Bound modes of open waveguides may be found in several different ways. In particular, in Chapter 6, a rigorous, full-wave approach will be presented. However, in several instances, bound modes may also be found by relatively simple approximate methods, such as the effective dielectric constant (EDC) method and conformal mapping. Such methods have been devised both for optical waveguides and for microwave guiding structures.

The method used for optical waveguides is the EDC and will be illustrated in the first Section of this Chapter. Not surprisingly the accuracy of the results obtained by this method improves as the frequency increases. It will be observed also that the results relative to the propagation constant are fairly accurate. This is valid for all methods since, as discussed in the last part of Section 4.1, the propagation constant is a variational quantity. An example of application of the EDC is then provided in Section 4.2, where a waveguide commonly used in integrated optics is investigated.

Open waveguides operating in the microwave frequency range are often investigated by a different approximate method, i.e. by conformal mapping. The latter is introduced by referring to the example of a microstrip line in the last Section of this Chapter.