volume | PIER Journals

Abstract

In this paper a new method based on the complex images technique has been presented to efficiently compute the Green's functions required in a Mixed Potential Integral Equation (MPIE) analysis of a periodic structure located in a layered medium. This method leads to a closed-form representation for these slowly convergent series valid for sub-wavelength as well as super-wavelength cell sizes for all source point to field point distances. Comparison between the results obtained by the proposed method with ones obtained from other numerical approaches verifies its accuracy. Fast convergence, simple final form and versatility of the proposed method are its main advantages which make it suitable for the analysis of the periodic structures using the integral equation techniques.

1. Maleki Javan, A. R. and N. Granpayeh, "Fast terahertz wave switch/modulator based on photonic crystal structures," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 2--3, 203-212, 2009.
doi:10.1163/156939309787604571

2. Khalilpour, J. and M. Hakkak, "S-shaped ring resonator as anisotropic uniaxial metamaterial used in waveguide tunneling," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 13, 1763-1772, 2009.
doi:10.1163/156939309789566879

3. Collin, R. E., Field Theory of Guided Waves, , IEEE Press, 1991.

4. Watanabec, K. and K. Yasumoto, "Accuracy improvement of the fourier series expansion method for floquet-mode analysis of photonic crystal waveguides," Progress In Electromagnetics Research, Vol. 92, 209-222, 2009.
doi:10.2528/PIER09032704

5. 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.
doi:10.1109/8.60985

6. 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.
doi:10.1109/8.97383

7. 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.
doi:10.1109/8.53491

8. Papaniicolaou, V. G., "Ewald's method revised rapidly convergent series representations of certain Green's functions," J. Comput. Anal. Applicat., Vol. 1, No. 1, 105-114, 1999.
doi:10.1023/A:1022622721152

9. Stevanovi'c, 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. Microwave Theory Tech., Vol. 54, No. 10, 3688-3697, Oct. 2006.
doi:10.1109/TMTT.2006.882876

10. Capolino, F., D. W. Wilton, and W. A. Johnson, "Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 2977-2984, Sep. 2005.
doi:10.1109/TAP.2005.854556

11. Park, M. J. and S. Nam, "Efficient calculation of the Green's function for multilayered planar periodic structures," IEEE Trans. Antennas Propag，, Vol. 46, No. 10, 1582-1583, Dec. 1998.
doi:10.1109/8.725293

12. Silveirinha, M. G. and C. A. Fernandes, "A new acceleration technique with exponential convergence rate to evaluate periodic Green's functions," IEEE Trans. Antennas Propag., Vol. 53, No. 1, 347-355, Jan. 2005.
doi:10.1109/TAP.2004.838793

13. Chow, Y. L., J. J. Yang, D. G. Fang, and G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 3, Mar. 1991.
doi:10.1109/22.75309

14. Kipp, R. A. and C. H. Chan, "A numerically efficient technique for the method of moments solution for planar periodic structures in layered media," IEEE Trans. Microwave Theory Tech., Vol. 42, 635-643, Apr. 1994.
doi:10.1109/22.285070

15. Shubair, R. M. and Y. L. Chow, "Efficient computation of the periodic Green's function in layered dielectric media," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 3, Mar. 1993.
doi:10.1109/22.223751

16. Alaeian, H. and R. Faraji-Dana, "Accurate and fast computation of the Green's function of periodic structures using complex images technique," 2007 IEEE Antennas and Propagation International Symposium, Honolulu, 2007.

17. Jarchi, S., J. Rashed-Mohassel, and R. Faraji-Dana, "Analysis of microstrip dipole antennas on a layered metamaterial substrate," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5--6, 755-764, 2010.
doi:10.1163/156939310791036278

18. Alaeian, H. and R. Faraji-Dana, "A novel Green's function analysis of wave scattering by an infinite grating using complex images technique," Applied Computational Electromagnetics Society (ACES) Journal, Vol. 24, No. 5, 511-517, Oct. 2009.

19. Hua, Y. and T. K. Sarkar, "Generalized Pencil-of-Function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag., Vol. 37, 229-234, 1989.
doi:10.1109/8.18710

20. Chow, Y. L., "An approximate dynamic spatial Green's function in three dimensions for finite length misrostrip lines," IEEE Trans. Microwave Theory Tech., Vol. 28, 393-397, 1980.
doi:10.1109/TMTT.1980.1130082

Dr. H. Bahadori

Dr. Hadiseh Alaeian

Professor Reza Faraji-Dana