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2011-10-26
Integral-Equation Analysis of Frequency Selective Surfaces Using Ewald Transformation and Lattice Symmetry
By
Progress In Electromagnetics Research, Vol. 121, 249-269, 2011
Abstract
In this paper, we present the space-domain integral-equation method for the analysis of frequency selective surfaces (FSS), consisting of an array of periodic metallic patches or a metal screens perforated periodically with arbitrarily shaped apertures. The computation of the spatial domain Green's function is accelerated by the Ewald transformation. The geometric model is simplified by the lattice symmetry, so that the unknowns are greatly reduced. Time of filling MOM matrix and solving linear system is dramatically reduced. Our technique shows much higher efficiency when compared with the available commercial software and the existing methods published.
Citation
Jianxun Su, Xiao-Wen Xu, Mang He, and Kang Zhang, "Integral-Equation Analysis of Frequency Selective Surfaces Using Ewald Transformation and Lattice Symmetry," Progress In Electromagnetics Research, Vol. 121, 249-269, 2011.
doi:10.2528/PIER11081902
References

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

2. Duan, Z., B.-I. Wu, S. Xi, H. Chen, and M. Chen, "Research progress in reversed cherenkov radiation in double-negative metamaterials," Progress In Electromagnetics Research, Vol. 90, 75-87, 2009.

3. Catedra, M. F. and R. P. Torres, "A scheme to analyze scattering from flat metallic periodic structures using the conjugate gradient and the fast fourier transform method," Progress In Electromagnetics Research, Vol. 4, 315-343, 1991.

4. Chen, C.-C., "Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes," IEEE Trans. Microw. Theory Tech., Vol. 19, No. 5, 475-481, May 1971.

5. Wu, T. K., "Frequency Selective Surface and Grid Array," Wiley, , New York, 1995.

6. Rao, S. M., D. R. Wilton, A. W. Glisson, "Electromagnetic scattering by surface of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-411, 1982.

7. Collin, R. E., Field Theory of Guided Waves, IEEE Press, New York, 1991.

8. Collin, R. E. and F. J. Zucker, Antenna Theory, Ch. 19 and 20, Mc-Graw-Hill, New York, 1969.

9. Jorgenson, R. E. and R. Mittra, "Efficient calculation of the free-space periodic Green's function," IEEE Trans. Antennas Propag., Vol. 38, No. 5, 633-642, May 1990.

10. Singh, S., W. F. Richards, J. R. Zinecker, and D. R. Wilton, "Accelerating the convergence of series representing the free periodic Green's function," IEEE Trans. Antennas Propag., Vol. 38, No. 12, 1958-1962, Dec. 1990.

11. Singh, S. and R. Singh, "On the use of ρ-algorithm in series acceleration," IEEE Trans. Antennas Propag., Vol. 39, No. 10, 1514-1517, Oct. 1991.

12. Ewald, P. P., "Die berechnung optischer und elektrostatischer gitterpotentiale," Ann. Phys., Vol. 64, 253-287, 1921, Translated by A. Cornell, Atomics International Library, 1964.

13. Stevanovic, I., P. Crespo-Valero, K. Blagovic, F. Bongard, and J. R. Mosig, "Integral-equation analysis of 3-D metallic objects arranged in 2-D lattices using the Ewald transformation," IEEE Trans. Antennas Propag., Vol. 54, No. 10, 3688-3697, Oct. 2006.

14. Mathis, W. and A. F. Peterson, "Efficient electromagnetic analysis of a doubly infinite array of rectangular apertures," IEEE Trans. Microw. Theory Tech., Vol. 46, No. 1, 46-54, Jan. 1998.

15. Eibert, T. F., J. L. Volakis, D. R. Wilton, and D. R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation," IEEE Trans. Antennas Propag., Vol. 47, No. 5, 843-850, May 1999.

16. Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010.

17. Kinayman, N. and M. I. Aksun, "Comparative study of acceleration techniques for integrals and series in electromagnetic problems," Radio Sci., Vol. 30, No. 6, 1713-1722, Nov./Dec. 1995.

18. Ewald, P. P., "Dispersion und doppelbrechung von elektronengittern (kristallen)," Dissertation, Munchen, 1912, also Ann. Phys., Vol. 49, 1, 1916.

19. Jordan, K. E., G. R. Richter, and P. Sheng, "An efficient numerical evaluation of the Green's function for the Helmholtz operator on periodic structures," J. Comp. Phys., Vol. 63, 222-235, 1986.

20. Stevanovic, Mosig, "Periodic Green's function for skewed 3-d lattices using the Ewald transformation," Microwave and Opt. Tech. Letters, Vol. 49, No. 6, 1353-1357, Jun. 2007.

21. Hanninen, I., M. Taskinen, and J. Sarvas, "Singularity subtraction integral formulae for surface integral equations with rwg, rooftop and hybrid basis functions," Progress In Electromagnetics Research, Vol. 63, 243-278, 2006.

22. McGrath, D. T. and V. P. Pyati, "Phased array antenna analysis with the hybrid finite element method," IEEE Trans. Antennas Propag., Vol. 42, No. 12, 1625-1630, 1994.

23. Chen, C.-C., "Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes," IEEE Trans. Microw. Theory Tech., Vol. 19, No. 5, 475-481, May 1971.

24. Bozzi, M., L. Perregrini, J. Weinzierl, and C. Winnewisser, "Efficient analysis of quasi-optical filters by a hybrid MoM/BI-RME method," IEEE Trans. Antennas Propag., Vol. 49, No. 7, 1054-1064, Jul. 2001.

25. Li, M. and W. C. Chew, "Applying divergence-free condition in solving the volume integral equation," Progress In Electromagnetics Research, Vol. 57, 311-333, 2006.

26. Fan, Z., R.-S. Chen, H. Chen, and D.-Z. Ding, "Weak form nonuniform fast fourier transform method for solving volume integral equations," Progress In Electromagnetics Research, Vol. 89, 275-289, 2009.

27. Shi, Y., X. Luan, J. Qin, C. Lv, and C.-H. Liang, "Multilevel Green's function interpolation method solution of volume/surface integral equation for mixed conducting/bi-isotropic objects," Progress In Electromagnetics Research, Vol. 107, 239-252, 2010.

28. Zhao, K., M. N. Vouvakis, and J. F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Trans. EMC, Vol. 47, No. 4, 763-773, Nov. 2005.