Numerical Studies of Metallic PBG Structures

doi:10.2528/PIER02010806

PIER
Progress In Electromagnetics Research	ISSN: 1070-4698, E-ISSN: 1559-8985

Home > Vol. 41 > pp. 133-157

Numerical Studies of Metallic PBG Structures

By A-C. Tarot, S. Collardey, and K. Mahdjoubi

Full Article PDF (4,550 KB)
Abstract:
Abstract-Photonic Bandgap (PBG) materials have been investigated for their versatility in controlling the propagation of electromagnetic waves [1, 2]. In order to determine PBG structures responses, several analytical or numerical methods are used, such as:

The plane wave method applied to solve Maxwell's equations [3].
The transfer matrix method, based on the wire grating impedance developed by N. Marcuvitz [4].
The Finite Element Method (FEM) exhibits, e.g., the frequency response of reflection and transmission coefficients of the PBG materials when they have infinite surfaces and are excited by plane wave. The FEM method can be also used in the case of finite structure fed by a dipole.
solves the discretized Maxwell's equations in the time domain and evaluates the electromagnetic field components. These EM fields are then obtained in the frequency domain thanks to a Fourier Transform.

First of all, we present a parametrical study using a 3D Finite Element method software. This study allows to estimate the role of any parameters on the reflection and transmission coefficients and then to design a PBG structure in the X-band (8-12 GHz). Continuous and discontinuous structures are presented. Then, we present a numerical analysis of PBG structures, using the FDTD method in order to understand the propagation phenomena in these periodic materials.

Citation:
A-C. Tarot, S. Collardey, and K. Mahdjoubi, "Numerical studies of metallic PBG structures," Progress In Electromagnetics Research, Vol. 41, 133-157, 2003.
doi:10.2528/PIER02010806
http://www.jpier.org/pier/pier.php?paper=0201086

References:
1. Yablonovitch, E., "Photonic band-gap structures," J. Opt. Soc. Amer. B, Vol. 10, No. 2, 283-295, 1993.

2. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals, Princeton Univ. Press, Princeton, NJ, 1995.

3. Zhang, Z. and S. Satpathy, "Electromagnetic waves in periodic structures: Bloch wave solution of Maxwell's equations," Physical Review Letters, Vol. 65, 1990.

4. Marcuvitz, N., Waveguide Handbook, MacGraw Hill Book Company, 1951.

5., Commercial 3D finite-element package., Vol. 7, Ansoft-HFSS (High Frequency Structure Simulator).

6. Ho, K. M, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, 1990.

7. Ozbay., E. et al., "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev., 1994.

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

9. De Lustrac, A., F. Gadot, S. Cabaret, J. M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, "Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths," Applied Physical Letters, Vol. 75, No. 9, 1625-1627, 1999.
doi:10.1063/1.124775

10. Taflove, A. and M. E. Brodwin, "Numerical solution of steady state electromagnetic scattering problems using the time-domain dependent Maxwell's equations," IEEE Microwave Theory and Techniques, Vol. 23, No. 8, 1975.

11. Taflove, A., Advances in Computational Electrodynamics, the Finite-Difference Time-Domain Method.

12. Thevenot, M., A. Reinex, and B. Jecko, "FDTD to analyze complex PBG structures in the reciprocal space," Microwave and Optical Technology Letters, Vol. 21, No. 1, 1999.
doi:10.1002/(SICI)1098-2760(19990405)21:1<25::AID-MOP7>3.0.CO;2-2

13. Guiffaut, C., FDTD Code Developed in RENNES..

14. MATLAB edited by The Mathworks Inc., Computation, Computation, Visualization and Programming Package..

15. Collardey, S., G. Poilasne, A.-C. Tarot, P. Pouliguen, K. Mahdjoubi, and C. Terret, "Metallic photonic band-gap propagation modes characterization," Microwave and Optical Technology Letters, No. 3, 2001.

16. Collardey, S., G. Poilasne, A.-C. Tarot, P. Pouliguen, K. Mahdjoubi, and C. Terret, "Propagation modes in k-space and radiation pattern of metallic photonic band gap materials," ISAP2000, 21-25, 2000.