volume | PIER Journals

Abstract

We report the transmission response of generalized Fibonacci photonic crystal F_l(m,n) in microwave domain for normal incidence, where l is the generation number, and m and n are parameters of the Fibonacci distribution. The transmission spectra are calculated through the transfer matrix method and studied by varying the Fibonacci parameters. The structure is exploited to design a microwave mirror with large photonic band gap and polychromatic stop band filters. Therefore, other structure configurations based on the generalized Fibonacci system are proposed. A juxtaposition of p multilayer systems built according to Fibonacci distribution [F_l(m,n)]^p makes possible to have switches like property (off-on-off-on-off-on-…). Then, an hybrid structure which is obtained by sandwiching p stacks of generalized Fibonacci photonic crystal between two periodic photonic crystals is proposed to enlarge the photonic band gap in microwave domain.

1. Li, Z. Y., "Principles of the plane-wave transfer-matrix method for photonic crystals ," Sci. and Tech. of Adv. Mat., Vol. 6, 837-841, 2005.
doi:10.1016/j.stam.2005.06.013 Google Scholar

2. Mouldi, A. and M. Kanzari, "Broad multilayer antireflection coating by apodized and chirped photonic crystal," Opt. Com., Vol. 284, 4124-4128, 2011.
doi:10.1016/j.optcom.2011.05.005 Google Scholar

3. Mouldi, A., M. Kanzari, and B. Rezig, "Broad antireflection grating by apodization of one dimensional photonic crystal," PIERS Proceedings, 1461-1464, Marrakesh, Morocco, Mar. 20-23, 2011. Google Scholar

4. Mouldi, A. and M. Kanzari, "Influence of the optical parameters on transmission properties of the chirped photonic crystal," ACES Journal, Vol. 26, No. 3, 259-266, 2011. Google Scholar

5. Mouldi, A. and M. Kanzari, "Design of an omnidirectional mirror using one dimensional photonic crystal with graded geometric layers thicknesses," Optik, Vol. 123, No. 2, 125-131, 2012.
doi:10.1016/j.ijleo.2011.03.010 Google Scholar

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

7. Kittel, C., Introduction to Solid State Physics, Wiley, New York, 1976.

8. Kumar, V., K. S. Singh, and S. P. Ojha, "Enhanced omni-directional reflection frequency range in Si-based one dimensional photonic crystal with defect," Optik, Vol. 122, 910-913, 2011.
doi:10.1016/j.ijleo.2010.06.016 Google Scholar

9. Li, H., H. Chen, and X. Qiu, "Band-gap extension of disordered 1D binary photonic crystals," Physica B, Vol. 279, 164-167, 2000.
doi:10.1016/S0921-4526(99)00716-4 Google Scholar

10. Zi, J., J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures ," Appl. Phys. Lett., Vol. 73, 2084-2086, 1998.
doi:10.1063/1.122385 Google Scholar

11. Wang, X., X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, "Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures," Appl. Phys. Lett., Vol. 80, 4291-4293, 2002.
doi:10.1063/1.1484547 Google Scholar

12. Guida, G., "Numerical studies of disordered photonic crystals," Progress In Electromagnetics Research, Vol. 41, 107-131, 2003.
doi:10.2528/PIER02010805 Google Scholar

13. Bertolotti, M., P. Masciulli, and C. Sibilia, "Spectral transmission properties of a auto-similar optical Fabry-Perot resonator," Optics Lett., Vol. 19, 777, 1994.
doi:10.1364/OL.19.000777 Google Scholar

14. Bertolotti, M., P. Masciulli, and C. Sibilia, "Linear and nonlinear integrated optics," SPIE, Vol. 2212, 607, 1994.
doi:10.1117/12.185132 Google Scholar

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 Google Scholar

16. Ben Abdelaziz, K., J. Zaghdoudi, M. Kanzari, and B. Rezig, "A broad omnidirectional reflection band obtained from deformed Fibonacci quasi-periodic one dimensional photonic crystals," J. Opt. A: Pure Appl. Opt., Vol. 7, 544-549, 2005.
doi:10.1088/1464-4258/7/10/005 Google Scholar

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

18. Macia, E., "Optical engineering with Fibonacci dielectric multilayers," Appl. Phys. Lett., Vol. 73, 3330-3332, 1998.
doi:10.1063/1.122759 Google Scholar

19. Aynaoua, H., E. H. El Boudoutia, Y. El Hassouania, A. Akjoujb, B. Djafari-Rouhanib, J. Vasseurb, L. Dobrzynskib, and V. R. Velasco, "Propagation of electromagnetic waves in periodic and Fibonacci photonic loop structures," Physica A, Vol. 358, 68-85, 2005.
doi:10.1016/j.physa.2005.06.007 Google Scholar

