In this Chapter we study, in a rigorous manner, the bound modes of several transmission lines which find applications in both the microwave and millimetre-wave frequency ranges, as well as in integrated optics. The bound modes of these transmission lines play a fundamental role in circuit design. As noted in Chapter 4, in several instances it is possible to derive their properties by using suitable approximations, e.g. the effective dielectric constant method. However, when propagation constants must be known with greater accuracy, or when the approximations break down, or when the field shape is of interest as in discontinuity problems, it becomes necessary to employ rigorous procedures such as those described hereafter. Note also that, as new structures are considered, it is sometimes unclear what approximations are feasible; in these cases a prudent approach suggests using rigorous full-wave analyses.

As opposed to modes pertaining to the continuum, which extend up to infinity, bound modes are necessarily confined near the guiding structure. Hence, it is possible to introduce a shielding enclosure, placed at a sufficient distance from the guide, without significantly perturbing the field of the bound modes. Thanks to this device, several numerical methods can be employed to determine the propagation characteristics, each having its own specific merits and disadvantages. In this respect, the reader is advised to look at the excellent book of Itoh, [16], as well as at papers [41, 15].

The approach followed throughout this Chapter...