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EM.Illumina

861 bytes added, 18:38, 13 June 2013
/* General Huygens Sources */
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:
:<math>\mathbf{E^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R}\left\lbrace \begin{align}& Z_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{J_j(r')} \\& -Z_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot J_j(r')) \hat{R} } \\& - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times M_j(r')) }\end{align} \right\rbrace</math>  :<math>\mathbf{H^{inc}(r)} = -jk_0 \sum_j \iint_{\Delta_j} \, ds' \frac{e^{-jk_0 R}}{4\pi R}\left\lbrace \begin{align}& Y_0 \left[ 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right] \mathbf{M_j(r')} \\& -Y_0 \left[ 1 - \frac{3j}{k_0 R} - \frac{3}{(k_0 R)^2} \right] \mathbf{ (\hat{R} \cdot M_j(r')) \hat{R} } \\& - \left[ 1 - \frac{j}{k_0 R} \right] \mathbf{ (\hat{R} \times J_j(r')) }\end{align} \right\rbrace</math><!--[[File:PO16.png]]-->
where the summation over index ''j'' is carried out for all the elementary cells &Delta;<sub>j</sub> that make up the Huygens box. In EM.Cube Huygens surfaces are cubic and are discretized using a rectangular mesh. Therefore, &Delta;<sub>j</sub> represents any rectangular cell located on one of the six faces of Huygens box. Note that the calculated near-zone electric and magnetic fields act as incident fields for the scatterers in your [[PO Module]] project. The Huygens source data are normally generated in one of EM.Cube's full-wave computational modules like FDTD, Planar or MoM3D. Keep in mind that the fields scattered (or reradiated) by your physical structure do not affect the fields inside the Huygens source.
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