20. Grushina, N. V., P. V. Korolenko, A. Y. Mishin, and A. M. Zotov, "Broad omnidirectional band of reflection from fibonacci one-dimensional photonic crystals," PIERS Online, Vol. 5, No. 6, 511-515, 2009. Google Scholar

21. Monsoriu, J. A., R. A. Depine, and E. Silvestre, "Non Bragg band gaps in 1D metamaterial aperiodic multilayers," J. of Europ. Opt. Soc., Vol. 2, 07002, Rapid Publications, 2007. Google Scholar

22. Zarate, J. E. and V. R. Velasco, "Electronic properties of quasiperiodic heterostructures," Phys. Rev. B, Vol. 65, 045304-045312, 2001.
doi:10.1103/PhysRevB.65.045304 Google Scholar

23. Zhang, C., F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys., Vol. 87, 3174-3176, 2000.
doi:10.1063/1.372318 Google Scholar

24. Srivastava, R., S. Pati, and S. P. Ojha, "Enhancement of omnidirectional reflection in photonic crystal heterostructures," Progress In Electromagnetics Research B, Vol. 1, 197-208, 2008.
doi:10.2528/PIERB07102903 Google Scholar

25. Manzanares-Martinez, J., R. Archuleta-Garcia, P. Castro-Garay, D. Moctezuma-Enriquez, and E. Urrutia-Banuelos, "One-dimensional photonic heterostructure with broadband omnidirectional reflection," Progress In Electromagnetics Research, Vol. 111, 105-117, 2011.
doi:10.2528/PIER10110404 Google Scholar

26. Liang, G., P. Han, and H. Wang, "Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure," Opt. Lett., Vol. 29, 192-194, 2004.
doi:10.1364/OL.29.000192 Google Scholar

27. Alagappan, G. and P. Wu, "Investigations of laser oscillation and switching using a resonance at the band edge crossover in an hetero-structure of one-dimensional photonic crystals," Photon. Nanostruct.: Fundam. Appl., Vol. 7, 137-142, 2009.
doi:10.1016/j.photonics.2009.06.001 Google Scholar

28. Qiang, H., L. Jiang, and X. Li, "Design of broad omnidirectional total reflectors based on one-dimensional dielectric and magnetic photonic crystal ," Opt. Las. Tech., Vol. 42, 105-109, 2010.
doi:10.1016/j.optlastec.2009.05.006 Google Scholar

29. Garcia, J. E. and M. E. Mora-Ramos, "Study of optical propagation in hybrid periodic/quasiregular structures based on porous silicon," PIERS Online, Vol. 5, No. 2, 167-170, 2009.
doi:10.2529/PIERS080906010703 Google Scholar

30. Klauzer-Kruszyna, A., W. Salejda, and M. H. Tyc, "Polarized light transmission through generalized Fibonacci multilayers: I. Dynamical maps approach," Optik, Vol. 115, No. 6, 257-276, 2004.
doi:10.1078/0030-4026-00360 Google Scholar

31. Dulea, M., M. Severin, and R. Riklund, "Transmission of light through deterministic aperiodic non-Fibonaccian multilayers," Phys. Rev. B, Vol. 42, 3680, 1990.
doi:10.1103/PhysRevB.42.3680 Google Scholar

32. Li, Z., "Principles of the plane-wave transfer-matrix method for photonic crystals," Sci. and Tech. of Adv. Mat., Vol. 6, 837-841, 2005.
doi:10.1016/j.stam.2005.06.013 Google Scholar

33. Abelès, F., Annales Physique, Vol. 12, 596, Paris, 1950.

34. Zhang, J., Y. Cao, and J. Zheng, "Fibonacci quasi-periodic superstructure fiber Bragg gratings," Optik, Vol. 121, 417-421, 2010.
doi:10.1016/j.ijleo.2008.08.002 Google Scholar

35. Chen, A. L., Y. S. Wanga, and C. Zhang, "Wave propagation in one-dimensional solid-fluid quasi-periodic and aperiodic phononic crystals," Physica B, Vol. 407, 324-329, 2012.
doi:10.1016/j.physb.2011.10.041 Google Scholar

36. Suh, W. and S. Fan, "Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top ref lection characteristics ," Opt. Lett., Vol. 28, No. 19, 1763-1765, 2003.
doi:10.1364/OL.28.001763 Google Scholar

37. Kanzari, M. and B. Rzig, "Optical polychromatic filter by combination of periodic and quasi periodic one dimensional dielectric photonic bandgap structures," J. Opt. A: Pure Appl. Opt., Vol. 3, 201-207, 2001.
doi:10.1088/1464-4258/3/6/372 Google Scholar

38. Kanzari, M., A. Bouzidi, and B. Rezig, "Interferential polychromatic filters," Eur. Phys. J. B, Vol. 36, 431-443, 2003.
doi:10.1140/epjb/e2004-00001-9 Google Scholar

Dr. Abir Mouldi

Dr. Mounir Kanzari