Resonance frequencies of arbitrarily shaped dielectric cylinders

ABSTRACT

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 of resonance (scattering) frequencies associated with these eigenvalues is proved. The technique involves the determination of characteristic numbers (CNs) of the Fredholm operator-valued functions of the problems constructed using Green's potentials. Separating principal parts in the form of meromorphic operator pencils, we apply the operator generalization of Rouché's theorem to verify the occurrence of CNs in close proximities of the pencil poles. The results are illustrated in detail using the case of a dielectric cylinder of circular cross section.

KEYWORDS:

• Resonance frequencies
• boundary integral equations
• operator-valued functions
• finite-meromorphic
• pole pencils

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35B34
• 45B05
• 45C05
• 45E99
• 47A10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study is supported by the Russian Science Foundation, project no. 20-11-20087.