volume | PIER Journals

Abstract

The transmission line transfer matrix method (TLTMM) is presented for the analysis of multilayer electric structures as frequency selective surfaces (FSS), whereby the reflection, transmission and absorption coefficients, field distribution and power flow may be computed inside and outside of the layers. The TLTMM formulation may be developed for any arbitrary angle of incidence, any polarization (linear TE or TM, circular, elliptical) of the incident plane wave, at any frequency of operation (microwave, millimeter wave, optical), any number dielectric layers with arbitrary thicknesses, lossless or low loss dielectric media, inclusion of dispersion relation, etc. A general formulation is given for both the TE and TM polarization of the incident wave. Several practical situations are treated by TLTMM namely, anti-reflection coatings, high reflection surfaces, computation of the axial ratio of the reflected and transmitted plane waves, distributed brag reflector (DBR), a narrow band filter consisting of two Fabry-Perot resonators, cantor superlattices in optics, field distribution and power flow for a multilayer structure. Consequently, it is verified that TLTMM is capable of analysis a variety of practical multilayer dielectric structures.

1. Mittra, R.C. H. Chan, and T. Cwik, "Techniques for analyzing frequency selective surfaces-a review," Proceedings of the IEEE, Vol. 76, No. 12, 1593-1615, 1988.

2. Parker, E. A. and A. N. A. El Sheikh, "Convoluted array elements and reduced size unit cells for frequency selective surfaces," IEE Proc. H, Vol. 138, No. 1, 19-22, 1991.

3. Parker, E. A.A. N. A. El Sheikh, C. De, and A. C. Lima, "Convoluted frequency selective array elements derived from linear and crossed dipoles," IEE Proc. H, Vol. 140, No. 5, 378-380, 1993.

4. Romeu, J. and Y. Rahmit-Samii, "Fractal FSS: a novel dual band frequency selective surface," IEEE Trans. Antennas Propagat., Vol. 48, No. 7, 1097-1105, 2000.
doi:10.1109/8.876329

5. Bertoni, H., L. H. Cheo, and T. Tamir, "Frequency selective reflection and transmission by periodic dielectric layer," IEEE Trans. Antennas Propagat., Vol. 37, No. 1, 78-83, 1989.
doi:10.1109/8.192167

6. Bornemann, J., "Computer aided design of multilayered dielectric frequency selective surfaces for circularly polarized millimeter wave applications," IEEE Trans. Antennas Propagat., Vol. 41, No. 11, 1588-1591, 1993.
doi:10.1109/8.267362

7. Sun, L. and J. Borneman, "Design of frequency selective surfaces formed by stratified dielectric layers," IEEE AP-S Int. Symp. Dig., Vol. 1, 408-411, 1992.

8. Kedar, A. and U. K. Revankar, "Parametric study of flat sandwich multilayer Radome," Progress In Electromagnetics Research, Vol. 66, 253-265, 2006.
doi:10.2528/PIER06111202

9. Xu, S. and Y. Li, "Frequency selective characteristics of dielectric periodic structures for millimeter wave application," International Journal of Infrared and Millimeter Waves, Vol. 19, No. 3, 1998.
doi:10.1023/A:1022563811487

10. Aissaoui, M., J. Zaghdoudi, M. Kanzari, and B. Rezig, "Optical properties of the quasi-periodic one-dimentional generalized multilayer Fibonacci structures," Progress In Electromagnetics Research, Vol. 59, 69-83, 2006.
doi:10.2528/PIER05091701

11. Tibuleac, S., R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 4, 553-561, 2000.
doi:10.1109/22.842027

12. Yang, H. D. and J. Wang, "Surface waves of printed antennas on planar artificial periodic dielectric structures," IEEE Trans. Antennas Propagat., Vol. 49, No. 3, 444-450, 2001.
doi:10.1109/8.918619

13. Yang, L. and S. Xu, "Investigation into effects of dielectric loss on frequency selective characteristics of dielectric periodic structures," IEE Proc. H, Vol. 148, No. 5, 302-306, 2001.

14. Coves, A., B. Gimeno, D. Camilleri, M. V. Andres, A. A. San Blas, and V. E. Boria, "Full wave analysis of dielectric frequency selective surfaces using a vectorial modal method," IEEE Trans. Antennas Propagat., Vol. 52, No. 8, 2091-2099, 2004.
doi:10.1109/TAP.2004.832507

15. Ishimaru, A., Electromagnetic Wave Propagation and Scattering, Radiation, 1991.

16. Kong, J. A., Theory of Electromagnetic Waves, Wiley Interscience, 2005.

17. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.
doi:10.2528/PIER01082101

18. Wu, T. K., Frequency Selective Surface and Grid Array, Wiley, 1995.

19. Qing, A. and C. K. Lee, "An improved model for full wave analysis of multilayered frequency selective surface with gridded square element," Progress In Electromagnetics Research, Vol. 30, 285-303, 2001.
doi:10.2528/PIER00041803

20. Cory, H., S. Shiran, and M.Heilper, "An iterative method for calculating the shielding effectiveness and light Transmittance of multilayered media," IEEE Trans. Electrogagnetic Compatibility, Vol. 35, No. 4, 451-456, 1993.
doi:10.1109/15.247859

21. Cory, H. and C. Zach, "Wave propagation in metamaterial multi layered structures," Microwave and Optical Technology Letters, Vol. 40, No. 6, 460-465, 2004.
doi:10.1002/mop.20005

22. Pendry, J. B. and A. MacKinnon, "Calculation of photon dispersion," Phys. Rev. Lett., Vol. 69, No. 19, 2772-2775, 1992.
doi:10.1103/PhysRevLett.69.2772

23. Pieper, R.M. Shirvaikar, and J. Salvatierra, "A transmission line model for analysis of thin film optical filters," IEEE System Theory Symposium, 186-191, 2006.

24. Pozar, D. M., Microwave Engineering, Wiley, 2004.

25. Gerardin, J. and A. Lakhtakia, "Negative index of refraction and distributed Bragg reflectors," Microwave and Optical Technology Letters, Vol. 34, No. 6, 409-411, 2002.
doi:10.1002/mop.10478

26. Wei, L. and J. W. Y. Lit, "Phase-shifted bragg grating filters with symmetrical structures," Journal of Lightwave Technology, Vol. 15, No. 8, 1997.

27. Bakhti, F. and P. Sansonetti, "Design and realization of multiple quarter-wave phase-shifts UV-written bandpass filters in optical fibers," Journal of Lightwave Technology, Vol. 15, No. 8, 1997.

28. Vasconcelos, M. S., E. L. Albuquerque, and A. M. Mariz, "Optical spectra of a cantor superlattice," Brazilian Journal of Physics, Vol. 26, No. 1, 376-380, 1996.

Professor Homayoon Oraizi

Dr. Majid Afsahi