volume | PIER Journals

Abstract

In this paper, photonic bandgaps (PBGs) of the quasiperiodic structures is calculated using the Fourier transform of the refractive index profile. Comparing the reflectivity and Fourier spectrum of multilayer structure refractive index, we find that a peak in the Fourier spectrum is equivalent to a sinusoidal term in the refractive index. The wavelength of the peak location in the Fourier spectrum is half the wavelength where a PBG is located. Using Fourier transform analysis of the refractive index of any multilayer structure, we can determine the location of the PBGs of that structure. Peaks in the Fourier spectrum can be used to design reflective band optical filters in optical communication systems. The filtering wavelengths are twice the peaks in the Fourier spectrum.

1. Archambault, J. L., L. Reekie, and P. St. J. Russell, "High reflectivity and narrow bandwidth fiber gratings written by a single excimer pulse," Electron. Lett., Vol. 26, 730-731, 1990.
doi:10.1049/el:19900476

2. Kashyap, R., J. R. Armitage, R. Wyatt, S. T. Davey, and D. L. Williams, "Allfiber narrowband reflection gratings at 1500 nm," Electron. Lett., Vol. 30, 1977-1978, Nov. 1994.
doi:10.1049/el:19941357

3. Angus Macleod, H., Thin Film Optical Filter, 2nd Ed., McGraw-Hill, New York, 1989.

4. Yablonovitch, E., "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059

5. ITU-T Recommendation G.698.1, 2005.

6. Packiaraj, D., K. J. Vinoy, and A. T. Kalghatgi, "Analysis and design of a compact multi-layer ultra wide band filter," Progress In Electromagnetics Research C, Vol. 7, 111-123, 2009.
doi:10.2528/PIERC09030606

7. Golmohammadi, S., M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, "Narrowband DWDM filters based on Fibonacci-class quasiperiodic structures," Opt. Express, Vol. 15, 10520-10532, 2007.
doi:10.1364/OE.15.010520

8. 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, 1951, 1984.
doi:10.1103/PhysRevLett.53.1951

9. Kohmoto, M., B. Sutherland, and K. Iguchi, "Localization inoptics: Quasiperiodic media," Physical Review Letters, Vol. 58, 2436, 1987.
doi:10.1103/PhysRevLett.58.2436

10. 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

11. Gellermann, W., M. Kohmoto, B. Sutherland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Physical Review Letters, Vol. 72, 633, 1994.
doi:10.1103/PhysRevLett.72.633

12. Macia, E., "Optical engineering with Fibonacci dielectric multilayers," Applied Physics Letters, Vol. 73, 3330, 1998.
doi:10.1063/1.122759

13. Lusk, D., I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasiperiodic one-dimensional photonic crystal," Optics Communications, Vol. 198, 273, 2001.
doi:10.1016/S0030-4018(01)01531-0

14. 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, 3063, 2002.
doi:10.1063/1.1468895

15. 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

16. 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

17. Golmohammadi, S., M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, "Spectral analysis of Fibonacci-class one-dimensional quasi-periodic structures," Progress In Electromagnetics Research, Vol. 75, 69-84, 2007.
doi:10.2528/PIER07051902

18. Vorob'ev, N. N., Fibonacci Numbers, a translation of Chisla Fibonachchi, Gostekhteoretizdat, Moscow-Leningrad, 1951.

19. Dumitriu, I., "On generalized Tribonacci sequences and additive partitions," Disc. Math., Vol. 219, 65-83, 2000.
doi:10.1016/S0012-365X(99)00369-6

20. Yeh, P., Optical Waves in Layered Media, Wiley, New York, 1988.

21. Born, E. and M. Wolf, Fundamentals of Optics,, 3rd Ed., Cambridge University Press, 1999.

Dr. Saeed Golmohammadi

Dr. Y. Rouhani

Dr. Karim Abbasian

Prof. Ali Rostami