Vol. 36
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2014-04-24
Numerical Investigation on the Spectral Properties of One-Dimensional Triadic-Cantor Quasi-Periodic Structure
By
Progress In Electromagnetics Research M, Vol. 36, 1-7, 2014
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
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