An analytical formulation based on physical optics is employed to determine the field and the radiated power distribution by open-ended circular waveguides. Using the incomplete Hankel functions, the line integrals yielding the electromagnetic field are evaluated in closed analytical form along the waveguide axis. It is shown that cylindrical waves are generated by the surface currents flowing on the waveguide walls, while spherical waves are produced by the currents and charges excited at the waveguide truncation. Cylindrical and spherical waves are shown to be responsible for the field synthesis in terms of waveguide modes and scattered fields at the waveguide mouth. Numerical results concerning the spatial distribution of the electromagnetic field and associated power density are compared with previously published results, showing the advantage of the incomplete Hankel functions formulation. Finally, the uniform asymptotic representation of the incomplete Hankel function is shown to be suitable to compute the field distribution on the waveguide axis except for the TE11 and TM01 modes.
1. Li, L. W., L. Zhou, M. S. Leong, T. S. Yeo, and P. S. Kooi, "An open-ended circular waveguide with an infinite conducting flange covered by a dielectric hemi-spherical radome shell: Fullwave analysis and Green's dyadics," Progress In Electromagnetics Research, Vol. 21, 221-245, 1999. doi:10.2528/PIER98080301
2. Li, B., B. Wu, and C.-H. Liang, "High gain circular waveguide array antenna using electromagnetic band-gap structure," J. Electromagn. Waves Appl., Vol. 20, No. 7, 955-966, 2006. doi:10.1163/156939306776149860
3. Lo, Y. T. and S. W. Lee, Antenna Handbook:The ory, Applications and Design, Van Nostrand Reinhold Company, New York, 1988.
4. Balanis, C. A., Antenna Theory:A nalysis and Design, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1982.
5. Jones, D. S., Acoustic and Electromagnetic Waves, Clarendon Press, Oxford, 1986.
6. Maci, S., F. Capolino, and F. Mioc, "Line integral representation of the modal radiation for an open-ended waveguide," IEEE Trans. Antennas Propagat., Vol. 45, No. 12, 1885-1887, 1997. doi:10.1109/8.650211
7. Ling, H., S. Lee, and R. Chou, "High-frequency RCS of open cavities with rectangular and circular cross sections," IEEE Trans. Antennas Propagat., Vol. 37, No. 5, 648-654, 1989. doi:10.1109/8.24193
8. Obelleiro, F., J. L. Rodriguez, and R. J. Burkholder, "An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities," IEEE Trans. Antennas Propagat., Vol. 43, No. 4, 356-361, 1995. doi:10.1109/8.376032
9. Naqvi, Q. A., A. A. Rizvi, and Z. Yaqoob, "Scattering of electromagnetic waves from a deeply burried circular cylinder," Progress In Electromagnetics Research, Vol. 27, 37-59, 2000. doi:10.2528/PIER99061401
10. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor cylinder," J. Electromagn. Waves Appl., Vol. 20, No. 13, 1853-1860, 2006. doi:10.1163/156939306779292219
11. Zhong, X.-M., C. Liao, and W. Chen, "Image reconstruction of arbitrary cross section conducting cylinder using UWB pulse," J. Electromagn. Waves Appl., Vol. 21, No. 1, 25-34, 2007. doi:10.1163/156939307779391786
12. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, The Golem Press, Boulder, Colorado, 1969.
13. Cicchetti, R. and A. Faraone, "Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics," IEEE Trans. Antennas and Propagat., Vol. 52, No. 12, 3373-3389, 2004. doi:10.1109/TAP.2004.835269
14. Cicchetti, R. and A. Faraone, "On the optical behavior of the electromagnetic field excited by a semi-infinite electric travelingwave current," IEEE Trans. Antennas and Propagat., Vol. 53, No. 12, 4015-4025, 2005. doi:10.1109/TAP.2005.856360
15. Cicchetti, R. and A. Faraone, "Analysis of open-ended circular waveguides using physical optics and incomplete Hankel functions formulation," IEEE Trans. Antennas and Propagat., Vol. 55, No. 6, 1887-1892, 2007. doi:10.1109/TAP.2007.895639
16. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, U.K., 1962.