The problem of scattering of electromagnetic waves on a homogeneous dielectric cylinder with a circular cross section is a classical task. Using the Fourier method it is possible to find an explicit solution written in the form of series [1]–​[3]. A rigorous justification of the Fourier method for solving this problem was first given in [4], [5].

Analysis of the scattering of electromagnetic waves by various open rectangular and cylindrical resonators and waveguides aimed at discovery of resonance effects has been carried out by many authors. However, an exhaustive answer and justification of the true mathematical nature of resonance effects in the general case has not been given until recent years. For a rectangular metal waveguide, mathematical justification of the existence of complex resonance frequencies is performed in [9]. Note also the works [6]–​[8] in which resonance phenomena in rectangular waveguides with metal inhomogeneities are studied using the method of partial regions. A rigorous proof of the existence of complex resonance frequencies associated with the plane wave scattering problem by a circular uniform dielectric cylinder is presented in [10], [11].

The present work is a continuation of [11]. The problem of diffraction of an E-polarized electromagnetic wave on a circular dielectric cylinder is studied with an objective to investigate the resonance scattering modes. A semi-analytical model is developed. Explicit form of the scattered-field expansion coefficient available for open cylindrical metal-dielectric scatterers with layered piece-wise homogeneous dielectric filling and circular symmetry enables one to correctly formulate the problem of finding the desired resonance parameters in terms of implicit complex-valued functions of one or several complex variables. Using the explicitly determined reference parameter values at which several expansion coefficients are simultaneously singular the Cauchy problem is formulated and solved within the model framework for the numerical determination of the spectral parameters corresponding to double and triple multiple-resonance scattering modes.