Document Type



contour integrals; Laplace transform; microwave tubes; modes of propagation; surface impedance; wave guides


Guided wave propagation is studied for the interior of circularly cylindrical domains; on the (cylindrical) boundary the ratios E2/Hφ and H2/Eφ are assigned functions of frequency and position, called surface impedances. Even in the case where the impedances are independent of position on the wall, the normal modes of propagation (expressed in terms of certain Bessel functions) do not form an orthogonal set on sections of the guide normal to the propagation direction. It follows that mode relative amplitudes cannot be determined by a Fourier-Bessel expansion of steady-state fields given on an input plane. To determine those amplitudes, the author introduces the Laplace transforms of Maxwell's equations, which are solved for the transforms of the field components E and H in the case that the impedances are (at most) functions of frequency. However, this method of analysis shows that the transform provides a method of attacking the variable impedance case. An example is then given, in which the transform of the axial component E, is inverted explicitly in the axially symmetric case for a simple choice of input field. The author concludes with some remarks on representation of electromagnetic fields by contour integrals, of which the Laplace inversion integral is a special case.

Publication Date

June 1973

Journal Title

Proceedings of the Iowa Academy of Science





First Page


Last Page



©1973 Iowa Academy of Science, Inc.



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