2012-09-25
Computation of the Modes of Elliptic Waveguides with a Curvilinear 2D Frequency-Domain Finite-Difference Approach
By
Progress In Electromagnetics Research M, Vol. 26, 69-84, 2012
Abstract
A scalar Frequency-Domain Finite-Difference approach to the mode computation of elliptic waveguides is presented. The use of an elliptic cylindrical grid allows us to take exactly into account the curved boundary of the structure and a single mesh has been used both for TE and TM modes. As a consequence, a high accuracy is obtained with a reduced computational burden, since the resulting matrix is highly sparse.
Citation
Alessandro Fanti, Giuseppe Mazzarella, Giorgio Montisci, and Giovanni Andrea Casula, "Computation of the Modes of Elliptic Waveguides with a Curvilinear 2D Frequency-Domain Finite-Difference Approach," Progress In Electromagnetics Research M, Vol. 26, 69-84, 2012.
doi:10.2528/PIERM12080806
References

1. Conciauro, G., et al. "Waveguide modes via an integral equation leading to a linear matrix eigenvalue problem," IEEE Trans. Microwave Theory Techniques,, Vol. 32, 1495-1504, 1984.
doi:10.1109/TMTT.1984.1132880        Google Scholar

2. Accatino, L., et al. "Elliptical cavity resonators for dual-mode narrowband filters," IEEE Trans. Microwave Theory Techniques, 2393-2401, 1997.
doi:10.1109/22.643850        Google Scholar

3. Wexler, A., "Solution of waveguide discontinuities by modal analysis," IEEE Trans. Microwave Theory Techniques, Vol. 15, 508-517, 1967.
doi:10.1109/TMTT.1967.1126521        Google Scholar

4. Chan, K. L. and S. R. Judah, "Mode-matching analysis of a waveguide junction formed by a circular and a larger elliptic waveguide," IEE Proc. Microw. Antennas Propag, Vol. 145, 123-127, 1998.
doi:10.1049/ip-map:19981216        Google Scholar

5. Collin, R. E., Field Theory of Guided Waves, 2nd Ed., Ch. 7, Wiley-IEEE Press, 2001.

6. Mazzarella, G., G. Montisci, and , "Accurate modeling of coupling junctions in dielectric covered waveguide slot arrays," Progress In Electromagnetics Research M, Vol. 17, 59-71, 2011.        Google Scholar

7. Montisci, G., G. Mazzarella, and G. A. Casula, "Effective analysis of a waveguide longitudinal slot with cavity," IEEE Trans. Antennas Propag., Vol. 60, 3104-3110, 2012.
doi:10.1109/TAP.2012.2196953        Google Scholar

8. Mazzarella, G. and G. Montisci, "Wideband equivalent circuit of a centered-inclined waveguide slot coupler," Journal of Electromagnetic Waves and Applications, Vol. 14, No. 1, 133-151, 2000.
doi:10.1163/156939300X00671        Google Scholar

9. Casula, G. A., G. Mazzarella, and G. Montisci, "Effective analysis of a microstrip slot coupler," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 9, 1203-1217, 2004.
doi:10.1163/1569393042955333        Google Scholar

10. Mazzarella, G. and G. Montisci, "A rigorous analysis of dielectric-covered narrow longitudinal shunt slots with finite wall thickness," Electromagnetics, Vol. 19, 407-418, 1999.
doi:10.1080/02726349908908660        Google Scholar

11. Mazzarella, G. and G. Montisci, "Accurate characterization of the interaction between coupling slots and waveguide bends in waveguide slot arrays," IEEE Trans. Microwave Theory Techniques, Vol. 48, 1154-1157, 2000.
doi:10.1109/22.848500        Google Scholar

12. Casula, G. A., G. Mazzarella, and G. Montisci, "Effect of the feeding t-junctions in the performance of planar waveguide slot arrays," IEEE Antennas and Wireless Propag. Letters, Vol. 11, 953-956, 2012.
doi:10.1109/LAWP.2012.2213233        Google Scholar

13. Chu, L. J., "Electromagnetic waves in elliptic hollow pipes of metal ," J. Appl. Phys., Vol. 9, 583-591, 1938.
doi:10.1063/1.1710459        Google Scholar

