Resonance scattering by a circular dielectric cylinder

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.