In this paper we present two simulation techniques for modeling periodic structures with three-dimensional elements in general. The first of these is based on the Method of Moments (MoM) and is suitable for thin-wire structures, which could be either PEC or plasmonic, e.g., nanowires at optical wavelengths. The second is a Finite Difference Time Domain (FDTD)-based approach, which is well suited for handling arbitrary, inhomogeneous, three-dimensional periodic structures. Neither of the two approaches make use of the traditional Periodic Boundary Conditions (PBCs), and are free from the difficulties encountered in the application of the PBC, as for instance slowness in convergence (MoM) and instabilities (FDTD).
Ravi Kumar Arya,
"Numerically Efficient Technique for Metamaterial Modeling (Invited Paper)," Progress In Electromagnetics Research,
Vol. 140, 263-276, 2013. doi:10.2528/PIER13051313
1. Mittra, R., C. H. Chan, and T. Cwik, "Techniques for analyzing frequency selective surfaces --- A review," IEEE Proc., Vol. 76, No. 12, 1593-1615, 1998. doi:10.1109/5.16352
2. Wu, T. K., Frequency Selective Surface and Grid Array, John Wiley & Sons Inc., 1995.
3. Munk, B. A., Frequency Selective Surfaces: Theory and Design, Wiley, New York, 2000.
4. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, New York, 1998.
5. Harrington, R. F., Field Computation by Moment Method, The Macmillan Company, New York, 1968.
6. Blackburn, J. and L. R. Arnaut, "Numerical convergence in periodic method of moments of frequency-selective surfaces based on wire elements ," IEEE Trans. on Antennas and Propag., Vol. 53, 3308-3315, Oct. 2005.
7. 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. on Microwave Theory and Tech., Vol. 54, No. 10, 3688-3697, Oct. 2006. doi:10.1109/TMTT.2006.882876
8. Prakash, V. V. S. and R. Mittra, "Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations ," Microwave and Optical Technology Letters, Vol. 36, No. 2, 95-100, Jan. 2003. doi:10.1002/mop.10685
9. Wan, J. X., J. Lei, and C. H. Liang, "An efficient analysis of large-scale periodic microstrip antenna arrays using the characteristic basis function method," Progress In Electromagnetics Research, Vol. 50, 61-81, 2005. doi:10.2528/PIER04050901
10. Yoo, K., N. Mehta, and R. Mittra, "A new numerical technique for analysis of periodic structures," Microwave and Optical Technology Letters, Vol. 53, No. 10, 2332-2340, Oct. 2011. doi:10.1002/mop.26250
11. Mittra, R., C. Pelletti, N. L. Tsitsas, and G. Bianconi, "A new technique for efficient and accurate analysis of FSSs, EBGs and metamaterials," Microwave and Optical Technology Letters, Vol. 54, No. 4, 1108-1116, Oct. 2011. doi:10.1002/mop.26730
12. Mittra, R., R. K. Arya, and C. Pelletti, "A new technique for efficient and accurate analysis of arbitrary 3D FSSs, EBGs and metamaterials," 2012 IEEE Antennas and Propagation Society International Symposium (APSURSI), 1-2, Chicago, IL, Jul. 2012. doi:10.1109/APS.2012.6348604
13. Mittra, R., C. Pelletti, N. L. Tsitsas, and G. Bianconi, "A new technique for efficient and accurate analysis of FSSs, EBGs and metamaterials," Microwave and Optical Technology Letters, Vol. 54, No. 4, 1108-1116, Apr. 2012. doi:10.1002/mop.26730
14. Rashidi, A., H. Mosallaei, and R. Mittra, "Numerically efficient analysis of array of plasmonic nanorods illuminated by an obliquely incident plane wave using the characteristic basis function method," J. Comput. Theor. Nanosci., Vol. 10, 427-445, 2013.
15. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd Ed., Artech House, Norwood, MA, 2005.
16. Hua, Y. and T. Sarkar, "Generalized pencil-of-functions method for extracting poles of an EM system from its transient response," IEEE Trans. on Antennas and Propag., Vol. 27, No. 2, 229-234, Feb. 1989. doi:10.1109/8.18710
17. Pelletti, C. and R. Mittra, "Three-dimensional FSS elements with wide frequency and angular responses," IEEE Antennas and Propagation Society International Symposium, 1-2, Chicago, IL, Jul. 2012.