The field generated by an arbitrary current distribution within a waveguide

Abstract

Formulas a re deri ved for t h e electromag netic field ge nerated by an a rbi t ra ry current d ist rib ut io n wit hin waveguid es of rectang ular, circular, and coaxia l cross Rect io ns. These formula s are ob ta in ed by ge nera li zing a na logous formula s obtained in a previo us paper 2 for cavities of th,e sam e cr oss sectio n. As a check on t h e formulas, it is sh ow n t hat t he fi eld from a n axially d irected dip ole w it h in a circular g uide redu ces to t he free s pace valu e a t he radius increase indefi nite ly.

Transversal Waves in Electromagnetics: A Survey with New Generalizations

“…These have been addressed, for the case of uniform dielectrics, by several authors (Balanis, 1989;Collin, 1973Collin, , 1991Felsen & Marcuvitz, 1973;Freeman, 1950;Kurokawa, 1958). Discussion of source conditions is deferred to the section on "Weaker Sufficient Conditions," where we treat the more general case.…”

“…Several authors (Balanis, 1989;Collin, 1973Collin, , 1991Felsen & Marcuvitz, 1973;Freeman, 1950;Harrington, 1961;Kurokawa, 1958;Tai, 1971;Van Bladel, 1952) have obtained results on this issue for separate cases of (i) variable ε, µ but no sources and (ii) certain types of sources but uniform ε, µ. We shall present here a series of theorems that generalize these results and ultimately show that the TE/TM modes are complete for arbitrary (and not merely piecewise constant) z-variation of ε, µ and arbitrary sources.…”

“…Some time ago a series of technical papers (Collin, 1973;Freeman, 1950;Kurokawa, 1958;Van Bladel, 1952) addressed the issue of the completeness of the TE/TM "modes" in the presence of arbitrary current sources (and homogeneous media); in fact, Collin's (1973) conclusive paper in the series was titled "On the Incompleteness of E and H Modes in Wave Guides." It is important to note that these authors were concerned with whether certain specific sets of eigenfunctions, each of which was TE or TM, were complete, and not with the issue of completeness of TE/TM decompositions in general.…”