For TM and for TE primary excitations, the parallel-plate-fed slot antenna is studied with the aim of optimising its matching efficiency and improving its gain via an internal and an external strip conductor in conjunction with multilayered dielectrics that fill the waveguide section. The relevant boundary-value problems are formulated exactly via systems of
singular integral-integrodifferential equations. For the solution, an exponentially converging Galerkin method and a recently developed exponentially converging Nystrцm method are independently applied. Both methods yield computationally efficient analytical expressions—requiring no numerical computation of spectral integrals—for all matrix elements. Both these methods are highly accurate, with their respective results coinciding within 11–13 significant figures in all numerical examples that have been carried out. The main conclusion of the paper is that both the gain and the matching efficiency of the antenna can be drastically improved by prop