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Refractive index from negative to positive with frequencies at the Dirac-like cone in a photonic crystal

  • Zeyu Wang
  • Guangwu Pan
  • Weibin QiuEmail author
  • Pingping Qiu
  • Junbo Ren
  • Zhili Lin
  • Qiang Kan
Article
  • 33 Downloads

Abstract

In this paper, we numerically study the threefold accidental degeneracy conical dispersion (Driac-like cone) at the Brillouin zone center of the two-dimensional photonic crystals, which are composed of silicon pillars arranging in a triangular lattice. The effective permittivity and permeability near the Dirac-like point evolve from negative to positive by using the method of eigen-field averaging. Also, the isotropic behaviour of the Dirac-like cone is revealed by analysing the isofrequency contours. Moreover, we carry out numerical simulations including the reverse Snell’s law effect, negative Goos–Hänchen shifts and superfocusing lens to verify the negative refractive index characteristics of the designed structure. The proposed structure might find significant applications in the on-chip photonic interconnect and the photonic integrated circuit techniques.

Keywords

Negative refraction Photonic crystal Dirac-like cone 

Notes

Acknowledgements

The authors are grateful to the support by the Natural Science Fund of China under Grant No. 11774103, Project for Cultivating Postgraduates’ Innovative Ability in Scientific Research of Huaqiao University (17013082023), Quanzhou City Science & Technology Program of China under Grant No. 2018C003, Open Project of Fujian Key Laboratory of Semiconductor Materials and Applications under No. 2019001.

