Method of Spectral Mappings for Nonselfadjoint Boundary-Value Problems Associated with Resonance Scattering by Open Structures

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We analyze parameter dependence of the complex resonance frequency (RF) spectrum of the nonselfadjoint boundary-value problems associated with a mathematical model of the resonance scattering by an infinite dielectric cylinder. The notions of spectral mapping and spectral set are introduced and applied to solve the addressed problem. A particular focus is toward RF evolution with respect to the varying complex refraction index, visualization of spectral sets, and developing robust methods aimed at the RF calculation and determination of spectral sets.