## 2 Formulation of the Problem and Proposed Solution  
Two equiaxial resistive disks with the same radius \(a\), thickness \(\tau_{i}\) and electric conductivity \(\sigma_{i}\), where \(i=1,2\) identifies the \(i\)-th disk, in free space are considered (see Figure 1). A Cartesian coordinate system, \((x,y,z)\), and a cylindrical coordinate system, \((\rho,\phi,z)\), are introduced so that the \(z\) axis coincides with the axis of the disks and the median surfaces of the disks are located at the abscissas \(z=z_{i}\). Henceforth, the symbols \(\varepsilon_{0}\), \(\mu_{0}\), \(f\), \(\omega=2\pi f\), \(\lambda\), \(k_{0}=2\pi/\lambda=\omega\sqrt{\varepsilon_{0}\mu_{0}}\) and \(Z_{0}=\sqrt{\mu_{0}/\varepsilon_{0}}\) will be used to denote the dielectric permittivity and magnetic permeability of free space, the frequency and the angular frequency, the wavelength, the free space wavenumber and intrinsic impedance, respectively. For high conductivity and thin disks, i.e., for \(\sigma_{i}\gg\omega\varepsilon_{0}\), \(\tau_{i}\ll a\) and \(\tau_{i}\ll\lambda\), the disks can be approximated with infinitesimally thin flat surfaces located at the abscissas \(z=z_{i}\)[6]. Effective surface current densities, \(\underline{l}_{i}(\rho,\phi)\), are excited on the disks by an impinging plane wave, \(\underline{E}^{\rm inc}\)\((\underline{r})=\underline{E}_{0}e^{-\frac{i}{\hbar}\underline{r}}\) and \(\underline{H}^{\rm inc}\)\((\underline{r})=\underline{H}_{0}e^{-\frac{i}{\hbar}\underline{r}}=\underline{k} \times\underline{E}_{0}e^{-\frac{i}{\hbar}\underline{r}}/(\omega\mu_{0})\), where \(\underline{r}=(\rho,\phi,z)\), \(\underline{k}=-k_{0}(\sin\theta_{0}\cos(\phi_{0}-\phi)\hat{\phi}+\sin\theta _{0}\sin(\phi_{0}-\phi)\hat{\phi}+\cos\theta_{0}\hat{z})\), \(\hat{\rho},\hat{\phi},\hat{z}\) denote the unit vectors in the \(\rho,\phi,z\) directions, respectively, and the incidence angles \(\theta_{0}\) and \(\phi_{0}\) are defined in Figure 1, which, in turn, generate scattered fields, \((\underline{E}^{\rm sc}_{i}(\underline{r}),\underline{H}^{\rm sc}_{i}( \underline{r}))\), such that the overall scattered field \((\underline{E}^{\rm sc}(\underline{r}),\underline{H}^{\rm sc}(\underline{r})) =(\underline{E}^{\rm sc}_{1}(\underline{r})+\underline{E}^{\rm sc}_{2}( \underline{r}),\underline{H}^{\rm sc}_{1}(\underline{r})+\underline{H}^{\rm sc }_{2}(\underline{r}))\) satisfies the conditions \(\underline{l}_{i}(\rho,\phi)=\hat{z}\times(\underline{H}^{\rm sc}(\rho, \phi,z_{i}^{+})-\underline{H}^{\rm sc}(\rho,\phi,z_{i}^{-}))\). A uniquely solvable boundary value problem for the Maxwell equations [8] is obtained by imposing the radiation condition, the local power boundedness condition and the following generalized boundary conditions on the disks [6]:  
\[\hat{z}\times\big{(}\underline{E}\big{(}\rho,\phi,z_{i}^{+}\big{)}+\underline {E}\big{(}\rho,\phi,z_{i}^{-}\big{)}\big{)}\times\hat{z}=2R_{i}\underline{l} \left(\rho,\phi\right) \tag{1}\]  
for \(\rho\leq a,0\leq\phi<2\pi\) and \(i=1,2\), where \((\underline{E}(\underline{r}),\underline{H}(\underline{r}))=\left(\underline{ E}^{\rm sc}(\underline{r})+\underline{E}^{\rm sc}(\underline{r}),\underline{H}^{\rm inc}( \underline{r})+\underline{H}^{\rm sc}(\underline{r})\right)\) denotes the total field and \(R_{i}=1/(\sigma_{i}\tau_{i})\) is the electric resistivity of the \(i\)-th disk. Figure 1: Geometry of the problem. It is well-known that the problem at hand can be equivalently formulated in terms of a system of 2-D integral equations for the effective surface current densities [9]. Moreover, the radiation condition can be automatically satisfied by the proper selection of the Green's function of the problem whereas the local power boundedness condition is guaranteed by the edge behavior prescribed for the fields.