References

  1. AbdelMalek, F., Belhadj, W., Haxha, S., Bouchriha, H.: Realization of a high coupling efficiency by employing a concave lens based on two-dimensional photonic crystals with a negative refractive index. J. Lightwave Technol. 25(10), 3168–3174 (2007).  https://doi.org/10.1109/jlt.2007.904027 CrossRefADSGoogle Scholar
  2. Berman, P.R.: Goos–Hanchen shift in negatively refractive media. Phys. Rev. E 66(6), 067603 (2002).  https://doi.org/10.1103/PhysRevE.66.067603 CrossRefADSGoogle Scholar
  3. Chen, C.W., Lin, W.C., Liao, L.S., Lin, Z.H., Chiang, H.P., Leung, P.T., Sijercic, E., Tse, W.S.: Optical temperature sensing based on the Goos–Hanchen effect. Appl. Opt. 46(22), 5347–5351 (2007).  https://doi.org/10.1364/ao.46.005347 CrossRefADSGoogle Scholar
  4. Chen, J., Wang, Y., Jia, B., Geng, T., Li, X., Feng, L., Qian, W., Liang, B., Zhang, X., Gu, M., Zhuang, S.: Observation of the inverse Doppler effect in negative-index materials at optical frequencies. Nat. Photonics 5(4), 239–242 (2011).  https://doi.org/10.1038/nphoton.2011.17 CrossRefADSGoogle Scholar
  5. Dong, J.W., Chang, M.L., Huang, X.Q., Hang, Z.H., Zhong, Z.C., Chen, W.J., Huang, Z.Y., Chan, C.T.: Conical dispersion and effective zero refractive index in photonic quasicrystals. Phys. Rev. Lett. (2015).  https://doi.org/10.1103/physrevlett.114.163901 CrossRefGoogle Scholar
  6. Dubois, M., Shi, C., Zhu, X., Wang, Y., Zhang, X.: Observation of acoustic Dirac-like cone and double zero refractive index. Nat. Commun. 8, 14871 (2017).  https://doi.org/10.1038/ncomms14871 CrossRefADSGoogle Scholar
  7. Foteinopoulou, S., Soukoulis, C.M.: Negative refraction and left-handed behavior in two-dimensional photonic crystals. Phys. Rev. B (2003).  https://doi.org/10.1103/physrevb.67.235107 CrossRefGoogle Scholar
  8. Hänchen, F.G.H.: Ein neuer und fundamental Versuch zur Totalreflexion. Ann. Phys. 1, 333–346 (1947)Google Scholar
  9. He, X.T., Huang, Z.Z., Chang, M.L., Xu, S.Z., Zhao, F.L., Deng, S.Z., She, J.C., Dong, J.W.: Realization of zero-refractive-index lens with ultralow spherical aberration. ACS Photon. 3(12), 2262–2267 (2016).  https://doi.org/10.1021/acsphotonics.6b00714 CrossRefGoogle Scholar
  10. Huang, Z., Narimanov, E.E.: Optical imaging with photonic hyper-crystals: Veselago lens and beyond. J. Opt. 16(11), 114009 (2014).  https://doi.org/10.1088/2040-8978/16/11/114009 CrossRefADSGoogle Scholar
  11. Huang, X.Q., Lai, Y., Hang, Z.H., Zheng, H.H., Chan, C.T.: Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10(8), 582–586 (2011).  https://doi.org/10.1038/nmat3030 CrossRefADSGoogle Scholar
  12. Husakou, A., Herrmann, J.: Superfocusing of optical beams below the diffraction limit by media with negative refraction. Phys. Status Solidi A 204(11), 3862–3877 (2007).  https://doi.org/10.1002/pssa.200776402 CrossRefADSGoogle Scholar
  13. Johnson, N.P., Tsakmakidis, K.L., Özbay, E., Kirby, E.I., Hamm, J., Ziolkowski, R.W., Zheludev, N.I., Hess, O.: Trapped rainbow storage of light in metamaterials. Nature 7711, 77111C (2010).  https://doi.org/10.1117/12.855120 CrossRefGoogle Scholar
  14. Li, Z.F., Zhao, R.K., Koschny, T., Kafesaki, M., Alici, K.B., Colak, E., Caglayan, H., Ozbay, E., Soukoulis, C.M.: Chiral metamaterials with negative refractive index based on four “U” split ring resonators. Appl. Phys. Lett. 97(8), 081901 (2010).  https://doi.org/10.1063/1.3457448 CrossRefADSGoogle Scholar
  15. Li, Y., Kita, S., Munoz, P., Reshef, O., Vulis, D.I., Yin, M., Loncar, M., Mazur, E.: On-chip zero-index metamaterials. Nat. Photonics 9(11), 738–745 (2015).  https://doi.org/10.1038/nphoton.2015.198 CrossRefADSGoogle Scholar
  16. Lu, Z.L., Prather, D.W.: Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals. Opt. Express 15(13), 8340–8345 (2007).  https://doi.org/10.1364/oe.15.008340 CrossRefADSGoogle Scholar
  17. Marques, R., Martel, J., Mesa, F., Medina, F.: Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides. Phys. Rev. Lett. 89(18), 183901 (2002).  https://doi.org/10.1103/PhysRevLett.89.183901 CrossRefADSGoogle Scholar
  18. Moitra, P., Yang, Y.M., Anderson, Z., Kravchenko, I.I., Briggs, D.P., Valentine, J.: Realization of an all-dielectric zero-index optical metamaterial. Nat. Photonics 7(10), 791–795 (2013).  https://doi.org/10.1038/nphoton.2013.214 CrossRefADSGoogle Scholar
  19. Notomi, M.: Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap. Phys. Rev. B 62(16), 10696–10705 (2000).  https://doi.org/10.1103/PhysRevB.62.10696 CrossRefADSGoogle Scholar
  20. Pendry, J.B.: Negative refraction makes a perfect lens. Phys. Rev. Lett. 85(18), 3966–3969 (2000).  https://doi.org/10.1103/PhysRevLett.85.3966 CrossRefADSGoogle Scholar
  21. Ramadurgam, S., Lin, T.G., Yang, C.: Tailoring optical and plasmon resonances in core-shell and core-multishell nanowires for visible range negative refraction and plasmonic light harvesting: a review. J. Mater. Sci. Technol. 31(6), 533–541 (2015).  https://doi.org/10.1016/j.jmst.2015.01.004 CrossRefGoogle Scholar
  22. Turduev, M., Hayran, Z., Kurt, H.: Focusing of light beyond the diffraction limit by randomly distributed graded index photonic medium. J. Appl. Phys. 120(24), 243102 (2016).  https://doi.org/10.1063/1.4972980 CrossRefADSGoogle Scholar
  23. Valentine, J., Zhang, S., Zentgraf, T., Zhang, X.: Development of bulk optical negative index fishnet metamaterials: achieving a low-loss and broadband response through coupling. Proc. IEEE 99(10), 1682–1690 (2011).  https://doi.org/10.1109/jproc.2010.2094593 CrossRefGoogle Scholar
  24. Veselago, V.G.: The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp. 92, 517–526 (1968)CrossRefGoogle Scholar
  25. Wang, L.-G., Zhu, S.-Y.: Large positive and negative Goos–Hänchen shifts from a weakly absorbing left-handed slab. J. Appl. Phys. 98(4), 043522 (2005).  https://doi.org/10.1063/1.2034084 CrossRefADSGoogle Scholar
  26. Wang, L.G., Chen, H., Zhu, S.Y.: Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials. Phys. Rev. B 70(24), 245102 (2004).  https://doi.org/10.1103/PhysRevB.70.245102 CrossRefADSGoogle Scholar
  27. Wang, J.R., Chen, X.D., Zhao, F.L., Dong, J.W.: Full polarization conical dispersion and zero-refractive-index in two-dimensional photonic hypercrystals. Sci. Rep. 6, 22739 (2016).  https://doi.org/10.1038/srep22739 CrossRefADSGoogle Scholar
  28. Wang, X.F., Ye, Q.B., Zhou, Y.J., Li, Y., Yu, H., Yang, J.Y., Jiang, X.Q.: Theoretical large positive and negative lateral beam shift of the metal cladding waveguide in the mid-infrared region. Appl. Opt. 57(16), 4714–4717 (2018).  https://doi.org/10.1364/ao.57.004714 CrossRefADSGoogle Scholar
  29. Yallapragada, V.J., Ravishankar, A.P., Mulay, G.L., Agarwal, G.S., Achanta, V.G.: Observation of giant Goos–Hanchen and angular shifts at designed metasurfaces. Sci. Rep. 6, 19319 (2016).  https://doi.org/10.1038/srep19319 CrossRefGoogle Scholar
  30. Yannopapas, V., Moroz, A.: Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges. J. Phys. Condens. Matter 17(25), 3717–3734 (2005).  https://doi.org/10.1088/0953-8984/17/25/002 CrossRefADSGoogle Scholar
  31. Zhang, S., Fan, W.J., Panoiu, N.C., Malloy, K.J., Osgood, R.M., Brueck, S.R.J.: Experimental demonstration of near-infrared negative-index metamaterials. Phys. Rev. Lett. 95(13), 137404 (2005).  https://doi.org/10.1103/PhysRevLett.95.137404 CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fujian Key Laboratory of Light Propagation and Transformation, College of Information Science and EngineeringHuaqiao UniversityXiamenChina
  2. 2.College of Materials Science and Opto-Electronic TechnologyUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.Institute of SemiconductorsChinese Academy of SciencesBeijingChina

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