Resonance frequencies of arbitrarily shaped dielectric cylinders

We consider eigenvalue problems for dielectric cylindrical scatterers of arbitrary cross with generalized conditions at infinity that enable one to take into account complex eigenvalues. The existence resonance (scattering) frequencies associated these eigenvalues is proved. technique involves the determination characteristic numbers (CNs) Fredholm operator-valued functions constructed using Green's potentials. Separating principal parts in form meromorphic operator pencils, we apply generalization Rouché's theorem verify occurrence CNs close proximities pencil poles. results are illustrated detail case a cylinder circular section.