Abstract

We investigate all-optical switching at the guided mode resonances originating near the Dirac point of a finite, 2-D photonic crystal consisting of a square lattice of dielectric columns possessing a cubic nonlinearity. The peculiar field localization properties of these Dirac-point guided mode resonances conspire to yield extremely low switching threshold at near-to-normal incidence for remarkably low filling factors of the nonlinear material.

© 2013 OSA

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals,Molding the Flow of Light. (Princeton University, 1995).
  4. J. M. Lourtioz, H. Benisty, V. Berger, J.-M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, (Springer, 2005).
  5. A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).
  6. J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett.21(19), 1547–1549 (1996).
    [CrossRef] [PubMed]
  7. J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
    [CrossRef]
  8. S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
    [CrossRef]
  9. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
    [CrossRef] [PubMed]
  10. A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic processes of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
    [CrossRef]
  11. F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
    [CrossRef] [PubMed]
  12. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
    [CrossRef]
  13. R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75(6), 063813 (2007).
    [CrossRef]
  14. 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]
  15. M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
    [CrossRef]
  16. 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]
  17. K. Sakoda, “Double Dirac cones in triangular-lattice metamaterials,” Opt. Express20(9), 9925–9939 (2012).
    [CrossRef] [PubMed]
  18. G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
    [CrossRef]
  19. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A13(5), 1024–1035 (1996).
    [CrossRef]
  20. G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).
  21. P. Vicent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B2(7), 1106–1116 (1985).
    [CrossRef]
  22. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  23. V. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express15(15), 9205–9221 (2007).
    [CrossRef] [PubMed]
  24. V. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett.14(20), 1140–1142 (1989).
    [CrossRef] [PubMed]

2013

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

2012

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

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
[CrossRef]

2009

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

2008

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

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

2005

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

2003

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

2001

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

1996

1989

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

1985

Andrejco, M. J.

Atkin, D. M.

Baker, N. J.

Bazaliy, Ya. B.

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75(6), 063813 (2007).
[CrossRef]

Beenakker, C. W. J.

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75(6), 063813 (2007).
[CrossRef]

Bertolotti, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Birks, T. A.

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Bowden, C. M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Centini, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Chan, C. T.

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]

Choi, D. Y.

Conti, C.

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

D'Aguanno, G.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Delong, K. W.

Diem, M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Dumeige, Y.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Eggleton, B. J.

Fan, S. H.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

Finsterbusch, K.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Fu, L.

Geim, A. K.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Guinea, F.

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

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

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]

Haus, J. W.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

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]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Knight, J. C.

Kolodziejski, L. A.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

Koschny, T.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
[CrossRef]

Koster, A.

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]

Lamont, M. R. E.

Levenson, J. A.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Li, L.

Loncar, M.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

Luther-Davies, B.

Madden, S.

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

Mizrahi, V.

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Moss, D. J.

Neto, A. H.

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

Neviere, M.

Nguyen, H. C.

Novoselov, K. S.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Okamoto, K.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

Paraire, N.

Peres, N. M. R.

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

Petrich, G. S.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

Raghu, S.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

Reinisch, R.

Russell, P. S.

Saifi, M. A.

Sakoda, K.

Scalora, M.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Scherer, A.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

Sepkhanov, R. A.

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75(6), 063813 (2007).
[CrossRef]

Sibilia, C.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Soljacic, M.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

Soukoulis, C. M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
[CrossRef]

Stegeman, G. I.

Ta’eed, V.

Tandon, S. N.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

Vicent, P.

Vidakovic, P.

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

Vuckovic, J.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yoshie, T.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

Zhang, X.

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]

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]

J. Korean Phys. Soc.

A. Scherer, T. Yoshie, M. Loncar, J. Vuckovic, and K. Okamoto, “Photonic Crystal Nanocavities for Efficient Light Confinement and Emission,” J. Korean Phys. Soc.42, 768–773 (2003).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Mater.

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]

Nature

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photonics Nanostruct. Fundam. Appl.3(1), 10–18 (2005).
[CrossRef]

Phys. Rev. A

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

R. A. Sepkhanov, Ya. B. Bazaliy, and C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A75(6), 063813 (2007).
[CrossRef]

Phys. Rev. B

G. D’Aguanno, N. Mattiucci, C. Conti, and M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B87(8), 085135 (2013).
[CrossRef]

Phys. Rev. E

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E64, 16609 (2001).

Phys. Rev. Lett.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[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]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

Physica B

M. Diem, T. Koschny, and C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B405(14), 2990–2995 (2010).
[CrossRef]

Rev. Mod. Phys.

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

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals,Molding the Flow of Light. (Princeton University, 1995).

J. M. Lourtioz, H. Benisty, V. Berger, J.-M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, (Springer, 2005).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

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Figures (4)

Fig. 1
Fig. 1

Cross sectional view of a 2-D PC consisting of a square array (period a) of dielectric columns with radius r and relative permittivity ε. The structure possesses a finite number N of rows along the z-direction and a total length L = Na. We suppose that the columns are made of a nonlinear Kerr-type material with a generic cubic coefficient χ(3). A plane electromagnetic wave with the electric field parallel to the axis of the columns is incident on the structure with its k-vector in the (x,z) plane (in-plane coupling) forming an angle ϑ with respect to the z-direction.

Fig. 2
Fig. 2

(a) Transmittance in the (ω,kx) plane. (b) Magnification of the transmittance around the Dirac point. The dashed line indicates the calculated dispersion of the Dirac-point GMR. The structure’s parameters are: N = 5, r/a = 0.2, ε = 12.5.

Fig. 3
Fig. 3

Cross sectional view of the field localization in the stop-band at the Dirac-point GMR for ϑ = 0.1°. The dashed circles indicate the position of the columns.

Fig. 4
Fig. 4

(Left panel) Linear transmittance (red) and nonlinear transmittance (circles) with the onset of optical bistability for different incident angles along the Dirac-point GMR. The control parameter is σ = 2χ(3) Iin0c where Iin is the input intensity, ε0 the vacuum permittivity and c the speed of light in vacuo. The marks on the linear transmittance (triangle, circle, square) indicate the tuning conditions for the nonlinear calculations reported in the right panel. (Right panel) Nonlinear transmittance vs. input intensity for the incident angle reported in the left panel. Note the change in scale for the input intensity as the incident angle increases.

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