14. Marcuvitz, N., Waveguide Handbook, Peregrinius, 1986.
doi:10.1049/PBEW021E

15. Kretzschmar, J. G., "Wave propagation in hollow conducting elliptical waveguides," IEEE Trans. Microwave Theory Techniques, Vol. 18, 547-554, 1970.
doi:10.1109/TMTT.1970.1127288        Google Scholar

16. Zhang, S. and Y. Chen, "Eigenmodes sequence for an elliptical waveguides with arbitrary ellipticity," IEEE Trans. Microwave Theory Techniques,, Vol. 43, 227-230, 1995.
doi:10.1109/22.362983        Google Scholar

17. Shu, C., "Analysis of elliptical waveguides by differential quadrature method," IEEE Trans. Microwave Theory Techniques, Vol. 48, 319-322, 2000.
doi:10.1109/22.821786        Google Scholar

18. Weiland, T., "Three dimensional resonator mode computation by finite difference method," IEEE Trans. Magn., Vol. 21, 2340-2343, 1985.
doi:10.1109/TMAG.1985.1064178        Google Scholar

19. Fanti , A., G. Mazzarella, and G. Montisci, "Curvilinear vector finite difference approach to the computation of waveguide modes," Advanced Electromagnetics, Vol. 1, 29-37, 2012.        Google Scholar

20. Zhao, , Y. J., K. L. Wu, and K. K. M. Cheng, "A compact 2-D full-wave finite-difference frequency-domain method for general guided wave structures," IEEE Trans. Microwave Theory Techniques, Vol. 50, 1844-1848, 2002.
doi:10.1109/TMTT.2002.800447        Google Scholar

21. Hwang, J. N., "A compact 2-D FDFD method for modeling microstrip structures with nonuniform grids and perfectly matched layer," IEEE Trans. Microwave Theory Techniques, Vol. 53, 653-659, 2005.
doi:10.1109/TMTT.2004.840569        Google Scholar

22. Kuzu, L., V. Demir, A. Z. Elsherbeni, and E. Arvas, "Electromagnetic scattering from arbitrarily shaped chiral objects using the ¯nite di®erence frequency domain method," Progress In Electromagnetics Research,, Vol. 67, 1-24, 2007.
doi:10.2528/PIER06083104        Google Scholar

23. Podwalski, J., P. Kowalczyk, and M. Mrozowski, "Efficient multiscale finite difference frequency domain analysis using multiple macromodels with compressed boundaries," Progress In Electromagnetics Research, Vol. 126, 463-479, 2012.
doi:10.2528/PIER12012008        Google Scholar

24. Rumpf, R. C., "Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain," Progress In Electromagnetics Research B, Vol. 36, 221-248, 2012.
doi:10.2528/PIERB11092006        Google Scholar

25. Lovranos, C. S. and G. A. Kyriacou, "Eigenvalue analysis of curved waveguides employing an orthogonal curvilinear frequency-domain finite-difference method," IEEE Trans. Microwave Theory Techniques, Vol. 57, 594-611, 2009.
doi:10.1109/TMTT.2009.2013314        Google Scholar

26. Taflove, A., Advances in Computational Electrodynamics --- The FDTD Method, Artech House, 1995.

27. Xiao, S., R. Vahldieck, and H. Jin, "Full-wave analysis of guided wave structures using a novel 2-D FDTD," IEEE Microwave Guided Wave Lett., Vol. 2, 165-167, 1992.
doi:10.1109/75.134342        Google Scholar

28. Choi, D. H. and W. J. R. Hoefer, "The finite-difference-time-domain method and its applications to eigenvalue problems," IEEE Trans. Microwave Theory Techniques, Vol. 34, 1464-1470, 1986.
doi:10.1109/TMTT.1986.1133564        Google Scholar

29. Fanti, A. and G. Mazzarella, "Finite differences single grid evaluation of TE and TM modes in metallic waveguides," Loughborough Antennas Propag. Conf., 517-520, Loughborough,UK, 2010.        Google Scholar

30. Itoh, T., Numerical Techniques for Microwave and Millimeter-wave Passive Structures, Sect. 1.1, Wiley, 1989.

31. Golub, G. H. and C. F. Van Loan, "The Matrix Computations," The Johns Hopkins University Press, Baltimore MD, 1996.        Google Scholar