Once the electric and magnetic surface currents are determined in the lit regions of the scatterer(s), they act as secondary sources and radiate into the free space. These secondary fields are the scattered fields that are superposed with the primary incident fields. The near fields at every point '''r''' in space are calculated from:
[[File:PO6.png]]<math>\mathbf{ E(r) = E^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J(r') } ds' + \iint_{S_M} \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M(r') } ds'</math>
where ''''''G:<submath>EJ</sub>''', '''\mathbf{ H(r) = H^{inc}(r) } + \iint_{S_J} \mathbf{ \overline{\overline{G<sub>EM</sub>''', '''G<sub>}}_{HJ</sub>''', }(r|r') \cdot J(r') } ds'+ \iint_{S_M} \mathbf{ \overline{\overline{G<sub>}}_{HM</sub>}(r|r'''''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively. In EM.Cube's PO Module, the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>) \expcdot M(-jk_0r)/(4\pi r')} ds'</math> and the near fields reduce to<!--[[File: PO6.png]]-->
[[File:PO7where '''G<sub>EJ</sub>''', '''G<sub>EM</sub>''', '''G<sub>HJ</sub>''', '''G<sub>HM</sub>''' are the dyadic Green's functions of electric and magnetic fields due to electric and magnetic currents, respectively.png]]In EM.Cube's PO Module, the background structure is the free space. Therefore, all these dyadic Green's functions reduce to the simple free-space Green's function of the form <math>\exp(-jk_0r)/(4\pi r)</math> and the near fields reduce to:
where R :<math>\begin{align}\mathbf{ E(r) = | ''E^{inc}(r) } & - jk_0 Z_0 \iint_{S_J} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J(r''')) \hat{R} } \right\}\frac{e^{-jk_0 R}}{4\pi R} ds'''\\& + jk_0 \iint_{S_M} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds'''|, k\end{align}<sub/math>0 :</submath> \begin{align}\mathbf{ H(r) = 2H^{inc}(r) } &- jk_0 Y_0 \iint_{S_M} \left\{ \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M(r')} - \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right\}\frac{e^{-jk_0 R}}{4\pi;/R} ds' \\λ<sub>0- jk_0 \iint_{S_J} \left[ 1-\frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J(r')) } \frac{e^{-jk_0 R}}{4\pi R} ds'\end{align}</submath> and Z<sub!--[[File:PO7.png]]-->0 where </submath> R=|r-r'| \text{, } k_0 = \tfrac{2\pi}{\lambda_0} \text{ and } Z_0 = 1/Y<sub>0</sub> Y_0 = η<sub>0\eta_0 </submath>.
When k<sub>0</sub>r >> 1, i.e. in the far-zone field of the scatterer, one can use the asymptotic form of the Green's functions and evaluate the radiation integrals using the stationary phase method to obtain far-field expressions for the electric and magnetic fields as follows:
:<math>\mathbf{E^{ff}(r)} = \frac{jk_0 e^{-jk_0 r}}{4\pi r} \left\{ Z_0 \mathbf{ \hat{r} \times \hat{r} } \times \iint_{S_J} \mathbf{J(r')} e^{-jk_0 \mathbf{\hat{r}\cdot r'}} ds' +\mathbf{\hat{r}} \times \iint_{S_M} \mathbf{M(r')} e^{-jk_0 \mathbf{ \hat{r} \cdot r' } } ds' \right\}</math> :<math> \mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math><!--[[File:PO8.png]]-->
=== Iterative Physical Optics (IPO) ===