An analytical method for evaluating pole-residues in spectral method of moments (MoM) formulations is presented. Spectral integral formulations for periodic structures involve the inverse of the MoM matrix, which exhibits a periodic set of pole singularities, corresponding to the zeros of the matrix's determinant. So far, these singularities have not been extracted and the corresponding pole-residues were calculated directly from the differential or integral definitions of the residue. In this work, we consider an analytical expression for the solution to the MoM matrix equation, which enables the extraction of pole singularities and the analytical evaluation of pole-residues. We also present a comparison to previous methods.
2. Yang, H. Y. D. and D. R. Jackson, "Theory of line-source radiation from a metal-strip grating dielectric-slab structure," IEEE Trans. Antennas Propagation, Vol. 48, 556-563, April 2000.
3. Capolino, F., D. R. Jackson, and D. R. Wilton, "Mode excitation from sources in two-dimensional EBG structures using the array scanning method," IEEE Microwave and Wireless Components Letters, Vol. 15, 49-51, February 2005.
4. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Wave, IEEE Press, New Youk, 1994.
5. Olyslager, F. and H. Derudder, "Series representation of green dyadics for layered media using PMLs," IEEE Trans. Antennas Propagation, Vol. 51, 2319-2326, September 2003.
6. Mesa, F. and D. R. Jackson, "A novel approach for calculating the characteristic impedance of printed-circuit lines," IEEE Microwave and Wireless Components Letters, Vol. 15, 283-285, April 2005.
7. Das, N. K., "A new theory of the characteristic impedance of general printed transmission lines applicable when power leakage exists," IEEE Trans. Microwave Theory and Tech., Vol. 48, 1108-1117, July 2000.
8. Kreyszig, E., Advanced Engineering Mathematics, 7th Ed., 770-777, John Wiley and Sons, Inc, New-York, 1993.
9. Horn, R. A. and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
10. Baccarelli, P., P. Burghignoli, C. D. Nallo, F. Frezza, A. Galli, P. Lampariello, and G. Ruggieri, "Full-wave analysis of printed leaky-wave phased arrays," Int. J. RF and Microwave Computer Aided Eng., Vol. 12, 272-287, May-June 2002.
11. Capolino, F., D. R. Jackson, and D. R. Wilton, "Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source," IEEE Trans. Antennas Propagation, Vol. 53, 91-99, January 2005.
12. Kay, S. M., "Fundamentals of Statistical Signal Processing: Estimation Theory," Prentice Hall, 1993, 73-74.
13. Stewart, G. W., "On the adjugate matrix," Linear Algebra and its App., Vol. 283, 151-164, 1998.
14. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Numerical Recipes in C: The Art of Scientific Computing," Cambridge University Press, 1992, 371.