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  • Cited by 4
  • Print publication year: 2008
  • Online publication date: July 2010

2 - FDTD method for periodic structure analysis

Summary

FDTD fundamentals

Introduction

A fundamental quest in electromagnetics and antenna engineering is to solve Maxwell's equations under various specific boundary conditions. In the last several decades, computational electromagnetics has progressed rapidly because of the increased popularity and enhanced capability of computers. Various numerical techniques have been proposed to solve Maxwell's equations [1]. Some of them deal with the integral form of Maxwell's equations while others handle the differential form. In addition, Maxwell's equations can be solved either in the frequency domain or time domain depending on the nature of applications. The success in computational electromagnetics has propelled modern antenna engineering developments.

Among various numerical techniques, the finite difference time domain (FDTD) method has demonstrated desirable and unique features for analysis of electromagnetic structures [2]. It simply discretizes Maxwell's equations in the time and space domains, and electromagnetics behavior is obtained through a time evolving process. A significant advantage of the FDTD method is the versatility to solve a wide range of microwave and antenna problems. It is flexible enough to model various media, such as conductors, dielectrics, lumped elements, active devices, and dispersive materials. Another advantage of the FDTD method is the capability to provide a broad band characterization in one single simulation. Since this method is carried out in the time domain, a wide frequency band response can be obtained through the Fourier transformation of the transient data.

Because of these advantages, the FDTD method has been widely used in many electromagnetic applications.

