Asymptotic theory of propagation in curved and nonuniform waveguides

To treat guided wave propagation in curved nonuniform waveguides, such as atmospheric, oceanic, and solid earth ducts, two methods of analysis are presented. The first is the ray method of Keller and Rubinow, which has been applied to waveguides by Maurer and Felsen. This method is illustrated by applying it to a straight uniform guide, for which it yields the exact result. It is also applied to a guide with concentric circular walls, and yields the asymptotic form of the exact result. Then it is applied to a gradually changing guide and yields a result which includes that of Rayleigh for narrow guides. The second method, which involves stretching of the transverse coordinate, has been applied to water waves by Keller to narrow guides by Matkowsky and to various guided wave problems by Rulf. It is applied to gradually changing guides and yields results which are more accurate than the ray method results for such guides.