Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-10-31T07:28:34.256Z Has data issue: false hasContentIssue false

2 - FDTD method for periodic structure analysis

Published online by Cambridge University Press:  06 July 2010

Fan Yang
Affiliation:
University of Mississippi
Yahya Rahmat-Samii
Affiliation:
University of California, Los Angeles
Get access

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.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Itoh, T., ed. Numerical Techniques for Microwave and Millimeter-wave Passive Structures, Wiley-Interscience, 1989.Google Scholar
Taflove, A. and Hagness, S., Computational Electrodynamics: The Finite Difference Time Domain Method, 2nd edn., Artech House, 2000.Google Scholar
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.Google Scholar
Jensen, M. A., Time-Domain Finite-Difference Methods in Electromagnetics: Application to Personal Communication, Ph.D. dissertation at University of California, Los Angeles, 1994.Google Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Engquist, B. and Majda, A., “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput, vol. 31, 629–51, 1977.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Berenger, J. P., “A perfectly matched player for the absorption of electromagnetic waves,” J. Computational Physics, vol. 114, 185–200, 1994.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Brillouin, L., Wave Propagation in Periodic Structures, 2nd edn., Dover Publications, 2003.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Collin, R. E., Field Theory of Guided Waves, 2nd edn., Wiley-IEEE Express, 1990.CrossRefGoogle Scholar
Zhang, K. and Li, D., Electromagnetic Theory for Microwaves and Optoelectronics, 2nd edn., Publishing House of Electronics Industry, 2001.Google Scholar
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.CrossRefGoogle Scholar
Munk, B. A., Frequency Selective Surface, John Wiley & Sons, Inc., 2000.CrossRefGoogle Scholar
Huang, J., “The development of inflatable array antennas,” IEEE Antennas Propagat. Mag., vol. 43 , no. 4, 44–50, 2001.CrossRefGoogle Scholar
Engheta, N. and Ziolkowski, R., Metamaterials: Physics and Engineering Explorations, John Wiley & Sons Inc., 2006.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×