2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 48 Number 5, May 2000

Table of Contents for this issue

Complete paper in PDF format

An FDTD Algorithm with Perfectly Matched Layers for General Dispersive Media

Guo-Xin Fan, Member, IEEE and Qing Huo Liu Senior Member, IEEE

Page 637.

Abstract:

A three-dimensional (3-D) finite-difference time-domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

References

  1. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propagat., vol. AP-14, pp.  302-307, May  1966.
  2. R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler and M. Schneider, "A frequency-dependent finite difference time domain formulation for dispersive materials", IEEE Trans. Electromagn. Compat., vol. 32, pp.  222-227, Aug.  1990.
  3. R. J. Luebbers, F. P. Hunsberger and K. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma", IEEE Trans. Antennas Propagat., vol. 39, pp.  29-39, Jan.  1991.
  4. R. J. Luebbers and F. P. Hunsberger, "FDTD for N th-order dispersive media", IEEE Trans. Antennas Propagat., vol. 40, pp.  1297-1301, Nov.  1992.
  5. R. J. Luebbers, D. Steich and K. Kunz, "FDTD calculation of scattering from frequency-dependent materials", IEEE Trans. Antennas Propagat., vol. 41, pp.  1249-1257, Sept.  1993.
  6. D. F. Kelley and R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD", IEEE Trans. Antennas Propagat., vol. 44, pp.  792-797, June  1996.
  7. M. D. Bui, S. S. Stuchly and G. I. Costache, "Propagation of transients in dispersive dielectric media", IEEE Trans. Microwave Theory Tech., vol. 39, pp.  1165-1171, July  1991.
  8. J. M. Bourgeois and G. S. Smith, "A full three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment", IEEE Trans. Geosci. Remote Sensing, vol. 34, pp.  36 -44, Jan.  1996.
  9. T. Kashiwa and I. Fukai, "A treatment by FDTD method of dispersive characteristics associated with electronic polarization", Microwave Opt. Tech. Lett., vol. 3, pp.  203-205, 1990.
  10. R. M. Joseph, S. C. Hagness and A. Taflove, "Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulse", Opt. Lett., vol. 16, pp.  1412-1414,  Sept.  1991.
  11. O. P. Gandhi, B.-Q. Gao and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media", IEEE Trans. Microwave Theory Tech., vol. 41, pp.  658-664, Apr.  1993.
  12. J. L. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies", IEEE Trans. Antennas Propagat., vol. 43, pp.  422-426, Apr.  1995.
  13. A. Taflove, Computational Electromagnetics: The Finite-Difference Time-Domain Method, Boston, MA: Artech House, 1995.
  14. D. M. Sullivan, "Frequency-dependent FDTD methods using Z transforms", IEEE Trans. Antennas Propagat., vol. 40, pp.  1223-1230, Oct.  1992.
  15. D. M. Sullivan, "Z -transform theory and the FDTD method", IEEE Trans. Antennas Propagat., vol. 44, pp.  28-34,  Jan.  1996.
  16. W. H. Weedon and C. M. Rappaport, "A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media", IEEE Trans. Antennas Propagat., vol. 45, pp.  401-410, Mar.  1997.
  17. E. L. Lindman, "‘Free-space’ boundary conditions for the time dependent wave equation", J. Computat. Phys., vol. 18, pp.  67-78,  May  1975.
  18. B. Engquist and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves", Math. Computat., vol. 31, pp.  629-651, July  1977.
  19. G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations", IEEE Trans. Electromagn. Compat., vol. EMC-23, pp.  377-382, Nov.  1981.
  20. Z. P. Liao, H. L. Wong, B.-P. Yang and Y.-F. Yuan, "A transmitting boundary for transient wave analysis", Sci. Sinica, vol. 27, no. 10, pp.  1063-1076, 1984.
  21. R. G. Keys, "Absorbing boundary conditions for acoustic media", Geophys., vol. 50, pp.  892-902, 1985.
  22. R. L. Higdon, "Absorbing boundary conditions for difference approximations to the multi-dimensional wave equations", Math. Computat., vol. 47, pp.  437-459, Oct.  1986.
