OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 25 — Dec. 12, 2005
  • pp: 10367–10381

Contour-path effective permittivities for the two-dimensional finite-difference time-domain method

Ahmad Mohammadi, Hamid Nadgaran, and Mario Agio  »View Author Affiliations

Optics Express, Vol. 13, Issue 25, pp. 10367-10381 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (219 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Effective permittivities for the two-dimensional Finite-Difference Time-Domain (FDTD) method are derived using a contour path approach that accounts for the boundary conditions of the electromagnetic field at dielectric interfaces. A phenomenological formula for the effective permittivities is also proposed as an effective and simpler alternative to the previous result. Our schemes are validated using Mie theory for the scattering of a dielectric cylinder and they are compared to the usual staircase and the widely used volume-average approximations. Significant improvements in terms of accuracy and error fluctuations are demonstrated, especially in the calculation of resonances.

© 2005 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(260.5740) Physical optics : Resonance
(290.0290) Scattering : Scattering

ToC Category:
Research Papers

Ahmad Mohammadi, Hamid Nadgaran, and Mario Agio, "Contour-path effective permittivities for the two-dimensional finite-difference time-domain method," Opt. Express 13, 10367-10381 (2005)

Sort:  Journal  |  Reset  


  1. Proceedings of the Fifth International Symposium on Photonic and Electromagnetic Crystal Structures (PECSV) (Kyoto, Japan, March 7-11, 2004); H. Benisty, S. Kawakami, D.J. Norris, and C.M. Soukoulis, eds, Phot. Nanostructures Fund. Appl. 2, 57-159 (2004); C. Jagadish, D.G. Deppe, S. Noda, T.F. Krauss, and O.J. Painter, eds, IEEE J. Sel. Top. Area Commun. 23, 1305-1423 (2005). [CrossRef]
  2. Special issue on nanostructured optical meta-materials: beyond photonic band gap effects, N. Zheludev, and V. Shalaev, eds., J. Opt. A: Pure and Applied Optics, 7, S1-S254 (2005). [CrossRef]
  3. Proceedings of the EOS Topical Meeting on Advanced Optical Imaging Techniques, (London, UK, June 29 - July 1, 2005).
  4. M.V.K. Chari, and S.J. Salon, Numerical methods in electromagnetism (Academic Press, San Diego, CA, 2000)
  5. K.S. Yee, "Numerical Solution of Initial Boundary Value Problems involving Maxwell's Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  6. A. Taflove, and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2005).
  7. K.K. Mei, A. Cangellaris, and D.J. Angelakos, "Conformal Time Domain Finite-Difference Method," Radio Sci. 19, 1145-1147 (1984). [CrossRef]
  8. R. Holland, "Finite-Difference Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates," IEEE Trans. Nucl. Sci. NS-30, 4589-4591 (1983). [CrossRef]
  9. M. Fusco, "FDTD Algorithm in Curvilinear Coordinates," IEEE Trans. Antennas Propag. 38, 76-89 (1990). [CrossRef]
  10. V. Shankar, A. Mohammadian, andW.F. Hall, "A Time-Domain Finite-Volume Treatment for the Maxwell Equations," Electromagnetics 10, 127-145 (1990). [CrossRef]
  11. N.K. Madsen, and R.W. Ziolkowski, "A Three-Dimensional Modified Finite Volume Technique for Maxwell's Equations," Electromagnetics 10, 147-161 (1990). [CrossRef]
  12. 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, 741-476 (1992). [CrossRef]
  13. T.G. Jurgens, A. Taflove, K. Umashankar, and T.G. Moore, "Finite-Difference Time-Domain Modeling of Curved Surfaces," IEEE Trans. Antennas Propag. 40, 357-365 (1992). [CrossRef]
  14. T.G. Jurgens, and A. Taflove, "Three-Dimensional Contour FDTD Modeling of Scattering from Single and Multiple Bodies," IEEE Trans. Antennas Propag. 41, 1703-1708 (1993). [CrossRef]
  15. C.J. Railton, I.J. Craddock, and J.B. Schneider, "Improved locally distorted CPFDTD algorithm with provable stability," Electron. Lett. 31, 1585-1586 (1995). [CrossRef]
