Once all the current distributions are known in a planar structure, the electric and magnetic fields can be calculated everywhere in that structure using the dyadic Greens's functions of the background structure:
:<math>\begin{align}\mathbf{E(r) = E_{inc}(r)} + & \sum_{n=1}^N I_n^{(J)} \iiint_V \overline{\overline{G}}_{EJ}(r|r') \cdot f_n^{(J)}(r') \, d\nu' + \\& \sum_{k=1}^K V_n^{(M)} \iiint_V \overline{\overline{G}}_{EM}(r|r') \cdot f_k^{(M)}(r') \, d\nu'\end{align}</math>Â :<math>\begin{align}\mathbf{H(r) = H_{inc}(r)} + & \sum_{n=1}^N I_n^{(J)} \iiint_V \overline{\overline{G}}_{HJ}(r|r') \cdot f_n^{(J)}(r') \, d\nu' + \\& \sum_{k=1}^K V_n^{(M)} \iiint_V \overline{\overline{G}}_{HM}(r|r') \cdot f_k^{(M)}(r') \, d\nu'\end{align}</math><!--[[File:PMOM92(2).png]]-->
The above equations can be cast into the spectral domain as follows:
:<math>\begin{align}\mathbf{E(r) = E_{inc}(r)} + \frac{1}{(2\pi)^2} \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty}\bigg[& \sum_{n=1}^N I_n^{(J)} \tilde{\overline{\overline{G}}}_{EJ}(k_{\rho}, z|z') \cdot \tilde{f}_n^{(J)}(k_x, k_y) + \\& \sum_{k=1}^K V_n^{(M)} \tilde{\overline{\overline{G}}}_{EM}(k_{\rho}, z|z') \cdot \tilde{f}_k^{(M)}(k_x, k_y)\bigg] \, dk_x \, dk_y\end{align}</math>Â :<math>\begin{align}\mathbf{H(r) = H_{inc}(r)} + \frac{1}{(2\pi)^2} \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty}\bigg[& \sum_{n=1}^N I_n^{(J)} \tilde{\overline{\overline{G}}}_{HJ}(k_{\rho}, z|z') \cdot \tilde{f}_n^{(J)}(k_x, k_y) + \\& \sum_{k=1}^K V_n^{(M)} \tilde{\overline{\overline{G}}}_{HM}(k_{\rho}, z|z') \cdot \tilde{f}_k^{(M)}(k_x, k_y)\bigg] \, dk_x \, dk_y\end{align}</math><!--[[File:PMOM93(1).png]]-->
Calculation of the near-zone fields (fields at the vicinity of the unknown currents) is done at the post-processing stage and in a Cartesian coordinate systems. These calculations involve doubly infinite spectral-domain integrals, which are computed numerically. As was mentioned earlier, EM.Cube's planar MoM engine rather uses a polar integration scheme, where the radial spectral variable k<sub>ρ</sub> is integrated over the interval [0, Mk<sub>0</sub>], M being a large enough number to represent infinity, and the angular spectral variable t is integrated over the interval [0, 2π]. You also saw some of the numerical parameters related to this spectral-domain integration scheme. '''Note that when the observation plane is placed very close to the radiating J and M currents, the Green's functions exhibit singularities, which translate to very slow convergence or divergence of the integrals.''' You need to be careful to place field sensors at adequate distances from these radiating sources.