Vol. 96

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

A Unified FDTD Approach for Electromagnetic Analysis of Dispersive Objects

By Yu-Qiang Zhang and De-Biao Ge
Progress In Electromagnetics Research, Vol. 96, 155-172, 2009


In order to obtain a unified approach for the Finite-Difference Time-Domain (FDTD) analysis of dispersive media described by a variety of models, the coordinate stretched Maxwell's curl equation in time domain is firstly deduced. Then the FDTD update formulas combined with the semi-analytical recursive convolution (SARC) in Digital Signal Process (DSP) technique for general dispersive media are obtained. In this method, the flexibility of FDTD in dealing with complicated object is retained; the advantages of absolute stability, high accuracy, less storage and high effectiveness of SARC in treating the linear system problem are introduced, and a more unified update formulation for a variety of dispersion media model including Convolution Perfectly Matched Layers (CPML) absorbing boundary is possessed. Therefore it can be applied to analysis of general dispersive media provided that the poles and corresponding residues in dispersive medium model of interest are given. Finally, three typical kinds of dispersive model, i.e. Debye, Drude and Lorentz medium are tested to demonstrate the feasibility of presented approach.


Yu-Qiang Zhang and De-Biao Ge, "A Unified FDTD Approach for Electromagnetic Analysis of Dispersive Objects," Progress In Electromagnetics Research, Vol. 96, 155-172, 2009.


    1. Luebbers, R. J. and F. P. Huusberger, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat., Vol. 32, No. 8, 222-227, 1990.

    2. Kelley, D. F. and R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas and Propagat., Vol. 44, No. 6, 792-797, 1996.

    3. Fan, G.-X. and Q. H. Liu, "An FDTD algorithm with perfectly matched layers for general dispersive media," IEEE Trans. Antennas and Propagat., Vol. 48, No. 5, 637-646, 2000.

    4. Takayama, Y. and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microwave and Wireless Components Letters, Vol. 12, No. 3, 102-104, 2002.

    5. Sullivan, D. M., "Z-transform theory and the FDTD method," IEEE Trans. Antennas and Propagat., Vol. 44, No. 1, 28-34, 1996.

    6. Engquist, B. and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput., Vol. 31, No. 139, 629-651, 1977.

    7. Mur, G., "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagntic field equations," IEEE Trans. Electromagn. Compat., Vol. 23, No. 4, 377-382, 1981.

    8. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., Vol. 114, No. 2, 185-200, 1994.

    9. Sacks, Z. S., D. M. Kingsland, D. M. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propagat., Vol. 43, No. 12, 1460-1463, 1995.

    10. Gedney, S. D., "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat., Vol. 44, No. 12, 1630-1639, 1996.

    11. Roden, J. A. and S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Micro. Opt. Tech. Lett., Vol. 27, No. 5, 334-339, 2000.

    12. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House, Norwood, MA, 2005.

    13. Chew, W. C. and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave Opt. Technol. Lett., Vol. 7, No. 13, 599-604, 1994.

    14. Shi, Y. and C.-H. Liang, "A strongly well-posed PML with unsplitfield formulations in cylindrical and spherical coordinates," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 13, 1761-1776, 2005.

    15. Zheng, K., W.-Y. Tam, D.-B. Ge, and J.-D. Xu, "Uniaxial PML absorbing boundary condition for truncating the boundary of Dng metamaterials," Progress In Electromagnetics Research Letters, Vol. 8, 125-134, 2009.

    16. Janke, W. and G. Blakiewicz, "Semi-analytical recursive algorithms for convolution calculations," IEE Proc. Circuits Devices Syst., Vol. 142, No. 2, 125-130, 1995.

    17. Pietrenko, W., W. Janke, and M. K. Kazimierczuk, "Application of semianalytical recursive convolution algorithms for large-signal time-domain simulation of switch-mode power converters," IEEE Trans. Circuits and Systems, Vol. 48, No. 10, 1246-1252, 2001.

    18. Liu, Y.-H., Q. H. Liu, and Z.-P. Nie, "A new efficient FDTD time-to-frequency domain conversion algorithm," Progress In Electromagnetics Research, PIER 92, 33-46, 2009.

    19. Zainud-Deen, S. H., A. Z. Botros, and M. S. Ibrahim, "Scattering from bodies coated with metamaterial using FDTD method," Progress In Electromagnetics Research B, Vol. 2, 279-290, 2008.

    20. Abd-El-Ranouf, H. and R. Mittra, "Scattering analysis of dielectric coated cones," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1857-1871, 2007.

    21. Wang, M. Y., J. Xu, J. Wu, Y. Yan, and H. L. Li, "FDTD study on scattering of metallic column covered by double-negative metamaterial," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1905-1914, 2007.

    22. Luebbers, R. J., D. Steich, and K. Kunz, "FDTD calculation of scattering from frequency-dependent materials," IEEE Trans. Antennas and Propagat., Vol. 41, No. 9, 1249-1257, 1993.