Complex acoustic and electromagnetic resonance frequencies of prolate spheroids and related elongated objects and their physical interpretation

A numerical calculation of the complex eigenfrequencies of prolate spheroids and ellipsoids, and of finite-length circular cylinders undergoing acoustic or electromagnetic eigenvibrations is reported. While mainly longitudinal eigenvibrations have been studied previously, here we obtained eigenfrequencies of vibrations which contain azimuthal components. These give rise (e.g., for the case of a cylinder) to helical surface waves, and we were able to interpret the corresponding eigenfrequencies in terms of resonances caused by the phase matching of such surface waves as they repeatedly engulf, and propagate around, the vibrating object. Phase and group velocities and absorption coefficients of the surface waves are obtained numerically from the set of complex eigenfrequencies.