An open waveguide may be defined as any physical device, with longitudinal axial symmetry and unbounded cross-section, capable of guiding electromagnetic waves. In contrast to closed waveguides, the electromagnetic field in the cross-section is not confined to a limited region of space, thus extending up to infinity. Examples of closed waveguides are well-known from basic electromagnetic courses [21]; they include coaxial cables, metallic waveguides (with rectangular or circular cross-section), etc. Their spectrum is also well-known, being made by an infinite, discrete set of modes, orthogonal and complete over the waveguide cross-section. On the other hand, any waveguide not entirely enclosed in a metal shielding, may be taken as an example of an open waveguide. It is also worth noting that, by cutting a slot parallel to the longitudinal axis in the metal enclosure of a closed waveguide, again an open waveguide is obtained. An open waveguide possesses a spectrum which is no longer discrete, but is constituted by a few bound modes, when present, plus a continuum of modes. In the next Chapter, in Section 2.8, we introduce the concept of the continuous spectrum of open waveguides, which is of fundamental importance throughout this book, by making reference to the well-known case of a closed 2D-waveguide of bounded cross-section with a well-defined modal spectrum, i.e. to a parallel plate waveguide. By removing to infinity one of the plates we obtain the case of a half-space, bounded on one side by the metal plate and unbounded on the other side.