Contents I. Introduction
Coaxial probes are often used as transitions to rectangular or parallel-plate waveguides. Such transitions have been studied in great detail by numerous authors [1]–[7]. When the geometry is separable, there are basically two ways of facing the problem. The first way requires dividing the problem in a number of canonical regions, expanding the fields in terms of the solutions of the Helmholtz equation in these regions, and enforcing the tangential-field continuity at the boundaries between them. This technique is commonly known as mode matching and some good examples of application to the problem of our concern are discussed in [1]–[4]. The second approach entails the use of the specialized Green's functions of the sources present within the guide [7]. Conventionally, mode-matching solutions are adopted over specialized Green's functions. A number of reasons can be alleged for this preference. Firstly because, for separable geometries, field solutions may be more straightforward to formulate. Secondly, this type of methods can cope with a fairly large variety of geometries of practical interest, such as coaxial sleeves [4], top-hat loading [1], multilayer insulation [5], etc., and thirdly, due to the recognized accuracy and computational efficiency of these methods.
