## 2 Materials and Methods  
A geometric configuration of our problem is depicted in Figure 1; Figure 1a displays the cross section of the general structure, while Figure 1b offers a 3D view of a simpler configuration that may serve as an example. The general configuration consists of a circular dielectric cylinder (affiliated to region 1) which is placed within the boundless free space (affiliated to region 0) and comprises \(L-1\) parallel circular stratified cylinders (each with two lossy dielectric layers, affiliated to regions \(2,\;3,\;4,\;5,\;\ldots,\;2L-2,\;2L-1\)). Each cylindrical region of space is identified by the index, \(i\;(i=0,\;1,\;2,\;3,\;4,\;5,\;\ldots,\;2L-2,\;2L-1)\), and is characterized by its dielectric permittivity, \(\varepsilon_{i}\), magnetic permeability, \(\mu_{i}\), electric conductivity, \(\sigma_{i}\), and radius, \(\alpha_{i}\). All \(L\) cylinders (the external as well as the embedded ones) are parallel to each other, with their axis-to-axis distances symbolized by \(D_{pq}\;(p,\;q=1,\;2,\ldots,L)\). We define \(L-1\) local cylindrical coordinate systems, \(\mathrm{O}_{p}(\rho_{p},\,\rho_{p},z)\), with \(p=1,\;2,\ldots,L\) and each one attached to the axis of the corresponding \(p\)-th cylinder, while the \(\mathrm{O}_{1}\;(\rho_{1},\rho_{1},z)\) system devoted to the outer cylinder's axis is used as reference. The primary excitation is provided by an EM plane wave with arbitrary polarization, impinging on the configuration of Figure 1a from the external region (0), where it propagates. The vector wavenumber of the aforementioned EM wave is given by  
\[\overline{\mathrm{K}}^{inc}(\theta^{\prime},\varphi^{\prime})=\mathrm{k}_{ \rho}\,\widetilde{\mathrm{k}}_{\rho}^{inc}+\beta\,\widetilde{z}\,=\mathrm{k}_ {0}\sin\theta^{\prime}\;(\cos\varphi^{\prime}\,\widetilde{x}+\sin\varphi^{ \prime}\,\widetilde{y})+\mathrm{k}_{0}\cos\theta^{\prime}\,\widetilde{z}\,, \tag{1}\]  
where \(\theta^{\prime}\) and \(\varphi^{\prime}\) are the angles of plane wave oblique incidence shown in Figure 2, \(\beta=\mathrm{k}\cos\theta^{\prime}\) is the propagation constant, \(\mathrm{k}_{\rho}=\mathrm{k}_{0}\sin\theta^{\prime}\) and \(\mathrm{k}_{0}=\omega\sqrt{\varepsilon_{0}\mathrm{i}_{0}}\) is the wavenumber of free space when \(\omega\) implies the circular frequency. Henceforth, the EM field \([\overline{\text{E}}^{\text{inc}}(\overline{\rho}),\ \overline{\text{H}}^{\text{inc}}( \overline{\rho})]\ e^{-\text{J}\beta z}=[\ \widetilde{z}\ \text{E}^{\text{inc}}_{\text{z}}( \overline{\rho})+\overline{\text{E}}^{\text{inc}}_{\text{t}}(\overline{\rho}), \ \widetilde{z}\ \text{H}^{\text{inc}}_{\text{z}}(\overline{\rho})+\overline{\text{H}}^{ \text{inc}}_{\text{t}}(\overline{\rho})\ ]\ e^{-\text{J}\beta z}\) with arbitrary polarization, which is excited at \(\overline{\rho}\in(0)\) of the cylindrical structure, is referred to as the incident field. The harmonic \(\exp[\text{j}(\omega t-\beta z)]\) dependence on time and \(z\) is suppressed throughout the analysis for brevity. Figure 1: (**a**) Cross-section (normal to the complex cylindrical structure’s axes) of the general configuration under consideration, consisting of \(L-1\) parallel stratified circular dielectric cylinders (\(2\), \(3\), \(\dots\), \(L\)), embedded in a dielectric circular cylindrical housing (\(1\)) surrounded by unbounded empty space (\(0\)). (**b**) A specific example of the configuration, consisting of a host cylinder with three cylindrical inclusions (3D view). Figure 2: Geometry of the arbitrarily polarized and obliquely incident plane wave impinging upon the general cylindrical structure of Figure 1.  
Using the coordinate system (O\({}_{1}\)) of the outer cylinder, the longitudinal components of the incident electromagnetic field may be written [50] as follows:  
\[ \begin{bmatrix}\mathrm{E}_{z}^{\mathrm{inc}}(\overline{\rho})\\ \mathrm{H}_{z}^{\mathrm{inc}}(\overline{\rho})\end{bmatrix} = \begin{bmatrix} \mathrm{E}_{0}\\ \mathrm{H}_{0}\end{bmatrix} \;\exp(-\mathrm{j}\;\overline{\mathrm{k}}_{\rho}^{ \mathrm{inc}}\cdot\overline{\rho})=