References
Itoh, T., ed. Numerical Techniques for Microwave and Millimeter-wave Passive Structures, Wiley-Interscience, 1989.
Taflove, A. and Hagness, S., Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Artech House, 2000.
Yee, K. S., “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. 14, 302–7, 1966.
Jensen, M. A., Time-Domain Finite-Difference Methods in Electromagnetics: Application to Personal Communication, Ph.D. dissertation at University of California, Los Angeles, 1994.
Taflove, A. and Hagness, S., “Chapter 9: Dispersive and nonlinear materials,” in Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Artech House, 2000.
Zheng, F., Chen, Z., and Zhang, J., “Toward the development of a three dimensional unconditionally stable finite-difference time-domain method,” IEEE Trans. Microwave Theory Tech., vol. 48, 1550–8, September 2000.
NaMiki, T., “3-D ADI-Finite Difference Time Domain method – unconditionally stable time-domain algorithm for solving full vector Maxwell's equations,” IEEE Trans. Microwave Theory Tech., vol. 48, 1743–8, October 2000.
Engquist, B. and Majda, A., “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput, vol. 31, 629–51, 1977.
Mur, G., “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagnetic Compatibility, vol. 23, 377–82, 1981.
Berenger, J. P., “A perfectly matched player for the absorption of electromagnetic waves,” J. Computational Physics, vol. 114, 185–200, 1994.
Gedney, S. D., “An anisotropic Perfectly Matched Layers absorbing media for Finite Difference Time Domain simulation of fields in lossy dispersive media,” Electromagnetics, vol. 16, 399–415, 1996.
S. D. Gedney and A. Taflove, “Chapter 7: Perfectly matched layer absorbing boundary conditions,” in Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Taflove, A. and Hagness, S., Artech House, 2000.
Jensen, M. A. and Rahmat-Samii, Y., “Performance analysis of antennas for hand-held transceiver using Finite Difference Time Domain,” IEEE Trans. Antennas Propagat., vol. 42, 1106–13, 1994.
Elsherbeni, A. Z. and Rahmat-Samii, Y., Finite Difference Time Domain Analysis of Printed Microstrip Antennas for Personal Communication, Technical Report, Department of Electrical Engineering, University of California, Los Angeles, December 1996.
Taflove, A. and Hagness, S., “Chapter 5: Incident wave source conditions,” in Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Artech House, 2000.
J. Maloney and M. P. Kesler, “Chapter 13: Analysis of periodic structures,” in Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Taflove, A. and Hagness, S., Artech House, 2000.
Brillouin, L., Wave Propagation in Periodic Structures, 2nd edn., Dover Publications, 2003.
Xiao, S., Vahldieck, R., and Jin, H., “Full-wave analysis of guided wave structures using a novel 2-D Finite Difference Time Domain,” IEEE Microw. Guided Wave Lett., vol. 2 , no. 5, 165–7, 1992.
Cangellaris, A. C., Gribbons, M., and Sohos, G., “A hybrid spectral/Finite Difference Time Domain method for electromagnetic analysis of guided waves in periodic structures,” IEEE Microw. Guided Wave Lett., vol. 3 , no. 10, 375–7, 1992.
Chan, H. S., Lou, S. H., Tsang, L., and Kong, J. A., “Electromagnetic scattering of waves by random rough surface: a finite difference time domain approach,” Microwave Optical Tech. Lett., vol. 4, 355–9, 1991.
Harms, P., Mittra, R., and Ko, W., “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for Frequency Selective Surface structures,” IEEE Trans. Antennas and Propagation, vol. 42, 1317–24, 1994.
Roden, J. A., Gedney, S. D., Kesler, M. P., Maloney, J. G., and Harms, P. H., “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal Finite Difference Time Domain implementations,” IEEE Trans. Microwave Theory and Techniques, vol. 46 , no. 4, 420–7, 1998.
Veysoglu, M. E., Shin, R. T., and Kong, J. A., “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagnetic Waves and Applications, vol. 7, 1595–607, 1993.
Ren, J., Gandhi, O. P., Walker, L. R., Fraschilla, J., and Boerman, C. R., “Floquet-based Finite Difference Time Domain analysis of two-dimensional phased array antennas,” IEEE Microwave and Guided Wave Lett., vol. 4, 109–12, 1994.
Holter, H. and Steyskal, H., “Infinite phased-array analysis using Finite Difference Time Domain periodic boundary conditions – pulse scanning in oblique directions,” IEEE Trans. Antennas and Propagation, vol. 47, 1508–14, 1999.
Marek, J. R. and MacGillivary, J., “A method for reducing run-times of out-of-core Finite Difference Time Domain problems,” Proc. 9th Annual Review of Progress in Applied Computational Electromagnetics, Montery, CA, pp. 344–51, March 1993.
Aminian, A. and Rahmat-Samii, Y., “Spectral Finite Difference Time Domain: a novel computational technique for the analysis of periodic structures,” IEEE APS Int. Symp. Dis., vol. 3, pp. 3139–42, June 2004.
Yang, F., Chen, J., Qiang, R., and Elsherbeni, A., “Finite Difference Time Domain analysis of periodic structures at arbitrary incidence angles: a simple and efficient implementation of the periodic boundary conditions,” IEEE APS Int. Symp. Dis., vol. 3, pp. 2715–18, 2006.
Collin, R. E., Field Theory of Guided Waves, 2nd edn., Wiley-IEEE Express, 1990.
Zhang, K. and Li, D., Electromagnetic Theory for Microwaves and Optoelectronics, 2nd edn., Publishing House of Electronics Industry, 2001.
Al-Zoubi, A., Yang, F., and Kishk, A., “A low profile dual band surface wave antenna with a monopole like pattern,” IEEE Trans. Antennas Propagat., vol. 55 , no. 12, 3404–12, 2007.
Munk, B. A., Frequency Selective Surface, John Wiley & Sons, Inc., 2000.
Huang, J., “The development of inflatable array antennas,” IEEE Antennas Propagat. Mag., vol. 43 , no. 4, 44–50, 2001.
Engheta, N. and Ziolkowski, R., Metamaterials: Physics and Engineering Explorations, John Wiley & Sons Inc., 2006.
Yang, F., Chen, J., Rui, Q., and Elsherbeni, A., “A simple and efficient Finite Difference Time Domain/Periodic Boundary Condition algorithm for periodic structure analysis,” Radio Sci., vol. 42 , no. 4, RS4004, July 2007.
Gianvittorio, J., Romeu, J., Blanch, S., and Rahmat-Samii, Y., “Self-similar prefractal frequency selective surfaces for multiband and dual-polarized applications,” IEEE Trans. Antennas and Propagation, vol. 51 , no. 11, 3088–96, 2003.
Pelton, E. L. and Munk, B. A., “Scattering from periodic arrays of crossed dipoles,” IEEE Trans. Antennas and Propagation, vol. 27 , no. 3, 323–30, 1979.
Mosallaei, H. and Rahmat-Samii, Y., “Periodic bandgap and effective dielectric materials in electromagnetics: characterization and applications in nanocavities and waveguides,” IEEE Trans. Antennas and Propagation, vol. 51 , no. 3, 549–63, 2003.
Aminian, A., Yang, F., and Rahmat-Samii, Y., “Bandwidth determination for soft and hard ground planes by spectral Finite Difference Time Domain: a unified approach in visible and surface wave regions,” IEEE Trans. Antennas Propagat., vol. 53 , no. 1, 18–28, 2005.
Yang, F., Elsherbeni, A., and Chen, J., “A hybrid spectral-Finite Difference Time Domain/Auto-Regressive Moving Average method for periodic structure analysis,” IEEE APS Int. Symp. Dis., Hawaii, June 2007.
Hua, Y. and Sarkar, T. K., “Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise,” IEEE Trans. Accoustics Speech and Signal Processing, vol. 38 , no. 5, 1990.
Ko, W. and Mittra, R., “A combination of FD-TD and Prony's methods for analyzing microwave integrated circuits,” IEEE Trans. Microwave Theory Tech., vol. 39, 2176–81, 1991.
Bi, Z., Shen, Y., Wu, K., and Litva, J., “Fast Finite Difference Time Domain analysis of resonators using digital filtering and spectrum estimation,” IEEE Trans. Microwave Theory Tech., vol. 40, 1611–19, 1992.
Kuempel, W. and Wolff, L., “Digital signal processing of time domain field simulation results using the system identification method,” IEEE MTT-S Int. Symp. Dig., vol. 2, pp. 793–6, June 1992.
Housmand, B., Huang, T. W., and Itoh, T., “Microwave structure characterization by a combination of Finite Difference Time Domain and system identification methods,” IEEE Microwave Guided Wave Lett., vol. 3, 262–4, August 1993.
Chen, J., Wu, C., Lo, T., Wu, K.-L., and Litva, J., “Using linear and non-linear predictors to improve the computational efficiency of the FD-TD algorithm,” IEEE Trans. Microwave Theory Tech., vol. 42, 1992–7, September 1994.
Shaw, A. K. and Naishadham, K., “Auto-Regressive Moving Average-based time-signature estimator for analyzing resonant structures by the Finite Difference Time Domain method,” IEEE Trans. Antennas Propagat., vol. 49, 327–39, 2001.
Yang, F. and Rahmat-Samii, Y., “Microstrip antenna analysis using fast Finite Difference Time Domain methods: a comparison of Prony and Auto-Regressive Moving Average techniques,” Proceedings of 3rd International Conference on Microwave and Millimeter Wave Technology, 661–4, Beijing, August 17–19, 2002.