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2013-04-17
Time-Domain Real-Valued TM-Modal Waves in Lossy Waveguides
By
Progress In Electromagnetics Research, Vol. 138, 675-696, 2013
Abstract
The waveguide has a perfectly conducting surface. Its cross section domain is bounded by a singly-connected contour of a rather arbitrary but enough smooth form. Possible waveguide losses are modeled by a homogeneous conductive medium in the waveguide. The boundary-value problem for the system of Maxwell's equations with time derivative is solved in the time domain. The real-valued solutions are obtained in Hilbert space L2 in a form of transverse-longitudinal decompositions. Every field component is a product of the vector element of the modal basis dependent on transverse coordinates, and the modal amplitudes dependent on time and the axial coordinate. Three examples are included. The dynamic properties of the modal waves and concomitant energetic waves are studied and their dependence on time illustrated graphically.
Citation
Oleg Tretyakov, and Mehmet Kaya, "Time-Domain Real-Valued TM-Modal Waves in Lossy Waveguides," Progress In Electromagnetics Research, Vol. 138, 675-696, 2013.
doi:10.2528/PIER13030206
References

1. Tretyakov, , O. A., F. Erden, and , "Evolutionary approach to electromagnetics as an alternative to the time-harmonic field method," IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting,, Jul. 2012.

2. Tretyakov, , O. A., , "Evolutionary equations for the theory of waveguides," IEEE AP-S Int. Symp. Dig., 2465-2471, Jun. 1994.

3. Tretyakov, , O. A., "Evolutionary waveguide equations," Soviet Journal on Communication Technology and Electronics (English Translation of Elektrosvyaz i Radiotekhnika), , Vol. 35, No. 2, 7-17, 1990.

4. Tretyakov, , O. A., , "Essentials of nonstationary and nonlinear electromagnetic field theory," Analytical and Numerical Methods in Electromagnetic Wave Theory,, 1993.

5. Aksoy, , S., O. A. Tretyakov, and , "Evolution equations for analytical study of digital signals in waveguides," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 12, 1665-1668, 2003.
doi:10.1163/156939303322760209

6. "http://www.springer.com/birkhauser/mathematics/journal/28.,".
doi:10.1163/156939303322760209

7. Tretyakov, , O. A., F. Erden, and , "Separation of the instantaneous and dynamic polarizations in studies of dispersive dielectrics," MSMW'07 Symposium Proceedings,, 42-48, Jun. 2007.

8. Erden, , F., O. A. Tretyakov, and , "Excitation by a transient signal of the real-valued electromagnetic fields in a cavity," Phys. Rev., E,, Vol. 77, 056605, May 2008.
doi:10.1103/PhysRevE.77.056605

9. Tretyakov, , O. A., O. Akgun, and , "Derivation of Klein-Gordon equation from Maxwell's Equations and study of relativistic time-domain waveguide modes," Progress In Electromagnetics Research,, Vol. 105, 171-191, 2010.
doi:10.2528/PIER10042702

10. Tretyakov, O. A. and The real-valued time-domain, "The real-valued time-domain TE-modes in lossy waveguides," Progress In Electromagn Research, Vol. 127, 405-426, 2012.
doi:10.2528/PIER12031402

11. Gabriel, , G. J., "Theory of electromagnetic transmission structures, Part I: Relativistic foundation and network formalism," Proc. IEEE,, Vol. 68, No. 3, 354-366, 1980.
doi:10.1109/PROC.1980.11646

12. Borisov, , V. V., , Transient Electromagnetic Waves, Leningrad Univ. Press, 1987.

13. Kristensson, , G., "Transient electromagnetic wave propagation in waveguides," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 5--6, 645-671, Sept. 1995.
doi:10.1163/156939395X00866

14. Shvartsburg, , A. B., "Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models)," Phys. Usp., Vol. 41, No. 1, 77-94, Jan. 1998..
doi:10.1070/PU1998v041n01ABEH000331

15. Slivinski, A. and E. Heyman, "Time-domain near-field analysis of short-pulse antennas | Part I: Spherical wave (multipole) expansion," IEEE Trans. on Antenn. and Propag.,, Vol. 47, 271-279, Feb. 1999.
doi:10.1109/8.761066

16. Geyi, , W., "A time-domain theory of waveguides," Progress In Electromagnetics Research, Vol. 59, 267-297, , 2006.

17. Dusseaux, , R., "Telegraphist's equations for rectangular waveguides and analysis in nonorthogonal coordinates," Progress In Electromagnetics Research, Vol. 88, 53-71, 2008.
doi:10.2528/PIER08101707

18. Polyanin, A. D., A. V. Manzhirov, and , "Handbook of Mathematics for Engineers and Scientists," Chapman & Hall/CRC Press, , 2006.

19. Polyanin, A. D., , Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, FL, 2002, Boca Raton, FL, 2002.

20. Miller, Jr., , W., " Symmetry and Separation of Variables," Addison-Wesley Publication Co., 1977.

21. Abramowitz, , M., I. A. Stegun, and , Handbook of Mathematical Functions, , Dover Publications, Inc., 1965.

22. Umov, , N. A., , "Ein theorem Äuber die wechselwirkungen in endlichen entfernungen," Zeitschrift FÄur Mathematik Und Physik, Vol. 97, 1874.

23. Poynting, , J. H., , "On the transfer of energy in the electromagnetic field," Philos. Trans. of the Royal Society of London, Vol. 175, 343-361, 1884.
doi:10.1098/rstl.1884.0016