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IEEE Microwave and Guided Wave Letters
Volume 10 Number 9, September 2000

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The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme

T. Hirono, Member, IEEE Y. Shibata, W. W. Lui, Member, IEEE S. Seki, Senior Member, IEEE and Y. Yoshikuni Member, IEEE

Page 359.

Abstract:

The reflection coefficient at the dielectric interface orthogonal to the Yee-lattice axis in the finite-difference time-domain scheme is explicitly obtained. In the expression, the effective permittivities assigned to the nodes in the vicinity of the interface are included as parameters. The suitable effective permittivities for the accurate modeling of the interface are investigated theoretically based on the reflection coefficient. Regardless of the angular frequency, the incident angle, and the interface position relative to the lattice, second-order accuracy is achieved by the use of effective permittivies based on the weighted harmonic mean and arithmetic mean of the material permittivities. The second-order accuracy is demonstrated by numerical examples.

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. A. Taflove, Computational Electrodynamics, the Finite-Difference Time-Domain Method, Norwood, MA: Artech House, 1995.
  3. A. C. Cangellaris and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena", IEEE Trans. Antennas Propagat., vol. 39, pp.  1518-1525, Oct.  1991.
  4. J. B. Schneider and K. L. Schlager, "FDTD simulations of TEM horns and the implications for staircased representations", IEEE Trans. Antennas Propagat., vol. 45, pp.  1830-1838, Dec.  1997.
  5. T. M. Jurgens, A. Taflove, K. Umashankar and T. G. Moore, "Finite-difference time-domain modeling of curved surfaces", IEEE Trans. Antennas Propagat., vol. 40, pp.  357-366,  Apr.  1992.
  6. S. Dey and R. Mittra, "A locally conformal finite-difference time-domain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects", IEEE Microwave Guided Wave Lett., vol. 7, pp.  273-275, Sept.  1997.
  7. C. J. Railton and J. B. Schneider, "An analytical and numerical analysis of several locally conformal FDTD schemes", IEEE Trans. Microwave Theory Tech., vol.  47, pp.  56-66, Jan.  1999.
  8. X. Zhang and K. K. Mei, "Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontinuities", IEEE Trans. Microwave Theory Tech., vol. 36, pp.  1775-1787, Dec.  1988.
  9. M. Celuch-Marcysiak and W. K. Gwarek, "Higher-order modeling of media interfaces for enhanced FDTD analysis of microwave circuits", in Proc. 24th European Microwave Conf., Cannes, France, 1994, pp.  1530-1535. 
  10. M. Born and E. Wolf, Principles of Optics, Oxford: U.K.: Pergamon, 1980, p.  40. 
  11. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, pp.  185-200, Oct.  1994.
  12. J. Yamauchi, M. Mita, S. Aoki and H. Nakano, "Analysis of antireflection coatings using the FD-TD method with the PML absorbing boundary condition", IEEE Photon. Technol. Lett., vol. 8, pp.  239-241, Feb.  1996.