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

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

http://dx.doi.org/10.1364/OPEX.13.010367

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### Abstract

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

**Citation**

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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-10367

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### References

- 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]
- 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]
- Proceedings of the EOS Topical Meeting on Advanced Optical Imaging Techniques, (London, UK, June 29 - July 1, 2005).
- M.V.K. Chari, and S.J. Salon, Numerical methods in electromagnetism (Academic Press, San Diego, CA, 2000)
- 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).
- A. Taflove, and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2005).
- K.K. Mei, A. Cangellaris, and D.J. Angelakos, "Conformal Time Domain Finite-Difference Method," Radio Sci. 19, 1145-1147 (1984). [CrossRef]
- R. Holland, "Finite-Difference Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates," IEEE Trans. Nucl. Sci. NS-30, 4589-4591 (1983). [CrossRef]
- M. Fusco, "FDTD Algorithm in Curvilinear Coordinates," IEEE Trans. Antennas Propag. 38, 76-89 (1990). [CrossRef]
- V. Shankar, A. Mohammadian, andW.F. Hall, "A Time-Domain Finite-Volume Treatment for the Maxwell Equations," Electromagnetics 10, 127-145 (1990). [CrossRef]
- N.K. Madsen, and R.W. Ziolkowski, "A Three-Dimensional Modified Finite Volume Technique for Maxwell's Equations," Electromagnetics 10, 147-161 (1990). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C.F. Bohren, and D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).
- A. Bossavit, "Generalized finite differences in computational electromagnetics," Progress in Electromagnetic Research, PIER 32, 45-64 (2001). [CrossRef]
- 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]
- 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]
- A. Kirchner, K. Busch, and C.M. Soukoulis, "Transport properties of random arrays of dielectric cylinders," Phys. Rev. B 57, 277-288 (1998). [CrossRef]

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