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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 1906–1917

A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

Ying Wu  »View Author Affiliations


Optics Express, Vol. 22, Issue 2, pp. 1906-1917 (2014)
http://dx.doi.org/10.1364/OE.22.001906


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Abstract

Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.

© 2014 Optical Society of America

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

ToC Category:
Photonic Crystals

History
Original Manuscript: November 26, 2013
Revised Manuscript: January 2, 2014
Manuscript Accepted: January 10, 2014
Published: January 21, 2014

Citation
Ying Wu, "A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal," Opt. Express 22, 1906-1917 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1906


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References

  1. P. R. Wallace, “The band theory of Graphite,” Phys. Rev.71(9), 622–634 (1947). [CrossRef]
  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, F. Guinea, 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. 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]
  5. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008). [CrossRef]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  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. V. Yannopapas, “Photonic analog of a spin-polarized system with Rashba spin-orbit coupling,” Phys. Rev. B83(11), 113101 (2011). [CrossRef]
  13. J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A.109(25), 9761–9765 (2012). [CrossRef] [PubMed]
  14. A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater.12(3), 233–239 (2012). [CrossRef] [PubMed]
  15. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature496(7444), 196–200 (2013). [CrossRef] [PubMed]
  16. Y. P. Bliokh, V. Freilikher, and F. Nori, “Ballistic charge transport in graphene and light propagation in periodic dielectric structures with metamaterials: A comparative study,” Phys. Rev. B87(24), 245134 (2013). [CrossRef]
  17. K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express20(4), 3898–3917 (2012). [CrossRef] [PubMed]
  18. K. Sakoda, “Proof of the universality of mode symmetries in creating photonic Dirac cones,” Opt. Express20(22), 25181–25194 (2012). [CrossRef] [PubMed]
  19. 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]
  20. Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for Dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express21(6), 7699–7711 (2013). [CrossRef] [PubMed]
  21. 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]
  22. D. Torrent, D. Mayou, and J. Sánchez-Dehesa, “Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates,” Phys. Rev. B87(11), 115143 (2013). [CrossRef]
  23. V. Pardo and W. E. Pickett, “Half-Metallic Semi-Dirac-Point Generated by Quantum Confinement in TiO2/VO2 Nanostructures,” Phys. Rev. Lett.102(16), 166803 (2009). [CrossRef] [PubMed]
  24. S. Banerjee, R. R. P. Singh, V. Pardo, and W. E. Pickett, “Tight-Binding Modeling and Low-Energy Behavior of the Semi-Dirac Point,” Phys. Rev. Lett.103(1), 016402 (2009). [CrossRef] [PubMed]
  25. G. Montambaux, F. Piéchon, J. N. Fuchs, and M. O. Goerbig, “Merging of Dirac points in a two-dimensional crystal,” Phys. Rev. B80(15), 153412 (2009). [CrossRef]
  26. M. O. Goerbig, “Electronic properties of graphene in a strong magnetic field,” Rev. Mod. Phys.83(4), 1193–1243 (2011). [CrossRef]
  27. H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science336(6078), 205–209 (2012). [CrossRef] [PubMed]
  28. J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010). [CrossRef]
  29. V. C. Nguyen, L. Chen, and K. Halterman, “Total Transmission and Total Reflection by Zero Index Metamaterials with Defects,” Phys. Rev. Lett.105(23), 233908 (2010). [CrossRef] [PubMed]
  30. Y. Wu and J. Li, “Total reflection and cloaking by zero index metamaterials loaded with rectangular dielectric defects,” Appl. Phys. Lett.102(18), 183105 (2013). [CrossRef]
  31. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006). [CrossRef] [PubMed]
  32. A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B87(15), 155130 (2013). [CrossRef]
  33. A. Alu, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007). [CrossRef]
  34. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008). [CrossRef] [PubMed]
  35. N. Engheta, “Materials Science. Pursuing Near-Zero Response,” Science340(6130), 286–287 (2013). [CrossRef] [PubMed]
  36. B. A. Foreman, “Theory of the effective Hamiltonian for degenerate bands in an electric field,” J. Phys. Condens. Matter12(34), R435–R461 (2000). [CrossRef]
  37. Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B74(8), 085111 (2006). [CrossRef]
  38. Y. Lai, Y. Wu, P. Sheng, and Z.-Q. Zhang, “Hybrid elastic solids,” Nat. Mater.10(8), 620–624 (2011). [CrossRef] [PubMed]
  39. H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys.14(12), 123010 (2012). [CrossRef]
  40. J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.100(22), 221903 (2012). [CrossRef]
  41. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial Power Combination for Omnidirectional Radiation via Anisotropic Metamaterials,” Phys. Rev. Lett.108(21), 213903 (2012). [CrossRef] [PubMed]

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