To model periodic structures with oblique incident waves/scan angles in FDTD, the field transformation method is successfully used to analyze their characteristics. In the field transformation method, Maxwell's equations are Floquet-transformed so that only a single period of infinite periodic structure can be modeled in FDTD by using periodic boundary conditions (PBCs). A new discretization method based on the exponential time differencing (ETD) algorithm is proposed here for the discretization of the modified Maxwell's equations in the periodic FDTD method. This new discretization method provides an alternative way to discretize the modified Maxwell's equations with simpler updating forms that requires less CPU time and memory than the traditional stability factor method (SFM). These two methods have the same numerical accuracy and stability in the periodic FDTD method. Some validation cases are provided showing perfect match between the results of both methods.
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. AP-14, No. 3, 302-307, 1966.
2. Munk, B. A., Frequency Selective Surfaces: Theory and Design, John Wiley, New York, 2000.
3. Yablonovitch, E., "Photonic band-gap structures," J. Opt. Soc. Amer. B., Vol. 10, No. 2, 283-294, 1993.
4. Maloney, J. G. and M. P. Kesler, "Analysis of antenna arrays using the split-field update FDTD method," Proc. IEEE AP-S Int. Symp., Vol. 4, 2036-2039, 1998.
5. Taflove, A. and S. C. Hagness, Computational Electromagnetics: the Finite-Difference Time-Domain Method, 2nd ed., Artech House, Norwood, 2000.
6. Veysoglu, M. E., R. T. Shin, and J. A. Kong, "A finite- difference time-domain analysis of wave scattering from periodic surfaces: oblique incident case," J. Electromagnetic Waves and Applications, Vol. 7, No. 12, 1595-1607, 1993.
7. Kao, Y. C. A. and R. G. Atkins, "A finite difference-time domain approach for frequency selective surfaces at oblique incidence," Proc. IEEE AP-S Int. Symp., Vol. 2, 1432-1435, 1996.
8. Kao, Y. C. A., "Finite-difference time domain modeling of oblique incidence scattering from periodic surfaces," Thesis, 1997.
9. Roden, J. A., "Electromagnetic analysis of complex structures using the fdtd technique in general curvilinear coordinates," Ph.D. Thesis, 1997.
10. Roden, J. A., S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, "Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations," IEEE Trans. Microwave Theory Tech., Vol. 46, 420-427, 1998. doi:10.1109/22.664143
11. Harms, P. H., J. A. Roden, J. G. Maloney, M. P. Kesler, E. J. Kuster, and S. D. Gedney, "Numerical analysis of periodic structures using the split-field algorithm," Proc. 13th Annual Review of Progress in Applied Computational Electromagnetics, 104-111, 1997.
12. Aminian, A., F. Yang, and Y. Rahmat-Samii, "Bandwidth determination for soft and hard ground planes by spectral FDTD: a unified approach in visible and surface wave regions," IEEE Trans. Antennas Propagat., Vol. 53, No. 1, 18-28, 2005. doi:10.1109/TAP.2004.840517
13. Gedney, S. and U. Navsariwala, "An unconditional stable finite element time-domain solution of the vector wave equation," IEEE Microwave Guided Wave Lett., Vol. 5, No. 10, 332-334, 1995. doi:10.1109/75.465046
14. Holland, R., "Finite-difference time-domain (FDTD) analysis of magnetic diffusion," IEEE Trans. Electromagnetic Compatibility, Vol. 36, No. 2, 32-39, 1994. doi:10.1109/15.265477
15. Luk, K. M. and K. W. Leung, Dielectric Resonator Antennas, Research Studies Press, Bristol, 2003.