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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 4 — Apr. 1, 2014
  • pp: 664–671

Passband and defective bands in photonic and quasi-crystals

Shaohui Xu, Yiping Zhu, Lianwei Wang, Pingxiong Yang, and Paul K. Chu  »View Author Affiliations

JOSA B, Vol. 31, Issue 4, pp. 664-671 (2014)

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The origin of the passband in one-dimensional photonic crystals and Fibonacci quasi-crystals is investigated by the transmission spectra and effective medium theory. The interference and coupling effects influence the formation and properties of the passbands, which can be divided into the basic band and subband formed by coupling interference modes and inhomogeneous dielectric constants, respectively. The optimal length can be obtained through a transcendental equation to show the maximum bandgap for a photonic crystal at the balance condition between interference and coupling effects. By changing the sequence of the two dielectric materials to fabricate a photonic crystal heterostructure, composed of the photonic crystal and quasi-crystal, an enlarging photonic bandgap can be obtained, since the width of the dielectric and air bands can be narrowed by decreasing the photon coupling effect, and the subband and defective band can be eliminated. The effective medium theory provides a good understanding about the formation mechanism of passbands in photonic and quasi-crystals.

© 2014 Optical Society of America

OCIS Codes
(230.4170) Optical devices : Multilayers
(050.2065) Diffraction and gratings : Effective medium theory

ToC Category:
Diffraction and Gratings

Original Manuscript: December 5, 2013
Revised Manuscript: January 7, 2014
Manuscript Accepted: January 29, 2014
Published: March 4, 2014

Shaohui Xu, Yiping Zhu, Lianwei Wang, Pingxiong Yang, and Paul K. Chu, "Passband and defective bands in photonic and quasi-crystals," J. Opt. Soc. Am. B 31, 664-671 (2014)

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef]
  3. J. D. Joannopoulos, R. D. Meads, and J. N. Winn, Photonic Crystal: Molding the Flow of Light (Princeton University, 1995).
  4. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasi-periodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987). [CrossRef]
  5. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994). [CrossRef]
  6. Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasi-crystals,” Nat. Photonics 7, 177–187 (2013). [CrossRef]
  7. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef]
  8. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
  9. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010). [CrossRef]
  10. Y. Fink, J. N. Winn, S. H. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. D. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef]
  11. J. N. Winn, Y. Fink, S. H. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998). [CrossRef]
  12. A. Poddubny, L. Pilozzi, M. Voronov, and E. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B 77, 113306 (2008). [CrossRef]
  13. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasi-crystals,” Nature 404, 740–743 (2000). [CrossRef]
  14. J. Lin, I. Bita, and E. L. Thomas, “Impact of geometry on the TM photonic band gaps of photonic crystals and quasi-crystals,” Phys. Rev. Lett. 107, 193901 (2011). [CrossRef]
  15. J. Lin, I. Bita, and E. L. Thomas, “Photonic density of states of two-dimensional quasi-crystalline photonic structures,” Phys. Rev. A 84, 023831 (2011). [CrossRef]
  16. J. Lin, I. Bita, and E. L. Thomas, “Level set photonic quasi-crystals with phase parameters,” Adv. Funct. Mater. 22, 1150–1157 (2012). [CrossRef]
  17. C. Rockstuhl, U. Peschel, and F. Lederer, “Correlation between single-cylinder properties and band-gap formation in photonic structures,” Opt. Lett. 31, 1741–1743 (2006). [CrossRef]
  18. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]
  19. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000). [CrossRef]
  20. S. H. Xu, X. M. Ding, and Z. Q. Zhu, “TE and TM defective bands splitting in one-dimensional coupled cavity waveguides,” Opt. Commun. 269, 304–309 (2007). [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  22. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in period stratified media: I. general theory,” J. Opt. Soc. Am. B 67, 423–438 (1977). [CrossRef]
  23. A. Yariv and P. Yeh, “Electromagnetic propagation in period stratified media: II. birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977). [CrossRef]
  24. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  25. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006). [CrossRef]

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