The discrete spectrum of the natural waves of an open partially shielded dielectric rod

It is shown that the natural wave spectrum of a round partially shielded dielectric rod (an open cylindrical slot line) forms an at-most-countable isolated subset on a Riemann surface. Natural waves are treated here as belonging to a wide class, i.e., a class of waves satisfying the outgoing radiation condition. The principal results can thus be extended to the leaky natural waves of an open waveguide.