According to the electromagnetic equivalence theorem, if we know the tangential components of E and H fields on a closed surface, we can determine all the E and H fields inside and outside that surface in a unique way. Such a surface is called a Huygens surface. At the end of a full-wave FDTD or MoM solution, all the electric and magnetic fields are known everywhere in the computational domain. We can therefore define a box around the radiating (source) structure, over which we can record the tangential E and H field components. The tangential field components are then used to define equivalent electric and magnetic surface currents over the Huygens surface as:
:<math>\begin{align}& \mathbf{ J(r) = \hat{n} \times H(r) } \\& \mathbf{ M(r) = -\hat{n} \times E(r) }\end{align}</math><!--[[File:PO10(1).png]]-->
In the physical optics domain, the known equivalent electric and magnetic surface currents (or indeed the known tangential E and H field components) over a given closed surface S can be used to find reradiated electric and magnetic fields everywhere in the space as follows:
The far fields of the Huygens surface currents are calculated from the following relations:
:<math>\mathbf{E^{ff}(r)} = \frac{jk_0}{4\pi} \frac{e^{-jk_0 r}}{r}\sum_j \iint_{\Delta_j} \left[ Z_0 \, \mathbf{ \hat{r} \times \hat{r} \times J_j(r') } + \mathbf{ \hat{r} \times M_j(r') } \right] e^{ -jk_0 \mathbf{\hat{r} \cdot r'} } \, ds'</math> :<math>\mathbf{H^{ff}(r)} = \frac{1}{Z_0} \mathbf{\hat{r} \times E^{ff}(r)} </math><!--[[File:PO17(1).png]]-->
== Physical Structure & Its Discretization ==