Optical properties of generalized dielectric Fibonacci multilayer generated by the rule Sl+1 = Snl Sml-1 with a pair of positive integers m and n were studied. The initial generations S1 and S2 are taken as S1 = H and S2 = L where H and L are two elementary layers with refractive indices nL = 1.45 and nH = 2.3, respectively. In the following numerical investigation, we chose SiO2 (L) and TiO2 (H) as two elementary layers. We use the so-called "antitrace" map to determine the transmission spectra of the structures. Based on the representation of the transmittance spectra in the visible range an analysis depending on the pair (n,m) is presented. We show that the whole structure Snl Sml-1 has an interesting application for well selection pairs (m, n) values.
1. Soukoulis, C. M., Photonic Band Gaps and Localization, Plenum, New York, 1993.
2. Joannopoulos, J., R. Meade, and J. Winn, Photonic Crystals, Princeton Press, Princeton, 1995.
3. Soukoulis, C. M., Photonic Band Gap Materials, Kluwer Academic Publishers, Dordrecht, 1996.
4. Rarity, J. and C. Weisbuch, In Microcavities and Photonic Bandgaps, Physics and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
5. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, NJ, 1995.
6. Soukoulis, C. M., Photonic Crystals and Light Localization in the 21st Century, Kluwer, Dordrecht, 2001.
7. Chigrin, D. N., A. V. Laverinko, D. A. Yarotsky, and S. V. Gapo- nenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and spontaneous emission control," J. Light. Technol., Vol. 17, 1999.
8. Zhang, D. Z., Z. L. Li, W. Hu, and B. Y. Cheng, "Broad-band optical reflector - an application of light localization in one-dimension," Appl. Phys. Lett., Vol. 67, 1995.
9. Han, P. and H. Z. Wang, "Effect of invariant transformation in one-dimensional randomly-perturbed photonic crystal," Chin. Phys. Lett., Vol. 20, 2003.
10. Merlin, R., K. Ba jema, R. Clarke, F. Y. Juang, and P. K. Bhat- tacharya, "Quasiperiodic GaAs-AlAs heterostructures," Phys. Rev. Lett., Vol. 55, 1985. doi:10.1103/PhysRevLett.55.1768
11. Kohmoto, M., B. Sutherland, and K. Iguchi, "Localization of optics: quasiperiodic media," Phys. Rev. Lett., Vol. 58, 1987. doi:10.1103/PhysRevLett.58.2436
12. Fujiwara, T. and T. Ogawa, "Chains, flowers, rings and peanuts: graphical geodesic lines and their application to penrose tiling," Quasicrystals, Vol. 93, 1990.
13. Gumbs, G. and M. K. Ali, "Dynamical maps, cantor spectra, and localization for fibonacci and related quasiperiodic lattices," Phys. Rev. Lett., Vol. 60, 1988. doi:10.1103/PhysRevLett.60.1081
14. Nori, F. and J. P. Rodriguez, "Acoustic and electronic properties of one-dimensional quasicrystals," Phys. Rev. B, Vol. 34, 1986. doi:10.1103/PhysRevB.34.2207
15. Capaz, R. B., B. Koiller, and S. L. A. de Queiroz, "Gap states and localization properties of 1-D fibonacci quasicrystals," Phys. Rev. B, Vol. 42, 1, 1990. doi:10.1103/PhysRevB.42.6402
16. Wang, X., U. Grimm, and M. Schreiber, "Trace and antitrace maps for aperiodic sequences, their extensions and applications," Phys. Rev. B, Vol. 62, 14020-14031, 2000. doi:10.1103/PhysRevB.62.14020