===Periodic FDTD Simulation Types===
Besides analyzing a periodic structure in a single-run simulation, EM.Cube's [[FDTD Module]] offers a number of sweep simulations for periodic structures. These include '''Frequency Sweep''', '''Angular Sweep''', '''R/T Macromodel Sweep '''and '''Dispersion Sweep'''. These options are available from the '''Simulation Mode''' dropdown list of the [[FDTD Module]]'s '''Run Dialog'''. Of these, frequency sweep and angular sweep are similar to the non-periodic case as discussed earlier. <font color="red"><u>'''Keep in mind that in this release of EM.Cube's [[FDTD Module]], for oblique plane wave incidences, you need to run a frequency sweep to get wideband reflection/transmission coefficient data. Similarly, you need to run an angular sweep to plot R/T coefficients vs. the incident angle.'''</u></font>
The '''R/T Macromodel Sweep''' option of the Simulation Mode dropdown list is only available for periodic structures. It is used to generate a lookup table model for the reflection and transmission coefficients of a periodic surface for both TM and TE polarizations. The results are written into a file named "PW_UserDefinedMacroData.mat". Through the Macromodel Settings dialog you can set the start and end value and number of samples for both the Theta (θ) and Phi (φ) angles of the incident plane wave. The R/T macormodels can be used by EM.Cube's [[Propagation Module]] to calculate the reflection and transmission coefficients of incident rays at the facets of obstructing blocks with "non-standard" periodic surfaces.
Figure 1: [[FDTD Module]]'s R/T Macromodel 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. <font color="red"><u>'''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>.'''</u></font> 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 f as specified in [[FDTD Module]]'s Plane Wave Dialog.
[[Image:FDTD144.png]]