Resonance frequencies and the phase matching of helicoidal surface waves on impenetrable spheroids

Abstract

The existence of the (complex) resonance frequencies of acoustic scatterers is explained by the generation of surface waves that match phases after repeated circumnavigations of the objects. The resonance frequencies can be predicted [B. L. Merchant et al., J. Acoust. Soc. Am. 80, 1754 (1986)] for prolate spheroidal objects, in the special case of axial incidence. Here sound‐soft, prolate‐spheroidal targets subject to obliquely incident signals are considered. The generated surface waves propagate along geodesics of helicoidal type, for which we obtain the condition for closing, and the set of discrete “pitch angles” at which closing takes place. An integral condition is formulated for the phase matching of helicoidal surface waves, using local wavelengths of Franz's surface waves. It is solved numerically for the complex resonance frequencies, found to agree closely with the m > 0 (i.e., containing azimuthal components) resonance frequencies obtained from an independent T‐matrix calculation. This agreement confirms the validity of the principle of phase matching for the general case, and the accuracy of the T‐matrix results. [Work supported in part by the Office of Naval Research.]