A method for calculating eigenfrequencies of arbitrarily shaped convex targets: eigenfrequencies of conducting spheroids and their relation to helicoidal surface wave paths

In a previous study by the authors (1986) the phase matching of surface waves on prolate, perfectly conducting spheroids generated, for example, by the scattering of an incident plane electromagnetic wave was investigated. Now, the considerably more complex spheroidal case with an obliquely incident primary wave, whose scattering will give rise to helicoidally (i.e. quasihelically) propagating surface waves is treated. The conditions under which phase matching of such types of surface waves, which propagate along helicoidal geodesics, can occur are investigated. It is found that only a discrete set of the required closed propagation paths exists, corresponding to a discrete set of allowed angled of incidence. These angles can be associated with different azimuthal quantum numbers m of the azimuthal propagation component around the symmetry axis, where m⩽n and n is the mode number which corresponds to the number of standing wavelengths at resonance