Vol. 36

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2014-04-24

Numerical Investigation on the Spectral Properties of One-Dimensional Triadic-Cantor Quasi-Periodic Structure

By Yassine Bouazzi, Osswa Soltani, Manel Romdhani, and Mounir Kanzari
Progress In Electromagnetics Research M, Vol. 36, 1-7, 2014
doi:10.2528/PIERM14032602

Abstract

We numerically investigate the optical spectra of a photonic band gap material realized by one-dimensional Triadic-Cantor quasi-periodic structure. The studied system is composed of two elementary layers H and L with refractive indices nL=1,45 (SiO2) and nH=2,3 (TiO2), respectively. Analytical calculations using a trace and antitrace maps approach have been used to find the reflection and transmission theoretical expressions in visible range under quarter wavelength condition. In our results we present the effect of iteration order of Triadic-Cantor sequence on the optical properties of these multilayer systems, namely the photonic band gap behavior and the optical windows presence, which makes this type of structures good candidates for interesting applications in the field of the nano-optical engineering.

Citation


Yassine Bouazzi, Osswa Soltani, Manel Romdhani, and Mounir Kanzari, "Numerical Investigation on the Spectral Properties of One-Dimensional Triadic-Cantor Quasi-Periodic Structure," Progress In Electromagnetics Research M, Vol. 36, 1-7, 2014.
doi:10.2528/PIERM14032602
http://www.jpier.org/PIERM/pier.php?paper=14032602

References


    1. Goddard, W. A., D. W. Brenner, S. E. Lyshevsky, and G. J. Iafrate, Handbook of Nanoscience, Engineering, and Technology, CRC Press, New York, 2003.

    2. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, No. 23, 2059-2062, 1987.
    doi:10.1103/PhysRevLett.58.2059

    3. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, No. 23, 2486-2489, 1987.
    doi:10.1103/PhysRevLett.58.2486

    4. Schechtman, D., I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett., Vol. 53, No. 20, 1951-1954, 1984.
    doi:10.1103/PhysRevLett.53.1951

    5. Fu, D., Introduction to the Cantor Set, University of Arizona, Arizona, 2012.

    6. Gilbert, H., "La théorie des ensembles en France avant la crise de 1905: Baire, Borel, Lebesgue et tous les autres," Revue d'Histoire des Mathmatiques, Vol. 1, No. 1, 39-81, 1995.

    7. Kanamori, A., "The mathematical development of set theory from Cantor to Cohen," B. Symb. Log., Vol. 2, No. 1, 1-71, 1996.
    doi:10.2307/421046

    8. Ferreirµos, J., "The motives behind Cantors set theory physical, biological, and philosophical questions," Sci. Context, Vol. 17, No. 1-2, 49-83, 2004.
    doi:10.1017/S0269889704000055

    9. Chovanec, F., "Cantor sets," Sci. Military J., Vol. 1, No. 1, 5-11, 2010.

    10. Palis, J., "A view on chaotic dynamical systems," Braz. J. Phys., Vol. 24, No. 4, 926-930, 1994.

    11. Negro, L. D. and S. V. Boriskina, "Deterministic aperiodic nanostructures for photonics and plasmonics applications," Laser & Photonics Rev., Vol. 6, No. 2, 178-218, 2012.
    doi:10.1002/lpor.201000046

    12. Chiadini, F., V. Fiumara, and A. Scaglione, "Filtering properties of optical Cantor multilayers," 18th International Conference on Applied Electromagnetics and Communications, ICECom 2005, 1-5, 2005.

    13. Chiadini, F., A. Scaglione, and V. Fiumara, "Transmission properties of perturbed optical Cantor multilayers," J. of Appl. Phys., Vol. 100, No. 2, 023119-1-023119-5, 2009.

    14. Escorcia-García, J., L. M. Gaggero-Sagerb, A. G. Palestino-Escobedoc, and V. Agarwala, "Optical properties of Cantor nanostructures made from porous silicon: A sensing application," Phot. Nano. Fund. Appl., Vol. 10, No. 4, 452-458, 2011.
    doi:10.1016/j.photonics.2012.02.002

    15. Sibilia, C., P. Masciulli, and M. Bertolotti, "Optical properties of quasiperiodic (self-similar) structures," Pure Appl. Opt., Vol. 7, No. 2, 383-391, 1998.
    doi:10.1088/0963-9659/7/2/028

    16. Werner, D. H. and R. Mittra, Frontiers in Electromagnetics, Wiley-IEEE Press, 2000.

    17. Chiadini, F., V. Fiumara, I. M. Pinto, and A. Scaglione, "Self-scaling properties of the reflection coe±cient of Cantor prefactal multilayers," Microw. Opt. Techn. Lett., Vol. 37, No. 5, 339-343, 2003.
    doi:10.1002/mop.10912

    18. Lavrinenko, A. V., S. V. Zhukovsky, S. V. Sandomirski, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor ¯lter," Phys. Rev. E, Vol. 65, No. 3, 36621-36629, 2002.
    doi:10.1103/PhysRevE.65.036621

    19. Aissaoui, M., J. Zaghdoudi, M. V. Kanzari, and B. Rezig, "\Optical properties of the quasi-periodic one-dimensional generalized multilayer Fibonacci structures," Progress In Electromagnetics Research, Vol. 69, 69-83, 2006.
    doi:10.2528/PIER05091701

    20. Bouazzi, Y. and M. Kanzari, "Interferential polychromatic filters based on the quasi-periodic one- dimensional generalized multilayer Thue-Morse structures," Opt. Appl., Vol. 39, No. 3, 489-498, 2009.

    21. Peng, R. W., X. Q. Huang, F. Qiu, Y. M. Liu, A. Hu, and S. S. Jiang, "Structural symmetry and optical properties of dielectric multilayer," Surf. Rev. Lett., Vol. 10, No. 2-3, 311-315, 2003.
    doi:10.1142/S0218625X03004950

    22. Menez, L., I. Zaquine, A. Maruani, and R. Frey, "Experimental investigation of intracavity Bragg gratings," Opt. Lett., Vol. 27, No. 7, 479-481, 2002.
    doi:10.1364/OL.27.000479