PeriodicPointSourceΒΆ

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Defines time-harmonic, Bloch-periodic, dipole sources at positions arranged in a one- or twofold periodic arrangement,

\begin{eqnarray*}
\VField{J}(\pvec{x}, t) & = & \sum_{l_1=-\infty}^{l_1=\infty} e^{i \pvec{k}_\mathrm{B} \cdot (l_1\pvec{a}_1} \VField{j}  \delta \left(\pvec{x}-\pvec{x}_0-l_1\pvec{a}_1 \right) e^{-i \omega t}\;\mbox{(onefold\;periodic)} \\
\VField{J}(\pvec{x}, t) & = & \sum_{l_1=-\infty}^{l_1=\infty} \sum_{l_2=-\infty}^{l_2=\infty} e^{i \pvec{k}_\mathrm{B} \cdot (l_1\pvec{a}_1+l_2 \pvec{a}_2)} \VField{j}  \delta \left(\pvec{x}-\pvec{x}_0-l_1 \pvec{a}_1 -l_2\pvec{a}_2 \right) e^{-i \omega t}\;\mbox{(twofold\;periodic)}
\end{eqnarray*}

Here, \pvec{a}_1, \pvec{a}_2 are the lattice vectors, \omega is the the angular frequency, \pvec{k}_\mathrm{B} the Bloch vector, \pvec{x}_0 is the position of the point source in the unit cell and \VField{j} is a constant strength vector. The lattice vectors are determined from the specified geometry. Other parameters are set using Omega, K, Position, and Strength, respectively.