volume | PIER Journals

Abstract

In this paper, frequency selective surfaces (FSSs) are analyzed and designed. The analytical procedure is based on method of moments (MoM). The generalized minimal residual recursive method combined with fast Fourier transform (GMRESR-FFT) is utilized to accelerate the solution of the matrix equation. Our numerical results show that the GMRESR-FFT method can converge at least 3 times faster than the generalized minimal residual fast Fourier transform method (GMRES-FFT). In this paper, the cross dipoles are first used to design the FSS filter with a passband at 300 GHz and a stopband at 450 GHz, and then the Jerusalem cross slots are utilized to avoid grating lobes and improve the bandwidth of FSS. Numerical results demonstrate the validity and efficiency of the presented method.

1. Munk, B. A., Frequency Selective Surfaces Theory and Design, John Wiley & Sons, Inc., 2000.
doi:10.1002/0471723770

2. Schimert, T. R., A. J. Brouns, C. H. Chan, and R. Mittra, "Investigation of millimeter-wave scattering from frequency selective surfaces," IEEE Trans. on Microwave Theory and Tech., Vol. 39, 315-322, 1991.
doi:10.1109/22.102976 Google Scholar

3. Shen, Z., N. Ito, E. Sakata, C. W. Domier, Y. Liang, N. C. Luhmann, Jr., and A. Mase, "Frequency selective surface notch filter for use in a millimeter wave imaging system," IEEE International Symposium on Antennas and Propagation, 4191-4194, 2006.
doi:10.1109/APS.2006.1711553 Google Scholar

4. Biber, S., M. Bozzi, and O. Gunther, "Design and testing of frequency-selective surfaces on silicon substrates for submillimeter-wave applications," IEEE Trans. Antennas Propagat., Vol. 54, 2638-2645, 2006.
doi:10.1109/TAP.2006.880663 Google Scholar

5. Wu, G., V. Hansen, E. Kreysa, and H. P. Gemuend, "Design and optimization of FSS structures for applications in (sub) millimeter astronomy using a PSO algorithm," IRMMW-THz 2006, 401, 2006. Google Scholar

6. Pirhadi, A., F. Keshmiri, M. Hakkak, and M. Tayarani, "Analysis and design of dual band high directive EBG resonator antenna using square loop FSS as superstrate layer," Progress In Electromagnetics Research, PIER 70, 1-20, 2007. Google Scholar

7. Oraizi, H. and M. Afsahi, "Analysis of planar dielectric multilayers as FSS by transmission line transfer matrix method (TLTMM),", PIER 74, 217-240, 2007. Google Scholar

8. Hosseini, M., A. Pirhadi, and M. Hakkak, "A novel AMC with little sensitivity to the angle of incidence using 2-layer jerusalem cross FSS," Progress In Electromagnetics Research, PIER 64, 43-51, 2006. Google Scholar

9. Delihacioglu, K., S. Uckun, and T. Ege, "FSS comprised of one-and two-turn square spiral shaped conductors on dielectric slab," Progress In Electromagnetics Research B, Vol. 6, 81-92, 2008.
doi:10.2528/PIERB08031213 Google Scholar

10. Wu, T. K., Frequency Selective Surface and Grid Array, John Wiley & Sons, Inc., 1995.

11. De Sturler, E., "Nest Krylov methods based on GCR," Journal of Computational and Applied Mathematics, Vol. 67, 15-41, 1996.
doi:10.1016/0377-0427(94)00123-5 Google Scholar

12. Van der Vorst, H. A. and C. Vuik, "GMRESR: A family of nested GMRES methods," Num. Lin. Alg. Appl., Vol. 1, 369-386, 1994.
doi:10.1002/nla.1680010404 Google Scholar

13. Rui, P. L. and R. S. Chen, "Robust GMRES recursive method for fast finite element analysis of 3-D electromagnetic problems," Microwave and Optical Technology Letters, Vol. 49, No. 5, 1010-1015, 2007.
doi:10.1002/mop.22333 Google Scholar

14. Eisenstat, S. C., H. C. Elman, and M. H. Schultz, "Variational iterative methods for non-symmetric systems of linear equations," SIAM J. Numer. Anal., Vol. 20, 345-357, 1983.
doi:10.1137/0720023 Google Scholar

15. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. Statist. Comput., Vol. 7, 856-869, 1986. Google Scholar

16. Chen, R. S., D. X. Wang, and E. K. N. Yung, "Efficient analysis of millimeter wave ferrite circulators by GMRES iterative algorithm," International Journal of Infrared and Millimeter Waves, Vol. 24, No. 7, 1199-1214, 2003.
doi:10.1023/A:1024777204159 Google Scholar

17. Ping, X. W., R. S. Chen, K. F. Tsang, and E. K. N. Yung, "The SSOR-preconditioned inner outer flexible GMRES method for the FEM analysis of EM problems," Microwave and Optical Technology Letters, Vol. 48, No. 9, 1708-1712, 2006.
doi:10.1002/mop.21758 Google Scholar

18. Ding, D. Z., R. S. Chen, D. X. Wang, W. Zhuang, and E. K. N. Yung, "Application of the inner-outer flexible GMRESFET method to the analysis of scattering and radiation by cavitybacked patch antennas and arrays," International Journal of Electronics, Vol. 92, No. 11, 645-659, 2005.
doi:10.1080/00207210500171364 Google Scholar

19. Chen, R. S., D. Z. Ding, Z. H. Fan, E. K. N. Yung, and C. H. Chan, "Flexible GMRES-FFT method for fast matrix solution: Application to 3D dielectric bodies electromagnetic scattering," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 17, No. 6, 523-537, 2004.
doi:10.1002/jnm.554 Google Scholar

