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Applied Optics

Applied Optics


  • Vol. 49, Iss. 7 — Mar. 1, 2010
  • pp: 1080–1096

Effective permittivities with exact second-order accuracy at inclined dielectric interface for the two-dimensional finite-difference time-domain method

Takuo Hirono, Yuzo Yoshikuni, and Takayuki Yamanaka  »View Author Affiliations

Applied Optics, Vol. 49, Issue 7, pp. 1080-1096 (2010)

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Accuracy degradation at a dielectric interface in simulations using the finite-difference time-domain method can be prevented by assigning suitable effective permittivities at the nodes in the vicinity of the interface. The effective permittivities with exact second-order accuracy at the interface inclined to the Yee-lattice axis are analytically derived for what we believe to be the first time. We discuss two interfaces with different inclined angles between their normal and the Yee-lattice axis in the case of two-dimensional TE polarization. The tangent of the angle is 1 for one interface and 1 / 2 for the other. With the derived effective permittivities, reflection and transmission at the interface are simulated with second-order accuracy with respect to cell size. The accuracy is demonstrated by numerical examples.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

Original Manuscript: November 11, 2009
Revised Manuscript: January 20, 2010
Manuscript Accepted: January 20, 2010
Published: February 22, 2010

Takuo Hirono, Yuzo Yoshikuni, and Takayuki Yamanaka, "Effective permittivities with exact second-order accuracy at inclined dielectric interface for the two-dimensional finite-difference time-domain method," Appl. Opt. 49, 1080-1096 (2010)

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  1. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302-307 (1966). [CrossRef]
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  3. T. G. Jurgens, A. Taflove, K. Umashankar, and T. G. Moore, “Finite-difference time-domain modeling of curved surfaces,” IEEE Trans. Antennas Propagat. 40, 357-366 (1992). [CrossRef]
  4. P. H. Harms, J. F. Lee, and R. Mittra, “A study of the nonorthogonal FDTD method versus the conventional FDTD technique for computing resonant frequencies of cylindrical cavities,” IEEE Trans. Microwave Theory Tech. 40, 741-746 (1992). [CrossRef]
  5. I. S. Kim and W. J. R. Hoefer, “A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations,” IEEE Trans. Microwave Theory Tech. 38, 812-815 (1990). [CrossRef]
  6. K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, “Staircase-free finite-difference time-domain formulation for general materials in complex geometries,” IEEE Trans. Antennas Propagat. 49, 749-756 (2001). [CrossRef]
  7. M. Celuch-Marcysiak and W. K. Gwarek, “Higher-order modelling of media interfaces for enhanced FDTD analysis of microwave circuits,” in Proceedings of the 24th European Microwave Conference (Wiley, 1994), pp. 1530-1535. [CrossRef]
  8. N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonators with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645-1649 (1997). [CrossRef]
  9. P. Yang, K. N. Liou, M. I. Mishchenko, and B.-C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727-3737 (2000). [CrossRef]
  10. M. Fujii, D. Lukashevich, I. Sakagami, and P. Russar, “Convergence of FDTD and wavelet-collocation modeling of curved dielectric interface with the effective dielectric constant technique,” IEEE Microw. Wireless Compon. Lett. 13, 469-471 (2003). [CrossRef]
  11. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367-10381(2005). [CrossRef] [PubMed]
  12. T. Hirono, Y. Shibata, W. W. Lui, S. Seki, and Y. Yoshikuni, “The second-order condition for the dielectric interface orthogonal to the Yee-lattice axis in the FDTD scheme,” IEEE Microwave Guided Wave Lett. 10, 359-361(2000). [CrossRef]
  13. T. Hirono and Y. Yoshikuni, “Accurate modeling of dielectric interfaces by the effective permittivities for the fourth-order symplectic finite-difference time-domain method,” Appl. Opt. 46, 1514-1524 (2007). [CrossRef] [PubMed]
  14. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974), pp. 7-17.
  15. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972-2974 (2006). [CrossRef] [PubMed]
  16. G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comput. Phys. 226, 1085-1101 (2007). [CrossRef]

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