volume | PIER Journals

Abstract

In this paper, we present a procedure to calculate the discrete modes propagated with Crank-Nicolson FDTD in metallic waveguides. This procedure enables the correct excitation of this kind of waveguides at any resolution. The problem is reduced to solving an eigenvalue equation, which is performed, both in a closed form, for the usual rectangular waveguide, and numerically in the most general case, validated here with a ridged rectangular waveguide.

1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, 302-307, Mar. 1966.
doi:10.1109/TAP.1966.1138693

2. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Boston, MA, 2005.

3. Zheng, F., Z. Chen, and J. Zhang, "A Finite-Difference Time-Domain method without the Courant stability conditions," IEEE Microwave Guided Wave Letters, Vol. 9, No. 11, 441-443, 1999.
doi:10.1109/75.808026

4. Namiki, T., "A new FDTD algorithm based on alternating-direction implicit method," IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 10, 2003-2007, 1999.
doi:10.1109/22.795075

5. Tan, E. L., "Unconditionally stable LOD-FDTD method for 3-D Maxwell's equations," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 2, 85-87, 2007.
doi:10.1109/LMWC.2006.890166

6. Liang, F. and G. Wan, "Fourth-order locally one-dimensional FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 14--15, 2035-2043, 2008.
doi:10.1163/156939308787538017

7. Lee, J. and B. Fornberg, "Some unconditionally stable time stepping methods for the 3D Maxwell's equations," Journal of Computational and Applied Mathematics, Vol. 166, 497-523, 2004.
doi:10.1016/j.cam.2003.09.001

8. Garcia, S. G., T.-W. Lee, and S. C. Hagness, "On the accuracy of the ADI-FDTD method," Antennas and Wireless Propagation Letters, Vol. 1, No. 1, 31-34, 2002.
doi:10.1109/LAWP.2002.802583

9. Garcia, S. G., R. G. Rubio, A. R. Bretones, and R. G. Martin, "On the dispersion relation of ADI-FDTD," IEEE Microwave and Wireless Components Letters, Vol. 16, No. 6, 354-356, Jun. 2006.
doi:10.1109/LMWC.2006.875619

10. Yang, Y., R. Chen, and E. Yung, "The unconditionally stable Crank-Nicolson FDTD method for three-dimensional Maxwell's equations," Microwave and Optical Technology Letters, Vol. 48, 1619-1622, 2006.
doi:10.1002/mop.21684

11. Yang, Y., H. Fan, D. Z. Ding, and S. B. Liu, "Application of the preconditioned GMRES to the Crank-Nicolson Finite-Difference Time-Domain algorithm for 3D full-wave analysis of planar circuits," Microwave and Optical Technology Letters, Vol. 50, No. 6, 1458-1463, 2008.
doi:10.1002/mop.23396

12. Garcia, S., R. G. Rubio, A. R. Bretones, and R. G. Lopez, "Revisiting the stability of Crank-Nicolson and ADI-FDTD," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 11, 3199-3203, 2007.
doi:10.1109/TAP.2007.908794

13. Rouf, H. K., F. Costen, and S. G. Garcia, "3D Crank-Nicolson Finite-Difference Time-Domain method for dispersive media," IET Electronics Letters, Vol. 45, No. 19, 961-962, 2009.
doi:10.1049/el.2009.1940

14. Rouf, H. K., F. Costen, S. G. Garcia, and S. Fujino, "On the solution of 3D frequency dependent Crank-Nicolson FDTD scheme," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2163-2175, 2009.
doi:10.1163/156939309790109261

15. Rouf, H. K., F. Costen, and S. G. Garcia, "3D Crank-Nicolson Finite-Difference Time-Domain method for dispersive media," IET Electronics Letters, Vol. 45, No. 19, 961-962, 2009.
doi:10.1049/el.2009.1940

16. Xu, K., Z. Fan, D. Z. Ding, and R. S. Chen, "GPU accelerated unconditionally stable Crank-Nicolson FDTD method for the analysis of three-dimensional microwave circuits," Progress In Electromagnetics Research, Vol. 102, 381-395, 2010.
doi:10.2528/PIER10020606

17. Celuch-Marcysiak, M. and W. K. Gwarek, "Formal equivalence and efficiency comparison of the FDTD, TLM and SN methods in application to microwave CAD programs," 21st European Microwave Conference, Vol. 1, 199-204, 1991.
doi:10.1109/EUMA.1991.336433

18. Railton, C. J. and J. P. McGeehan, "The use of mode templates to improve the accuracy of the finite difference time domain method," 21st European Microwave Conference, Vol. 2, 1278-1283, 1991.
doi:10.1109/EUMA.1991.336521

19. Jin, H., R. Vahldieck, and S. Xiao, "A full-wave analysis of arbitrary guiding structures using a two dimensional TLM mesh," 21st European Microwave Conference, Vol. 1, 205-210, 1991.
doi:10.1109/EUMA.1991.336434

20. Arndt, F., V. Brankovic, and D. V. Krupezevic, "An improved FDTD full wave analysis for arbitrary guiding structures using a two-dimensional mesh," IEEE MTT-S International Microwave Symposium, Vol. 1, 389-392, 1992.

21. Asi, A. and L. Shafai, "Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD," IET Electronics Letters, Vol. 28, No. 15, 1451-1452, 1992.
doi:10.1049/el:19920923

22. Gwarek, W. K., T. Morawski, and C. Mroczkowski, "Application of the FDTD method to the analysis of circuits described by the two-dimensional vector wave equation," IEEE Transactions on Microwave Theory and Techniques, Vol. 41, No. 2, 311-317, 1993.
doi:10.1109/22.216473

23. Xiao, S., R. Vahldieck, and H. Jin, "Full-wave analysis of guided wave structures using a novel 2-D FDTD," IEEE Microwave and Guided Wave Letters, Vol. 2, No. 5, 165-167, 1992.
doi:10.1109/75.134342

24. Gwarek, W. and M. Celuch-Marcysiak, "Wide-band S-parameter extraction from FDTD simulations for propagating and evanescent modes in inhomogeneous guides," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 8, 2003.
doi:10.1109/TMTT.2003.815265

25. Mrozowski, M., "Function expansion algorithms for the time-domain analysis of shielded structures supporting electromagnetic waves," International Journal of Numerical Modelling, Vol. 7, No. 1, 77-84, 1994.
doi:10.1002/jnm.1660070203

26. Hadi, M. F. and S. F. Mahmoud, "Optimizing the compact-FDTD algorithm for electrically large waveguiding structures," Progress In Electromagnetics Research, Vol. 75, 253-269, 2007.
doi:10.2528/PIER07060703

27. Luo, S. and Z. Chen, "An efficient modal FDTD for absorbing boundary conditions and incident wave generator in waveguide structures," Progress In Electromagnetics Research, Vol. 68, No. 229, 2007.

28. Garcia, S., A. Bretones, M. Pantoja, and R. Lopez, "Yet another look at FDTD numerical errors," IEEE Antennas and Propagation Magazine, Vol. 49, No. 3, 156-161, 2007.
doi:10.1109/MAP.2007.4293958

Professor Salvador Gonzalez Garcia

Prof. Fumie Costen

Dr. Mario Fernandez Pantoja

Mr. Luis Diaz Angulo

Dr. Jesus Alvarez