The high-order symplectic finite-difference time-domain scheme is applied to modeling and simulation of waveguide structures. First, the perfect electric conductor boundary is treated by the image theory. Second, to excite all possible modes, an efficient source excitation method is proposed. Third, the modified perfectly matched layer is extended to its high-order form for absorbing the evanescent waves. Finally, a high-order scattering parameter extraction technique is developed. The cases of waveguide resonator, waveguide discontinuities, and periodic waveguide structure demonstrate that the high-order symplectic finite-difference time-domain scheme can obtain better numerical results than the traditional finite-difference timedomain method and save computer resources.
Wei E. I. Sha,
"Waveguide Simulation Using the High-Order Symplectic Finite-Difference Time-Domain Scheme," Progress In Electromagnetics Research B,
Vol. 13, 237-256, 2009. doi:10.2528/PIERB09012302
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media ," IEEE Trans. on Antennas and Propagation, Vol. 14, 302-307, 1966. doi:10.1109/TAP.1966.1138693
2. Taflove, A., Computational Electrodynamics: The Finitedifference Time-domain Method, Artech House, Norwood, MA, 1995.
3. Christ, A. and H. L. Hartnagel, "Three-dimensional finitedifference method for the analysis of microwave-device embedding," IEEE Trans. on Microwave Theory and Techniques, Vol. 35, 688-696, 1987. doi:10.1109/TMTT.1987.1133733
4. Chu, S. T., W. P. Huang, and S. K. Chaudhuri, "Simulation and analysis of wave-guide based optical integrated-circuits," Computer Physics Communications, Vol. 68, 451-484, Nov. 1991. doi:10.1016/0010-4655(91)90213-5
5. Krupezevic, D. V., V. J. Brankovic, and F. Arndt, "Wave-equation FD-TD method for the efficient eigenvalue analysis and S-matrix computation of waveguide structures," IEEE Trans. on Microwave Theory and Techniques, Vol. 41, 2109-2115, 1993. doi:10.1109/22.260694
6. Vielva, L. A., J. A. Pereda, A. Prieto, and A. Vegas, "FDTD multimode characterization of waveguide devices using absorbing boundary conditions for propagating and evanescent modes," IEEE Microwave and Guided Wave Letters, Vol. 4, 160-162, 1994. doi:10.1109/75.294278
7. Zhao, A. P. and A. V. Raisanen, "Application of a simple and efficient source excitation technique to the FDTD analysis of waveguide and microstrip circuits," IEEE Trans. on Microwave Theory and Techniques, Vol. 44, 1535-1539, 1996. doi:10.1109/22.536601
8. Shibata, T. and T. Itoh, "Generalized-scattering-matrix modeling of waveguide circuits using FDTD field simulations," IEEE Trans. on Microwave Theory and Techniques, Vol. 46, 1742-1751, 1998. doi:10.1109/22.734574
9. Gwarek, W. K. and M. Celuch-Marcysiak, "Wide-band Sparameter extraction from FD-TD simulations for propagating and evanescent modes in inhomogeneous guides," IEEE Trans. on Microwave Theory and Techniques, Vol. 51, 1920-1928, 2003. doi:10.1109/TMTT.2003.815265
10. Wang, S. and F. L. Teixeira, "An equivalent electric field source for wideband FDTD simulations of waveguide discontinuities," IEEE Microwave and Wireless Components Letters, Vol. 13, 27-29, 2003. doi:10.1109/LMWC.2002.807714
11. Gwarek, W. K. and M. Celuch-Marcysiak, "Differential method of reflection coefficient extraction from FDTD simulations," IEEE Microwave and Guided Wave Letters, Vol. 6, 215-217, 1996. doi:10.1109/75.491510
12. Young, J. L., D. Gaitonde, and J. S. Shang, "Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach ," IEEE Trans. on Antennas and Propagation, Vol. 45, 1573-1580, Nov. 1997. doi:10.1109/8.650067
13. Yefet, A. and P. G. Petropoulos, "A staggered fourth-order accurate explicit finite difference scheme for the timedomain Maxwell's equations," Journal of Computational Physics, Vol. 168, 286-315, Apr. 2001. doi:10.1006/jcph.2001.6691
14. Krumpholz, M. and L. P. B. Katehi, "MRTD: New time-domain schemes based on multiresolution analysis," IEEE Trans. on Microwave Theory and Techniques, Vol. 44, 555-571, 1996. doi:10.1109/22.491023
15. Cao, Q. S., Y. C. Chen, and R. Mittra, "Multiple image technique (MIT) and anistropic perfectly matched layer (APML) in implementation of MRTD scheme for boundary truncations of microwave structures," IEEE Trans. on Microwave Theory and Techniques, Vol. 50, 1578-1589, Jun. 2002. doi:10.1109/TMTT.2002.1006420
16. Shao, Z., Z. Shen, Q. He, and G. Wei, "A generalized higher order finite-difference time-domain method and its application in guided-wave problems," IEEE Trans. on Microwave Theory and Techniques, Vol. 51, 856-861, 2003. doi:10.1109/TMTT.2003.808627
17. Hirono, T., W. Lui, S. Seki, and Y. Yoshikuni, "A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator," IEEE Trans. on Microwave Theory and Techniques, Vol. 49, 1640-1648, Sep. 2001. doi:10.1109/22.942578
18. Sha, W., Z. X. Huang, M. S. Chen, and X. L. Wu, "Survey on symplectic finite-difference time-domain schemes for Maxwell's equations," IEEE Trans. on Antennas and Propagation, Vol. 56, 493-500, Feb. 2008. doi:10.1109/TAP.2007.915444
19. Yoshida, H., "Construction of higher order symplectic integrators," Physica D: Nonlinear Phenomena, Vol. 46, 262-268, Nov. 1990.
20. Sha, W., X. L. Wu, Z. X. Huang, and M. S. Chen, "Maxwell's equations, symplectic matrix, and grid," Progress In Electromagnetics Research B, Vol. 8, 115-127, 2008. doi:10.2528/PIERB08052303
21. Sha, W., Z. X. Huang, X. L. Wu, and M. S. Chen, "Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation," Journal of Computational Physics, Vol. 225, 33-50, Jul. 2007. doi:10.1016/j.jcp.2006.11.027
22. Chen, B., D. G. Fang, and B. H. Zhou, "Modified Berenger PML absorbing boundary condition for FDTD meshes," IEEE Microwave and Guided Wave Letters, Vol. 5, 399-401, Nov. 1995. doi:10.1109/75.473529
23. Abarbanel, S. and D. Gottlieb, "A mathematical analysis of the PML method," Journal of Computational Physics, Vol. 134, 357, 1997. doi:10.1006/jcph.1997.5717
24. Sullivan, D. M., Electromagnetic Simulation Using the FDTD Method, Wiley-IEEE Press, New York, 2000.