20. Mo, L., R. S. Chen, P. L. Rui, and X. P. Feng, "Fast analysis of microwave integrated circuits by use of the inner-outer flexible GMRES-FFT method ," Microwave and Optical Technology Letters, Vol. 43, No. 5, 409-413, 2004.
doi:10.1002/mop.20485 Google Scholar

21. Chen, R. S., E. K. N. Yung, A. H. Yang, and C. H. Chan, "Application of preconditioned Krylov subspace iterative FFT techniques to method of lines for analysis of the infinite plane metallic grating," Microwave and Optical Technology Letters, Vol. 35, No. 2, 160-167, 2002.
doi:10.1002/mop.10546 Google Scholar

22. Chen, R. S., E. K. N. Yung, C. H. Chan, and D. G. Fang, "Application of preconditioned CG-FFT technique to method of lines for analysis of the infinite plane metallic grating," Microwave and Optical Technology Letters, Vol. 24, No. 3, 170-175, 2000.
doi:10.1002/(SICI)1098-2760(20000205)24:3<170::AID-MOP8>3.0.CO;2-S Google Scholar

23. Chen, R. S., Z. H. Fan, and E. K. N. Yung, "Analysis of electromagnetic scattering of three-dimensional dielectric bodies using Krylov subspace FFT iterative methods," Microwave and Optical Technology Letters, Vol. 39, No. 4, 261-267, 2003.
doi:10.1002/mop.11186 Google Scholar

24. Rui, P. L., R. S. Chen, Z. H. Fan, E. K. N. Yung, C. H. Chan, Z. Nie, and J. Hu, "Fast analysis of electromagnetic scattering of 3D dielectric bodies with augmented GMRES-FFT method," IEEE Trans. Antennas Propagat., Vol. 53, No. 11, 3848-3852, 2005.
doi:10.1109/TAP.2005.858833 Google Scholar

25. Rui, P. L., R. S. Chen, X. P. Feng, L. Mo, and E. K. N. Yung, "Fast analysis of microwave integrated circuits by use of the loose GMRES-FFT method," International Journal of RF and Microwave CAD Engineering, Vol. 15, No. 6, 578-586, 2005.
doi:10.1002/mmce.20101 Google Scholar

26. Ding, D. Z., R. S. Chen, Z. H. Fan, E. K. N. Yung, and C. H. Chan, "Fast analysis of electromagnetic scattering of 3D dielectric bodiesby use of the loose GMRES-FFT method," International Journal of Electronics, Vol. 92, No. 7, 401-415, 2005.
doi:10.1080/00207210500031907 Google Scholar

27. Chen, R. S., L. Mo, and E. K. N. Yung, "Multifrontal method preconditioned GMRES-FFT algorithm for fast analysis of microstrip circuits," International Journal for Computational and Mathematics in Electrical and Electronic Engineering, Vol. 24, No. 1, 94-106, 2005.
doi:10.1108/03321640510571075 Google Scholar

28. Chen, R. S., X. W. Ping, E. K. N. Yung, C. H. Chan, et al. "Application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite element analysis of Helmholtz equations," IEEE Trans. Antennas Propagat., Vol. 54, No. 5, 1604-1608, 2006.
doi:10.1109/TAP.2006.874358 Google Scholar

29. Chen, R. S., X. W. Ping, and E. K. N. Yung, "SSOR preconditioned GMRES for the FEM analysis of waveguide discontinuities with anisotropic dielectric," International Journal of Numerical Modelling, Vol. 17, No. 2, 105-118, 2004.
doi:10.1002/jnm.526 Google Scholar

30. Chen, R. S., E. K. N. Yung, C. H. Chan, and D. G. Fang, "Application of SSOR preconditioned conjugate gradient algorithm to edge-FEM for 3-dimensional full wave electromagnetic boundary value problems," IEEE Trans. on Microwave Theory and Tech., Vol. 50, No. 4, 1165-1172, 2002.
doi:10.1109/22.993420 Google Scholar

31. Chen, R. S., K. F. Tsang, and E. K. N. Yung, "Application of SSOR preconditioning technique to method of lines for millimeter wave scattering ," International Journal of Infrared and Millimeter Waves, Vol. 21, No. 8, 1281-1301, 2000.
doi:10.1023/A:1026452101058 Google Scholar

32. Chen, R. S., K. F. Tsang, and E. K. N. Yung, "An effective multigrid preconditioned CG algorithm for millimeter wave scattering by an infinite plane metallic grating," nternational Journal of Infrared and Millimeter Waves, Vol. 21, No. 6, 945-963, 2000.
doi:10.1023/A:1026453819519 Google Scholar

33. Chen, R. S., D. G. Fang, K. F. Tsang, and E. K. N. Yung, "Analysis of electromagnetic wave scattering by an electrically large metallic grating using wavelet-based algebratic multigrid preconditioned CG method," Progress In Electromagnetics Research, PIER 31, 89-112, 2001. Google Scholar

34. Huang, J., T. K.Wu, and S. W. Lee, "Tri-band frequency selective surface with circular ring elements," IEEE Trans. Antennas Propagat., Vol. 42, No. 2, 166-175, 1994.
doi:10.1109/8.277210 Google Scholar

35. Ansoft, Designer, "User guide and example,", Ansoft Corporation, 225 West Square Suite 200, Pittsburgh, PA 15219-1119. Google Scholar

Dr. Wei Zhuang

Prof. Zhenhong Fan

Dr. Da-Zhi Ding

Dr. Yuyuan An