In this paper, for developing analytical and semi-analytical methods to evaluate band structure in photonic quasicrystals the perturbation theory is examined. It is shown that more isotropic and complete photonic band gap can be observed under low dielectric contrast for photonic quasicrystals in comparison with ordinary crystals and because of this feature of photonic quasicrystals, perturbation theory is suitable for evaluation of these structures. In this work, we show that using perturbation semianalytical method one can obtain complete band structure for quasicrystals that are interesting for terahertz technology especially and microwave and optical engineering too. Also, we investigate that complete band gap is appeared in quasicrystals in low refractive index contrast and with increasing number of fold in quasicrystals gap size and isotropy are increased.
2. Jansssen, T., G. Chapuis, and M. de Boissieu, Aperiodic Crystals: From Modulated Phases to Quasicrystals, Oxford University Press, Oxford, 2007.
3. Janssen, T., "Crystallography of quasicrystals," Acta. Cryst., Vol. A42, 261-271, 1986.
4. Levine, D., "Quasicrystals," J. de Physique, Vol. C8, 397-402, 1985.
5. Zoorob, M. E., M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, "Complete photonic band gaps in 12-fold symmetric quasicrystals," Lett. to Nature, Vol. 404, 740-743, 2000.
6. Shechtman, D., I. Blech, D. Gratias, and J. W. Canh, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett., Vol. 53, 1951-1954, 1984.
7. Levine, D. and P. Steinhardt, "Quasicrystals I. Definition and structure," Phys. Rev. B, Vol. 34, 596-615, 1986.
8. Kaliteevski, M. A., S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "P. Millar, R. M. De La Rue,".
9. Rechtsman, M. C., H. C. Jeong, P. M. Chaikin, and S. Torquato P. J. Steinhardt, "Optimized structures for photonic quasicrystals," Phys. Rev. Lett., Vol. 101, 073902, 2008.
10. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, "Photonic Crystals: Molding the Flow of Light," Princeton University Press, 1995.
11. Janssen, T., "Quasicrystals, comparative dynamics," Nature Materials, Vol. 6, 925-926, 2007.
12. Romero-Vivas, J., D. N. Chigrin, A. V. Lavrinenko, and C. M. Sotomayor Torres, "Resonant add-drop filter based on a photonic quasicrystal," Optics Express, Vol. 13, No. 3, 826-835, 2005.
13. Mnaymneh, K. and R. C. Gauthier, "Mode localization and band-gap formation in defect-free photonic quasicrystals," Optics Express, Vol. 15, No. 8, 5090-5099, 2007.
14. Gauthier, R. C., "FDTD analysis of out-of-plane propagation in 12-fold photonic quasi-crystals," Optics Communications, Vol. 269, 395-410, 2007.
15. Lu, T.-W., P.-T. Lee, C.-C. Tseng, and Y.-Y. Tsai, "Modal properties and thermal behaviors of high quality factor quasi-photonic crystal microcavity with different central post sizes," Optics Express, Vol. 16, No. 17, 12591-12598, 2008.
16. Zito, G., B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, "FDTD analysis of photonic quasicrystals with di®erent tiling geometries and fabrication by single-beam computer-generated holography," J. Opt. A: Pure Appl. Opt., Vol. 11, 024007, 2009.
17. Hiett, B. P., D. H. Beckett, S. J. Cox, J. M. Generowicz, and M. Molinari, "Photonic band gaps in 12-fold symmetric quasicrystals," Journal of Material Science: Materials in Electronics, Vol. 14, 413-416, 2003.
18. Zhang, X., Z. Li, B. Cheng, and D.-Z. Zhang, "Non-near-field focus and maging of an unpolarized electromagnetic wave through high-symmetry quasicrystals," Optics Express, Vol. 15, No. 3, 1292-1300, 2007.
19. Chen, A.-L., Y.-S. Wang, Y.-F. Guo, and Z.-D. Wang, "Band structures of Fibonacci phononic quasicrystals," Solid State Communications, Vol. 145, 103-108, 2008.
20. Yang, Y. and G. P. Wang, "Two-dimensional photonic crystals constructed with a portion of photonic quasicrystals," Optics Express, Vol. 15, No. 10, 5991-1996, 2007.
21. Ochiai, T. and K. Sakoda, "Nearly free-photon approximation for two-dimensional photonic crystal slabs," Phys. Rev. B, Vol. 64, 045108, 2001.
22. Brennan, K. F., The Physics of Semiconductors (With Applications to Optoelectronic Devices), Cambridge University Press, 1999.
23. Sakurai, J. J., "Addison-Wesley Publishing Company," Modern Quantum Mechanics, 1994.