Abstract-In this paper, spectral properties of the Fibonacci-class one-dimensional quasi-periodic structures, FCJ(n), as an important optical structure are investigated. Analytical relations for description of the spectral properties of FCJ(n) are used. Fast Fourier Transform (FFT) for investigation of the spectral properties of these structures is proposed. FFT spectrum of the Fibonacci-class one-dimensional quasi-periodic structures contains peaks that are equivalent to photonic bandgaps or multiband reflection filter. Based on the proposed relations and FFT simulation results, the optical bandgap and other properties of these structures are studied. In this paper, the effects of the optical and geometrical parameters on optical properties of the Fibonacci quasi-periodic structures are considered. Our proposed relations show that the spectral contents of the Fibonacci-class onedimensional quasi-periodic structures have two main terms including the low and high frequency parts. Our results illustrate that the high frequency term depends up on the class order, n, and the width of the layer B, db, while the low frequency term depends on the width of the layer A, da. According to the proposed method, the spectral contents of FCJ(n) includes multi narrowband peaks multiplied by a quasi periodic envelope function. The number of multi narrow bands within a periods of the envelope function can be controlled by varying db and n and also the number of period of envelope function can be manipulated by da. Results obtained from our proposed analytical relations and FFT based simulation results are close together.
1. Shechtman, D., I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Physical Review Letters, Vol. 53, 1984. doi:10.1103/PhysRevLett.53.1951
2. Kohmoto, M., B. Sutherland, and K. Iguchi, "Localization in optics: quasi-periodic media," Physical Review Letters, Vol. 58, 1987. doi:10.1103/PhysRevLett.58.2436
3. Gellermann, W., M. Kohmoto, B. Sutherland, and P. C. Taylor, "Localization of light waves in fibonacci dielectric multilayers," Physical Review Letters, Vol. 72, 1994. doi:10.1103/PhysRevLett.72.633
4. Sibilia, C., P. Masciulli, and M. Bertolotti, "Optical properties of quasiperiodic (self-similar) structures," Pure Appl. Opt., Vol. 7, 383-391, 1998. doi:10.1088/0963-9659/7/2/028
5. Abal, G., R. Donangelo, A. Romanelli, A. C. S. Schifino, and R. Siri, "Dynamical localization in quasiperiodic driven systems," Journal of Physical Review E, Vol. 65, 046236-2, 2002. doi:10.1103/PhysRevE.65.046236
6. Macia, E., "Optical engineering with Fibonacci dielectric multilayers," Applied Physics Letters, Vol. 73, 1998. doi:10.1063/1.122759
7. Lusk, D., I. Abdulhalim, and F. Placido, "Omnidirectional reection from Fibonacci quasi-periodic one-dimensional photonic crystal," Optics Communications, Vol. 198, 2001. doi:10.1016/S0030-4018(01)01531-0
8. Peng, R. W., M. Mazzer, X. Q. Huang, F. Qiu, M. Wang, A. Hu, and S. S. Jian, "Symmetry-induced perfect transmission of light waves in quasiperiodic dielectric multilayers," Applied Physics Letters, Vol. 80, 2002.
9. Qin, Y. Q., Y. Y. Zhu, S. N. Zhu, and N. B. Ming, "Quasiphase- matched harmonic generation through coupled parametric processes in a quasiperiodic optical superlattice," Journal of Applied Physics, Vol. 84, 1998. doi:10.1063/1.368988
10. Zhu, S. N., Y. Y. Zhu, and N. B. Ming, "Quasi-phasematched third-harmonic generation in a quasi-periodic optical superlattice," Science, Vol. 278, 1997. doi:10.1126/science.278.5339.843
11. Macia, E., "Exploiting quasiperiodic order in the design of optical devices," Physical Review B, Vol. 63, 205421, 2001. doi:10.1103/PhysRevB.63.205421
13. Yang, X., Y. Liu, and X. Fu, "Transmission properties of light through the Fibonacci-class multilayers," Journal of Physical Review B, Vol. 59, 1999.
14. Huang, X. Q., S. S. Jiang, R. W. Peng, and A. Hu, "Perfect transmission and self-similar optical transmission spectra in symmetric Fibonacci-class multilayers," Journal of Physical Review E, Vol. 59, 245104-2, 2001. doi:10.1103/PhysRevB.63.245104
15. Aissaoui, M., J. Zaghdoudi, M. Kanzari, and B. Rezig, "Optical properties of the quasi-periodic one-dimensional generalized multilayer fibonacci structures," Progress In Electromagnetics Research, Vol. 59, 69-83, 2006. doi:10.2528/PIER05091701
16. Watanabe, K. and K. Kuto, "Numerical analysis of optical waveguides based on periodic Fourier transform," Progress In Electromagnetics Research, Vol. 64, 1-21, 2006. doi:10.2528/PIER06060802
17. Khalaj-Amirhosseini, M., "Analysis of periodic and aperiodic coupled nonuniform transmission lines using the Fourier series expansion," Progress In Electromagnetics Research, Vol. 65, 15-26, 2006. doi:10.2528/PIER06072701