The continuum of an open waveguide describes radiation as simply, in principle, as the discrete spectrum of a classical guide describes any physical field in it. In fact, the knowledge of the modal spectra for open waveguides allows us to apply to discontinuity problems in open environments the same techniques originally developed for closed waveguides. However, this part of the spectrum, the continuum, has received little attention for most open guides. Therefore, this Chapter is devoted to an introduction of the continuum. The Chapter can be considered to be divided into two parts. In the first part we introduce the main characteristics of this part of the spectrum. In the second part we exemplify the procedure by deriving the continuum for some practical transmission lines such as coplanar, rib and inset waveguides.

In particular, in Section 7.1 we explore the main ideas which lead to finding the continuum and we also discuss its main features. In order to illustrate such a derivation we establish the continuum of a flange-backed rectangular waveguide slotted on its narrow wall as, in this example, the lack of a dielectric layer significantly simplifies the problem. In fact, the flange backed rectangular waveguide does not possess any bound mode; moreover the fields can be considered as purely TE, without the need to introduce hybrid fields. Note that, in this case, the continuum is derived by considering the phase shift imposed on a plane wave incident from infinity by the presence of the slot and of the...