMed]
  14. M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
    [Crossref]
  15. 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]
  16. 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]
  17. R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
    [Crossref]

2014 (1)

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[Crossref]

2013 (4)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (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. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[Crossref] [PubMed]

2012 (3)

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]

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (2012).
[Crossref]

F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).

2011 (2)

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

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]

2010 (3)

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]

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

2007 (2)

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

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

2003 (1)

2002 (1)

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

Albert, J. P.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Barkhofen, S.

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
[Crossref]

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Bartal, G.

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

Bassi, P.

Bazaliy, Y. B.

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

Bellanca, G.

Bellec, M.

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
[Crossref]

Bittner, S.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

Briggs, D. P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Cassagne, D.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

Castaldini, D.

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]

F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (2012).
[Crossref]

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

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]

Chen, H.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Chen, X.

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]

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]

de Forges de Parny, L.

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Deng, F. S.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[Crossref]

Dietz, B.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

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]

Gnan, M.

Hang, Z. H.

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (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]

Hossain, T.

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Huang, X.

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (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]

Huang, X. Q.

F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

Jiang, H. T.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Kaliteevski, M. A.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

Kravchenko, I. I.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Kuhl, U.

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
[Crossref]

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Lai, Y.

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

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.

Li, Y. H.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Liu, F. M.

F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

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]

Martinez, J. M.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

Mei, J.

Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[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]

Miski-Oglu, M.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

Moitra, P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Mortessagne, F.

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
[Crossref]

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Oria Iriarte, P.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

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]

Richter, A.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

Schäfer, F.

S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

Segev, M.

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]

Sepkhanov, R. A.

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

Shi, Y. L.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Stöckmann, H.-J.

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Sun, Y.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Tudorovskiy, T.

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

Valentine, J.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Wang, X.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Wu, Y.

Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[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]

Yan, C.

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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]

Yang, Y.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Zandbergen, S. R.

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]

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).
[Crossref]

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).
[Crossref] [PubMed]

Zoli, R.

Adv. Optoelectron. (1)

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. Optoelectron. 2012, 313984 (2012).
[Crossref]

Appl. Phys. Lett. (1)

F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett. 100(7), 071911 (2012).

Europhys. Lett. (2)

X. Wang, H. T. Jiang, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals,” Europhys. Lett. 108(1), 14002 (2014).
[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. (1)

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]

Nat. Photonics (1)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Opt. Express (2)

Phys. Rev. A (1)

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

Phys. Rev. B (6)

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, P. Oria Iriarte, A. Richter, and F. Schäfer, “Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene,” Phys. Rev. B 82(1), 014301 (2010).
[Crossref]

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B 82(9), 094308 (2010).
[Crossref]

S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, “Disordered graphene and boron nitride in a microwave tight-binding analog,” Phys. Rev. B 87(3), 035101 (2013).
[Crossref]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B 66(11), 113101 (2002).
[Crossref]

F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0 in photonic crystals,” Phys. Rev. B 84(22), 224113 (2011).

Phys. Rev. Lett. (2)

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]

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]

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Figures (5)

Fig. 1
Fig. 1

(a) The band structure of a 2D PhC for the TE polarization. The rods have a relative permittivity 8.35, r=3 mm and a=13.36 mm . At the Γ point (see the inset), a Dirac-like point is formed at 13.24 GHz. (b) Three-dimensional surface plot of the band structure shown in (a) as a function of wave vectors in x and y directions. (c) The electric field patterns of the threefold degenerate modes near the Dirac-like point with a very small k along ΓX direction.

Fig. 2
Fig. 2

(a) A view of the experimental set-up which is used to measure the transmission. The top slab of the rectangular waveguide is not shown. (b) The amplified schematic diagram of the red dotted area in (a), showing how disorder is introduced in the PhCs.

Fig. 3
Fig. 3

(a) The simulated transmission spectra for different samples as the random degree δ increases from 0 to 0.088 with a step of 0.022. The dotted vertical line indicates the Dirac-like point. The gray bars indicate the regions of averaging used in (b). (b) The averaged transmissions versus δ when the frequencies are at 12.5 GHz (black squares), 13.17 GHz (red triangles) and 13.5 GHz (blue circles), respectively The error bars indicate the tolerance. The lines with different styles are guide to the eyes.

Fig. 4
Fig. 4

The electric field distribution after a beam goes through the perfect PhC at different frequencies. The entrance face is marked by a purple short line.

Fig. 5
Fig. 5

(a) The measured transmission spectra for different samples as the random degree δ increases from 0 to 0.088 with a step of 0.022. (b) The averaged transmissions versus δ when the frequencies are at 12.5, 13.21 (the Dirac-like point) and 13.5 GHz, respectively. The lines with different styles are guide to the eyes.

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