  16. Y. Hao, and C.J. Railton, "Analyzing Electromagnetic Structures with Curved Boundaries on Cartesian FDTD Meshes," IEEE Trans. Microwave Theory Tech. 46, 82-88 (1998). [CrossRef]
  17. T.I. Kosmanis, and T.D. Tsiboukis, "A Systematic and Topologically Stable Conformal Finite-Difference Time- Domain Algorithm for Modeling Curved Dielectric Interfaces in Three Dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003). [CrossRef]
  18. 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]
  19. S.S. Zivanovic, K.S. Yee, and K.K. Mei, "A Subgridding Method for the Time-Domain Finite-Difference Method to Solve Maxwell's Equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991). [CrossRef]
  20. J.G. Maloney, and G.S. Smith, "The Efficient Modeling of Thin Material Sheets in the Finite-Difference Time- Domain (FDTD) Method," IEEE Trans. Antennas Propag. 40, 323-330 (1992). [CrossRef]
  21. 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]
  22. 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]
  23. K.-P. Hwang, and A.C. Cangellaris, "Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces," IEEE Microwave Wireless Comp. Lett. 11, 158-160 (2001). [CrossRef]
  24. S. Dey, and R. Mittra, "A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators," IEEE Trans. Microwave Theory Tech. 47, 1737-1739 (1999). [CrossRef]
  25. W. Yu, and R. Mittra, "On the modeling of periodic structures using the finite-difference time-domain algorithm," Microw. Opt. Technol. Lett. 24, 151-155 (2000). [CrossRef]
  26. P. Yang, G.W. Kattawar, K.-N. Liou, and J.Q. Lu, "Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles," Appl. Opt. 43, 4611-4624 (2004). [CrossRef] [PubMed]
  27. 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]
  28. W. Yu, and R. Mittra, "A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces," IEEE Microwave Wireless Comp. Lett. 11, 25-27 (2001). [CrossRef]
  29. W. Sun, and Q. Fu "Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices," Appl. Opt. 39, 5569 (2000). [CrossRef]
  30. J.-Y. Lee, and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microw. Opt. Technol. Lett. 23, 245-249 (1999). [CrossRef]
  31. J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D Tensor FDTD-Formulation for Treatment of Slopes Interfaces in Electrically Inhomogeneous Media," IEEE Trans. Antennas Propag. 51, 1760- 1770 (2003). [CrossRef]
  32. 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 Propag. 49, 749-756 (2001). [CrossRef]
  33. A. Ditkowski, K. Dridi, and J.S. Hesthaven, "Convergent Cartesian Grid Methods for Maxwell's Equations in Complex Geometries," J. Comp. Phys. 170, 39-80 (2001). [CrossRef]
  34. M. Fujii, D. Lukashevich, I. Sakagami, and P. Russer, "Convergence of FDTD andWavelet-Collocation Modeling of Curved Dielectric Interface with the Effective Dielectric Constant Technique," IEEE Microwave Wireless Comp. Lett. 13, 469-471 (2003). [CrossRef]
  35. T. Xiao, and Q.H. Liu, "A Staggered Upwind Embedded Boundary (SUEB) Method to Eliminate the FDTD Staircasing Error," IEEE Trans. Antennas Propag. 52, 730-740 (2004). [CrossRef]
  36. C.F. Bohren, and D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).
  37. A. Bossavit, "Generalized finite differences in computational electromagnetics," Progress in Electromagnetic Research, PIER 32, 45-64 (2001). [CrossRef]
  38. K.L. Shlager, J.B. Schneider, "Comparison of the Dispersion Properties of Several Low-Dispersion Finite- Difference Time-Domain Algorithms," IEEE Trans. Antennas Propag. 51, 642-652 (2003). [CrossRef]
  39. J.A. Roden, and S.D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFSPML for arbitrary media," Microw. Opt. Technol. Lett. 27, 334-339 (2000). [CrossRef]
  40. A. Kirchner, K. Busch, and C.M. Soukoulis, "Transport properties of random arrays of dielectric cylinders," Phys. Rev. B 57, 277-288 (1998). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited