[[Image:Info_icon.png|40px]] Click here to learn more about the theory of '''[[Basic_FDTD_Theory#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]]'''.
[[Image:FDTD134.png|thumb|360px|EM.Tempo's Periodicity Settings dialog]]
===Defining a Periodic Structure in EM.Tempo===
* Enter new values for '''X Spacing''' and '''Y Spacing '''in project units and close the dialog.
* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC.
Â
<table>
<tr>
<td>
[[Image:FDTD134.png|thumb|360px|EM.Tempo's periodicity settings dialog.]]
</td>
</tr>
</table>
===Exciting Periodic Structures as Radiators in EM.Tempo===
=== Running a Dispersion Sweep in EM.Tempo ===
[[Image:FDTD144.png|thumb|250px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]
The '''Dispersion Sweep '''option of the Simulation Mode dropdown list performs a sweep of constant k<sub>l</sub> wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.Cube]]'s [[FDTD Module]] uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k<sub>li</sub>, you can find the reflection and transmission coefficients for all combinations of frequency f<sub>j</sub> and incident angle θ<sub>j</sub> such that (2π/c) . f<sub>j</sub>. sin θ<sub>j</sub> = k<sub>li</sub>. This provides a complete picture of the dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the eigenvalues of the periodic structure. The horizontal axis represents the constant transverse wavenumber k<sub>l</sub> (or beta). The vertical axis represents frequency. Sometimes, the free space wave number k<sub>0</sub> = (2π/c).f is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] plots frequency vs. wavenumber. Both the horizontal and vertical axes start from 0 and extend to f<sub>max</sub> and k<sub>l,max</sub>, respectively, where f<sub>max</sub> = f<sub>0</sub> + Δf/2, and Δf is the specified bandwidth of the project. For this sweep option you have to specify the number of wavenumber samples. Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle φ as specified in [[FDTD Module]]'s Plane Wave Dialog.
Â
<table>
<tr>
<td>
[[Image:FDTD144.png|thumb|250px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]
</td>
</tr>
</table>
<table>