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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 7699–7711

Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals

Yan Li, Ying Wu, Xi Chen, and Jun Mei  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 7699-7711 (2013)
http://dx.doi.org/10.1364/OE.21.007699


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Abstract

We developed a selection rule for Dirac-like points in two-dimensional dielectric photonic crystals. The rule is derived from a perturbation theory and states that a non-zero, mode-coupling integral between the degenerate Bloch states guarantees a Dirac-like point, regardless of the type of the degeneracy. In fact, the selection rule can also be determined from the symmetry of the Bloch states even without computing the integral. Thus, the existence of Dirac-like points can be quickly and conclusively predicted for various photonic crystals independent of wave polarization, lattice structure, and composition.

© 2013 OSA

OCIS Codes
(260.2030) Physical optics : Dispersion
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: January 4, 2013
Manuscript Accepted: March 5, 2013
Published: March 21, 2013

Citation
Yan Li, Ying Wu, Xi Chen, and Jun Mei, "Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals," Opt. Express 21, 7699-7711 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7699


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References

  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]
  2. 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]
  3. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008). [CrossRef]
  4. R. A. Sepkhanov, Y. 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]
  5. R. A. Sepkhanov and C. W. J. Beenakker, “Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure,” Opt. Commun.281(20), 5267–5270 (2008). [CrossRef]
  6. X. Zhang and Z. Liu, “Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals,” Phys. Rev. Lett.101(26), 264303 (2008). [CrossRef] [PubMed]
  7. 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]
  8. Q. Liang, Y. Yan, and J. Dong, “Zitterbewegung in the honeycomb photonic lattice,” Opt. Lett.36(13), 2513–2515 (2011). [CrossRef] [PubMed]
  9. 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]
  10. 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]
  11. T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B80(15), 155103 (2009). [CrossRef]
  12. D. Torrent and J. Sánchez-Dehesa, “Acoustic analogue of graphene: observation of Dirac cones in acoustic surface waves,” Phys. Rev. Lett.108(17), 174301 (2012). [CrossRef] [PubMed]
  13. L.-G. Wang, Z.-G. Wang, and S.-Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” Europhys. Lett.86(4), 47008 (2009). [CrossRef]
  14. 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]
  15. F. M. Liu, X. Q. Huang, and C. T. Chan, “Dirac cones at k→=0in acoustic crystals and zero refractive index acoustic materials,” Appl. Phys. Lett.100(7), 071911 (2012). [CrossRef]
  16. F. M. Liu, Y. Lai, X. Q. Huang, and C. T. Chan, “Dirac cones atk→=0in photonic crystals,” Phys. Rev. B84(22), 224113 (2011). [CrossRef]
  17. 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. B86(3), 035141 (2012). [CrossRef]
  18. K. Sakoda and H.-F. Zhou, “Role of structural electromagnetic resonances in a steerable left-handed antenna,” Opt. Express18(26), 27371–27386 (2010). [CrossRef] [PubMed]
  19. K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express20(4), 3898–3917 (2012). [CrossRef] [PubMed]
  20. K. Sakoda, “Double Dirac cones in triangular-lattice metamaterials,” Opt. Express20(9), 9925–9939 (2012). [CrossRef] [PubMed]
  21. J. Mathews and R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Addison-Wesley, 1970).
  22. P. M. Hui, W. M. Lee, and N. F. Johnson, “Theory of scalar wave propagation in periodic composites: ak→⋅p→, ” Solid State Commun.91(1), 65–69 (1994). [CrossRef]
  23. B. A. Foreman, “Theory of the effective Hamiltonian for degenerate bands in an electric field,” J. Phys. Condens. Matter12(34), R435–R461 (2000). [CrossRef]
  24. M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory: Application to the Physics of Condensed Matter (Springer-Verlag, 2008).

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