An Overview of Creeping Wave Formulation and Its Relationship to Surface Waves

Abstract

Interface phenomena in the propagation of plane or spherical acoustic waves over plane interfaces between two media are well known; the corresponding “lateral” and “Schmidt head waves” were studied theoretically and experimentally. Less well understood are the analogous effects at curved surfaces, although considerable progress was made here in the last few years. For impenetrable obstacles of simple shape (cylinders, spheres), Franz's theory of circumferential waves, based on the Watson transformation, can be directly taken over from the electromagnetic to the acoustic case (Überall, Nussenzveig); the corresponding “creeping waves” can be shown to emerge from the conventional normal-mode solution (Rudgers), and their existence was demonstrated experimentally (Harbold and Steinberg; Neubauer; Wright). For general smooth convex surfaces, Levy's and Keller's theory leads to similar “diffracted surface rays.” This may be generalized to penetrable elastic media (Keller and Karal; Chen; Rulf), and made quantitative for simple shapes (Beckmann and Franz; Mishra; Streifer and Kodis; Doolittle, Überall, and Uginčius; Nussenzveig; Ludwig). Transmitted waves (Brill and Überall) complicate the experimental search for surface waves (Bunney, Goodman, and Marshall; Neubauer and Dragonette). The characteristics of surface waves may be studied independently of their mode of excitation (Viktorov; Wait; Norwood and Miklowitz; Brekhovskikh; Lapin; Junger and Feit).