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

Optics Express, Vol. 22, Issue 2, pp. 1906-1917 (2014)

http://dx.doi.org/10.1364/OE.22.001906

Enhanced HTML Acrobat PDF (3058 KB)

### 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

Sort: Year | Journal | Reset

### References

- P. R. Wallace, “The band theory of Graphite,” Phys. Rev.71(9), 622–634 (1947). [CrossRef]
- A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- V. Yannopapas, “Photonic analog of a spin-polarized system with Rashba spin-orbit coupling,” Phys. Rev. B83(11), 113101 (2011). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express20(4), 3898–3917 (2012). [CrossRef] [PubMed]
- K. Sakoda, “Proof of the universality of mode symmetries in creating photonic Dirac cones,” Opt. Express20(22), 25181–25194 (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. B86(3), 035141 (2012). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. O. Goerbig, “Electronic properties of graphene in a strong magnetic field,” Rev. Mod. Phys.83(4), 1193–1243 (2011). [CrossRef]
- 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]
- J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- N. Engheta, “Materials Science. Pursuing Near-Zero Response,” Science340(6130), 286–287 (2013). [CrossRef] [PubMed]
- B. A. Foreman, “Theory of the effective Hamiltonian for degenerate bands in an electric field,” J. Phys. Condens. Matter12(34), R435–R461 (2000). [CrossRef]
- 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]
- Y. Lai, Y. Wu, P. Sheng, and Z.-Q. Zhang, “Hybrid elastic solids,” Nat. Mater.10(8), 620–624 (2011). [CrossRef] [PubMed]
- 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]
- 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]
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.