## 4 Discussion and Comparisons  
Figure 3 illustrates the scattered electric far-field polar pattern \(|\text{E}_{2}^{\text{sc}}(\varphi_{1})|\) of the structure shown in the inset, for \(\varphi^{\prime}=90^{\circ}\) and for several values of \(\theta^{\prime}\). The structure is stimulated by an E-polarized plane wave which is obliquely incident. In Figure 4, we present the scattered magnetic far-field polar pattern \(|\text{H}_{2}^{\text{sc}}(\varphi_{1})|\) of the inset structure, in the excitation case of an obliquely incident H-polarized plane wave with \(\varphi^{\prime}=0^{\circ}\) and \(\theta^{\prime}=30^{\circ}\), \(45^{\circ}\), \(90^{\circ}\). The occasion of normal incidence, i.e., \(\theta^{\prime}=90^{\circ}\), is included in both figures for reference. Moreover, exhaustive comparisons with previously published results that correspond to much simpler, marginal cases of the complex geometric structure treated herein were performed. Two examples are provided in Figures 3 and 4 by plotting the corresponding numerical results, for normal incidence, given in Figure 5 of [11] and Figure 3 of [27], respectively, as indicated in the insets. It is evident that our results coincide with the published ones. Other results, not presented herein for the sake of brevity, indicate that our general solution is capable of reproducing Figures 3-10 of [22]; all these plots refer to normal incidence and the corresponding configurations fall within the geometry illustrated in Figure 1.  
The scattered far-field pattern \(|\mathrm{E}_{\mathrm{z}}^{\mathrm{sc}}(\varphi_{1})|\) of two stratified cylinders for oblique incidence (as shown in the inset) is depicted in Figures 5 and 6. The former is produced by setting \(\theta^{\prime}=60^{\circ}\) and \(\varphi^{\prime}=45^{\circ}\), while \(\theta^{\prime}=70^{\circ}\) and \(\varphi^{\prime}=45^{\circ}\) were assumed for the latter. Several values of the dielectric constant of the cladding regions, with \(\epsilon_{2}=\epsilon_{4}\), are tested in Figure 5, whereas the effect of the electric conductivity of the cladding regions \((\sigma_{2}=\sigma_{4})\) on \(|\mathrm{E}_{\mathrm{z}}^{\mathrm{sc}}(\varphi_{1})|\) is investigated through Figure 6. The main remark to be made about Figures 5 and 6 is the presence of several lobes, with the main one at \(\varphi_{1}\approx 229^{\circ}\) for the case \(\epsilon_{2}=\epsilon_{4}\
eq\epsilon_{0}\) (Figure 5) or at \(\varphi_{1}\approx 227^{\circ}\) for the case \(\sigma_{2}=\sigma_{4}\) (Figure 6). Figures 5 and 6 suggest that the position of the main lobe does not depend strongly on the electrical characteristics of the cladding regions. Moreover, it should be noted that a further increase in the cladding regions' conductivities \(\sigma_{2}\) and \(\sigma_{4}\) has practically no effect on the solid curve field pattern that corresponds to \(\sigma_{2}=\sigma_{4}=50\) S/m. Figures 7 and 8 present the total scattering cross section normalized to the free space wavenumber (k\({}_{0}\)\(\sigma_{1}\)) versus the incidence angle \(\varphi^{\prime}\) for the configuration shown in the insets; several values for the off-axis distance, D\({}_{23}\) (Figure 7), or the cladding regions' radii, \(\alpha_{2}\) and \(\alpha_{4}\) (Figure 8), were considered. Due to the symmetrical scatterer geometry, the k\({}_{0}\)\(\sigma_{1}\) values are also symmetrical about the vertical xz-plane (\(\varphi^{\prime}=90^{\circ}\)). Figure 7 indicates that \(\sigma_{t}\) is strongly dependent on D\({}_{23}\), provided that \(54^{\circ}<\varphi^{\prime}<126^{\circ}\), while the dependence of the total scattering cross section \(\sigma_{1}\) on the cylinders' radius (size) is rather strong for most values for the angle \(\varphi^{\prime}\). Thus, changing D\({}_{23}\) and/or \(\alpha_{2}\),\(\alpha_{4}\) properly may offer the feasibility to handle the scattering cross section of the cylindrical structure.