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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 24 — Aug. 20, 2011
  • pp: 4868–4872

Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Jianjun Liu, Zhigang Fan, Haosu Xiao, Wang Zhang, Chunying Guan, and Libo Yuan  »View Author Affiliations


Applied Optics, Vol. 50, Issue 24, pp. 4868-4872 (2011)
http://dx.doi.org/10.1364/AO.50.004868


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Abstract

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [ 0 , 0.3 a ] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F = q 1 q 2 q 3 ε π r 2 for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.

© 2011 Optical Society of America

OCIS Codes
(160.5293) Materials : Photonic bandgap materials
(160.5298) Materials : Photonic crystals

ToC Category:
Materials

History
Original Manuscript: April 4, 2011
Manuscript Accepted: July 12, 2011
Published: August 19, 2011

Citation
Jianjun Liu, Zhigang Fan, Haosu Xiao, Wang Zhang, Chunying Guan, and Libo Yuan, "Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals," Appl. Opt. 50, 4868-4872 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-24-4868


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References

  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]
  3. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000). [CrossRef] [PubMed]
  4. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]
  5. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef] [PubMed]
  6. P. Russell, “Photonic crystal fibers,” Science 299, 358–362(2003). [CrossRef] [PubMed]
  7. S. A. Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010). [CrossRef]
  8. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]
  9. H. G. Park, S. H. Kim, S. H. Kwon, G. J. Young, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004). [CrossRef] [PubMed]
  10. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
  11. X. Y. Chen, P. Shum, and J. J. Hu, “Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide,” Opt. Commun. 276, 93–96 (2007). [CrossRef]
  12. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75, 1848–1850 (1999). [CrossRef]
  13. J. L. Yin, X. G. Huang, S. H. Liu, and S. J. Hu, “Photonic bandgap properties of 8-fold symmetric photonic quasicrystals,” Opt. Commun. 269, 385–388 (2007). [CrossRef]
  14. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998). [CrossRef]
  15. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000). [CrossRef] [PubMed]
  16. M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals,” Phys. Rev. B 66, 214205 (2002). [CrossRef]
  17. M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009). [CrossRef]
  18. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand, and R. A. Abram, “Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells,” J. Mod. Opt. 53, 407–416 (2006). [CrossRef]
  19. K. Wang, “Light localization in photonic band gaps of quasiperiodic dielectric structures,” Phys. Rev. B 82, 045119 (2010). [CrossRef]
  20. K. Wang, “Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: a comparative study,” Phys. Rev. B 76, 085107 (2007). [CrossRef]
  21. Y. Lai, Z. Q. Zhang, C. H. Chan, and L. Tsang, “Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures,” Phys. Rev. B 74, 054305 (2006). [CrossRef]
  22. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005). [CrossRef] [PubMed]
  23. Y. Q. Wang, X. Y. Hu, X. S. Xu, B. Y. Chen, and D. Z. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003). [CrossRef]
  24. A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14, 1–7 (2006). [CrossRef]

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