  23. C. Cerjan, D. Kosloff, R. Kosloff and M. Reshef, "A nonreflecting boundary condition for discrete acoustic and elastic wave equations", Geophys., vol. 50, pp.  705-708, Apr.  1985.
  24. R. Kosloff and D. Kosloff, "Absorbing boundaries for wave propagation problems", J. Computat. Phys., vol. 63, pp.  363-376, Apr.  1986 .
  25. C. M. Rappaport and L. Bahrmasel, "An absorbing boundary condition based on anechoic absorber for EM scattering computation", J. Electromagn. Waves Applicat., vol. 6, no. 12, pp.  1621-1634, 1992.
  26. C. M. Rappaport and T. Gürel, "Reducing the computational domain for FDTD scattering simulation using the sawtooth anechoic chamber ABC", IEEE Trans. Magn., vol. 31, pp.  1546-1549, May  1995 .
  27. K. K. Mei and J. Fang, "Superabsorption-A method to improve absorbing boundary conditions", IEEE Trans. Antennas Propagat., vol. 40, pp.  1001-1010,  Sept.  1992.
  28. K. K. Mei, R. Pous, Z. Q. Chen, Y. W. Liu and M. Prouty, "The measured equation of invariance: A new concept in field computation", IEEE Trans. Antennas Propagat., vol. 42, pp.  202-214, Mar.  1994.
  29. R. Gordon, R. Mittra, A. Glisson and E. Michielssen, "Finite element analysis of electromagnetic scattering by complex bodies using an efficient numerical boundary condition for mesh truncation", Electron. Lett., vol. 29, pp.  1102-1103, June  1993.
  30. O. M. Ramahi, "Complementary operator: A method to annihilate artificial reflections arising from the truncation of the computational domain in the partial differential equations", IEEE Trans. Antennas Propagat., vol. 43, pp.  697-704, July  1995.
  31. J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Computat. Phys., vol. 114, pp.  185-200, Oct.  1994.
  32. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates", Microwave Opt. Tech. Lett., vol. 7, pp.  599-604, Sept.  1994.
  33. Z. S. Sacks, D. M. Kingsland, R. Lee and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing condition", IEEE Trans. Antennas Propagat., vol. 43, pp.  1460-1463, Dec.  1995.
  34. S. D. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices", IEEE Trans. Antennas Propagat., vol. 46, pp.  1630-1639, Dec.  1996.
  35. R. W. Ziolkowski, "Time-derivative Lorentz material model-based absorbing boundary condition", IEEE Trans. Antennas Propagat., vol. 45, pp.  1530-1535, Oct.  1997.
  36. J. Fang and Z. Wu, "Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media", IEEE Trans. Microwave Theory Tech., vol. 44, pp.  2216-2222, Dec.  1996 .
  37. Q. H. Liu, "An FDTD algorithm with perfectly matched layers for conductive media", Microwave Opt. Tech. Lett., vol. 14, pp.  134-137,  Feb.  1997.
  38. S. D. Gedney, "An anisotropic PML absorbing media for the FDTD simulation of fields in lossy and dispersive media", Electromagn. , vol. 16, pp.  399-415, July/Aug.  1996.
  39. T. Uno, Y. He and S. Adachi, "Perfectly matched layer absorbing condition for dispersive medium", IEEE Microwave Guided Wave Lett., vol. 7, pp.  264-266,  Sept.  1997.
  40. F. L. Teixeira, W. C. Chew, M. Straka, M. L. Oristaglio and T. Wang, "Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous and conductive soils", IEEE Trans. Geosci. Remote Sensing, vol. 36, pp.  1928-1937, Nov.  1998.
  41. J. N. Brittingham, E. K. Miller and J. L. Wilows, "Pole extraction from real-frequency information", Proc. IEEE, vol. 68, pp.  263-273, Feb.  1980.
  42. R. W. P. King and G. S. Smith, Antennas in Matter: Fundamentals, Theory, and Applications, Cambridge, MA: MIT Press, 1981.
  43. G.-X. Fan and Q. H. Liu, "A PML-FDTD algorithm for general dispersive media", in 14th Annu. Rev. Progress Appl. Computat. Electromagn., Monterey, CA, Mar. 1998, pp.  655- 662. 
  44. J. W. Schuster and R. J. Luebbers, "An accurate FDTD algorithm for dispersive media using piecewise constant recursive convolution technique", in IEEE Antennas Propagat. Soc. Int. Symp., Atlanta, GA, June 1998, pp.  2018-2021.