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Green's Function Expansions in Dyadic Root Functions for Shielded Layered Waveguides
By
, Vol. 39, 61-91, 2003
Abstract
Dyadic Green's functions for inhomogeneous parallel-plate waveguides are considered. The usual residue series form of the Green's function is examined in the case of modal degeneracies, where secondorder poles are encountered. The corresponding second-order residue contributions are properly interpreted as representing "associated functions" of the structure by constructing a new dyadic root function representation of the Hertzian potential Green's dyadic. The dyadic root functions include both eigenfunctions (corresponding to first-order residues) and associated functions, analogous to the idea of Jordan chains in finite-dimensional spaces. Numerical results are presented for the case of a two-layer parallel-plate waveguide.
Citation
, "Green's Function Expansions in Dyadic Root Functions for Shielded Layered Waveguides," , Vol. 39, 61-91, 2003.
doi:10.2528/PIER02082205
http://www.jpier.org/PIER/pier.php?paper=0208225
References

1. Hanson, G. W. and A. B. Yakovlev, Operator Theory for Electromagnetics: An Introduction, Springer, New York, 2001.

2. Gohberg, I. C. and M. G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators, American Mathematical Society, Providence, RI, 1969.

3. Shevchenko, V. V., "Spectral expansions in eigenfunctions and associated functions of a non-self-adjoint Sturm-Liouville problem on the whole real line," Differential Equations (translated from Differentsial'nye Uravneniya), Vol. 15, No. 11, 1431-1443, 1979.

4. Kresnushkin, P. E. and E. I. Moiseev, "Excitation of forced oscillations in a layered radio-wave guide," Sov. Phys. Dokl., Vol. 27, No. 6, 458-460, 1983.

5. Shevchenko, V. V., "The transverse boundary-value problem for the eigenwaves in a dielectric waveguide (rigorous theory)," Radio Engineering and Electronic Physics (translated from Radiotekhnika i Elektronika), Vol. 27, No. 1, 1-10, 1982.

6. Shevchenko, V. V., "Excitation of waves in the presence of associated waves," J. Communications Tech. and Electronics (translated from Radiotekhnika i Elektronika), Vol. 31, No. 7, 26-35, 1986.

7. Gureev, A. V., "Properties of normal and adjoined waves in screened inhomogeneous waveguides," Radiophysics and Quantum Electronics (translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Vol. 33, No. 8, 701-709, 1991.

8. Shevchenko, V. V., "Degeneracy and quasi-degeneracy of the spectrum and transformation of waves in dielectric and optical waveguides: a review," J. Communications Tech. and Electronics (translated from Radiotekhnika i Elektronika), Vol. 45, No. 10, 1039-1048, 2000.

9. Ilyinsky, A. S., G. Ya. Slepyan, and A. Ya. Slepyan, Propagation, Scattering and Dissipation of Electromagnetic Waves, Peregrinus, London, 1993.

10. Yakovlev, A. B. and G. W. Hanson, "On the nature of critical points in leakage regimes of a conductor-backed coplanar strip line," IEEE Trans. Microwave Theory Tech., Vol. 45, No. 1, 87-94, 1997.
doi:10.1109/22.552036

11. Hanson, G. W. and A. B. Yakovlev, "An analysis of leaky-wave dispersion phenomena in the vicinity of cutoff using complex frequency plane singularities," Radio Science, Vol. 33, No. 4, 803-820, 1998.
doi:10.1029/98RS01440

12. Hanson, G. W. and A. B. Yakovlev, "Investigation of mode interaction on planar dielectric waveguides with loss and gain," Radio Science, Vol. 34, No. 6, 1349-1359, 1999.
doi:10.1029/1999RS900096

13. Yakovlev, A. B. and G. W. Hanson, "Analysis of mode coupling on guided-wave structures using Morse critical points," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 7, 966-974, 1998.
doi:10.1109/22.701450

14. Yakovlev, A. B. and G. W. Hanson, "Mode transformation and mode continuation regimes on waveguiding structures," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 1, 67-75, 2000.
doi:10.1109/22.817473

15. Yakovlev, A. B. and G. W. Hanson, "Fundamental modal phenomena on isotropic and anisotropic planar slab dielectric waveguides," IEEE Trans. Ant. Prop. (in press), No. 3, 2003.

16. Hanson, G. W., A. B. Yakovlev, and J. Hao, "Leaky-wave analysis of transient fields due to sources in planarly-layered media," IEEE Trans. Ant. Prop. (in press), No. 12, 2002.

17. Bagby, J. S. and D. P. Nyquist, "Dyadic Green's functions for integrated electronic and optical circuits," IEEE Trans. Microwave Theory Tech., Vol. MTT-35, No. 2, 206-210, 1987.

18. Nosich, A. I., "Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering," J. Electromagn. Waves Applications, Vol. 8, No. 3, 329-353, 1994.

19. Nosich, A. I., "Foundations of the theory of open waveguides," J. Telecommun. Infor. Tech., 42-45, 2000.

20. Lindell, I. V., Methods for Electromagnetic Field Analysis, IEEE Press, Piscataway, NJ, 1995.

21. Naimark, M. A., Linear Differential Operators, Part I, Frederick Ungar, New York, 1967.

22. Baumgartel, H., Analytic Perturbation Theory for Matrices and Operators, Birkhauser Verlag, Boston, 1984.

23. Keldysh, M. V., "On eigenvalues and eigenfunctions for some classes of non-selfadjoint equations," Dokl. Akad. Nauk SSSR 77 (in Russian), 11-14, 1951.

24. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd edition, Cambridge University Press, Cambridge, 1992.