Pavelyev Photonic band gap structure of the three-dimensional aproximants quasicrystal
P.N. Dyachenko, J.V. Miklyaev, V.E. Dmitrienko, V.S. Pavelyev

Image Processing Systems Institute RAS, Samara, Russia,
South-Ural State University, Dept. of Optics and Spectroscopy, Chelyabinsk, Russia,

A. V. Shubnikov Institute of Crystallography Russian Academy of Sciences, Moscow, Russia

Full text of article: Russian language.

Abstract:
For the first time, the band structure of three-dimensional cubic photonic approximants of quasicrystals is studied theoretically. The approximants of different orders are found to have large, near-isotropic band gaps in a wide range of permittivity values. The effect of atom coordination on the size and threshold of the photonic band gap is explored. The existence of a complete band gap in the cubic photonic quasicrystal with a body-centered six-dimensional lattice is demonstrated.

Key words:
photonic quasicrystals, photonic band gap.

Citation: Dyachenko PN, Miklyaev JuV, Dmitrienko VE, Pavelyev VS. Photonic band gap structure of the three-dimensional aproximants quasicrystal. Computer Optics 2008; 32(3): 216-22.

References:

  1. Shechtman D. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 1984; 53: 1951-1953.
  2. Macia E. The role of aperiodic order in science and technology. Rep. Prog. Phys. 2006; 69: 397-441.
  3. Quilichini M, Janssen T. Phonon excitations in quasicrystals. Rev. Mod. Phys. 1997; 69: 277-314.
  4. Vekilov YuKh, Isaev EI, Arslanov SF. Influence of phason flips, magnetic field, and chemical disorder on the localization of electronic states in an icosahedral quasicrystal. Phys. Rev. B 2000; 62: 14040-14048.
  5. Krajci M, Hafner  J. Topologically induced semiconductivity in icosahedral Al-Pd-Re and its approximants. Phys. Rev. B 2007; 75: 024116.
  6. Chan YS, Chan CT, Liu ZY. Photonic Band Gaps in Two Dimensional Photonic Quasicrystals. Phys. Rev. Lett. 1998; 80: 956-959.
  7. Yablonovitch Y. Inhibited spontaneous emission in solidstate physics and electronics. Phys. Rev. Lett. 1987; 58: 2059-2062.
  8. John S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 1987; 58: 2486-2489.
  9. Johnson SJ, Joannopoulos JD. Photonic Crystals: The Road from Theory to Practice. Kluwer Academic Publishers, London 2003.
  10. Joannopoulos JD, Meade RD, Winn JN. Photonic Crystals: Molding the Flow of Light. Princeton University Press, Singapore 1999.
  11. Ho KM, Chan CT, Soukoulis CM. Existence of a photonic gap in periodic dielectric structures. Phys. Rev. Lett. 1990; 65: 3152.
  12. Zoorob ME. Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature 2000; 404: 740-743.
  13. Man W. Experimental measurement of the photonic properties of icosahedral quasicrystals. Nature 2005; 436: 993-996.
  14. Lidermann A. Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths. Nature Mater. 2006; 5: 942-945.
  15. Xu J. Icosahedral quasicrystals for visible wavelengths by optical interference holography. Opt. Express 2007; 15: 4287-4295.
  16. Peach M. Quasicrystals step out of the shadows. Materials Today 2006; 9: 44-47.
  17. Wang K. Photonic band gaps in quasicrystal-related approximant structures. J. Mod. Opt. 2003; 50: 2095-2105.
  18. Dyachenko PN, Miklyaev YuV. Band structure calculations of 2D photonic pseudoquasicrystals obtainable by holographic lithography. Proc. of SPIE 2006; 6182: 61822I.
  19. Dmitrienko VE, Kleman M. Icosahedral order and disorder in semiconductors. Philos. Mag. Lett. 1999; 79: 359-367.
  20. Dmitrienko VE, Kleman M, Mauri F. Quasicrystal-related phases in tetrahedral semiconductors: Structure, disorder, and ab initio calculations. Phys. Rev. B 1999; 60: 9383-9389.
  21. Johnson SG, Joannopoulos JD. Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Opt. Express 2001; 8: 173-190.
  22. Harrison W. Solid State Theory [In Russian]. Moscow: “Mir” Publisher; 1972.

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