volume | PIER Journals

Abstract

This paper proposes a new analysis of the transmission coefficient at normal incidence for 2-D periodic crystals (also called Electromagnetic Band Gap (EBG) structures), which are finite in the direction of wave-propagation and are composed of metallic wires. The crystal is considered as a set of parallel Partially Reflecting Surfaces (PRSs), whose transmission and reflection characteristics are obtained rigorously using the Finite Difference Time Domain (FDTD) method. The transmission coefficient of the EBG structure is then obtained by using a plane-wave cascading approach considering single mode interactions between PRSs. The accuracy of the results given by the hybrid method is assessed compared to those obtained directly by the Finite Difference Time Domain (FDTD) method. The minima and maxima envelops and the resonance frequencies of the transmission coefficient are studied, with analytical expressions, for both, excitation from outside and excitation from inside. A discussion is also presented concerning the strength of the coefficient greater than one obtained when the plane-wave source is inside the EBG structure. In addition, by using a transmission line model, a normalized version for this coefficient is proposed, which considers the available power by the source.

1. Yablonovitch, E., "Inhibited spontaneous emission in solid state physics," Physical Review Letters, Vol. 58, No. 20, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059 Google Scholar

2. Joannopoulos, J., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 1995.

3. Yang, F. and Y. Rahmat-Samii, "Microstrip antennas integrated with electromagnetic bandgap (EBG) structures: a low mutual coupling design for array applications," IEEE Trans. on Antennas Prop., Vol. 51, No. 10, 2936-2946, 2003.
doi:10.1109/TAP.2003.817983 Google Scholar

4. Poilasne, G., P. Pouliguen, K. Mahdjoubi, L. Desclos, and C. Terret, "Active metallic photonic band-gap materials (MPBG): experimental results on beam shaper," IEEE Trans. on Antennas Prop., Vol. 48, No. 1, 117-119, 2000.
doi:10.1109/8.827392 Google Scholar

5. Lourtioz, J. M., A. De Lustrac, F. Gadot, S. Rowson, A. Chel- nokov, T. Brillat, A. Ammouche, J. Danglot, O. Vanbesien, and D. Lippens, "Toward controllable photonic crystals for centimeter and millimeter wave devices," Journal of Lightwave Technology, Vol. 17, No. 11, 2025-2031, 1999.
doi:10.1109/50.802990 Google Scholar

6. Thevenot, M., C. Cheype, A. Reineix, and B. Jecko, "Directive photonic band-gap antennas," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 11, 2115-2122, 1999.
doi:10.1109/22.798007 Google Scholar

7. Cheype, C., C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, "An electromagnetic bandgap resonator antenna," IEEE Trans. on Antennas Prop., Vol. 50, No. 9, 1285-1290, 2002.
doi:10.1109/TAP.2002.800699 Google Scholar

8. Biswas, R., E. Ozbay, B. Temelkuran, M. Bayandir, M. Sigalas, and K.-M. Ho, "Exceptionally directional sources with photonic band-gap crystals," Optical Society of America, Vol. 18, No. 11, 1684-1689, 2001. Google Scholar

9. Akalin, A., J. Danglot, O. Vanbesien, and D. Lippens, "A highly directive dipole antenna embedded in a fabry-perot type cavity," IEEE Microwave Wireless Comp. Lett., Vol. 12, No. 2, 48-50, 2002.
doi:10.1109/7260.982873 Google Scholar

10. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett., Vol. 89, No. 21, 213902-1, 2002.
doi:10.1103/PhysRevLett.89.213902 Google Scholar

11. Felbacq, D., G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A, Vol. 11, No. 9, 2526-2538, 1994. Google Scholar

12. Hall, R. C., R. Mittra, and K. M. Mitzner, "Analysis of multilayered periodic structures using generalized scattering matrix," IEEE Trans. on Antennas Prop., Vol. 36, No. 4, 111-117, 1988. Google Scholar

13. Munk, B. A., Frequency Selective Surfaces: Theory and Design, Wiley-Interscience Publication, 2000.

14. De Lima, A. C. and E. A. Parker, "Fabry-Perot approach to the design of double layer FSS," IEE Proc. Microwave Antennas Propagat., Vol. 143, No. 4, 157-162, 1996.
doi:10.1049/ip-map:19960236 Google Scholar

15. Lee, S. W., G. Zarrillo, and C. L. Law, "Simple formulas for transmission through grids or plates," IEEE Trans. on Antennas Prop., Vol. 30, No. 9, 904-909, 1982.
doi:10.1109/TAP.1982.1142923 Google Scholar

16. Ozbay, E., B. Temelkuran, and M. Bayindir, "Microwave applications of photonic crystals," Progress In Electromagnetics Research, Vol. 41, 185-209, 2003. Google Scholar

17. Guida, G., P. N. Stavrinou, G. Parry, and J. B. Pendry, "Time reversal symmetry, microcavities and photonic crystals," Journ. Modern. Opt., Vol. 48, 581-595, 2001.
doi:10.1080/09500340151031765 Google Scholar

18. Hecht, E., Optics, 421-425, 421-425, 1988.

19. Pozar, D., Microwave Engineering, 2nd ed., 1998.

20. Boutayeb, H., K. Mahdjoubi, A. C. Tarot, and T. Denidni, "Directivity of an antenna embedded inside a Fabry-Perot cavity: Analysis and design," Microw. Opt. Technol. Lett., Vol. 48, No. 1, 12-17, 2006.
doi:10.1002/mop.21249 Google Scholar

21. Balanis, C. A., Antenna Theory: Analysis and Design, second edition, 1997.

Prof. Halim Boutayeb

Dr. Kouroch Mahdjoubi

Dr. Anne-Claude Tarot