The effective index method is used to collapse the 3D geometry into a 2D representation.
When you run the simulation, the structure is meshed, and for each unique vertical cross
section of the device, an effective material is calculated from the vertical slab mode
profile and the vertical material profile at that point.
Once we have the effective 2D materials at each XY point in the simulation, we can run
a 2D FDTD simulation.
One way to think about the effective 2D material at each XY point is basically a weighted average
of the vertical stack of materials at that point, weighted by the vertical slab mode
The actual calculation is more complex, accounting for things like the field polarization.
There are 2 supported approaches to the calculating the effective index that you can choose from
in the varFDTD solver region settings.
The variational approach, and the reciprocity approach.
The equations used to calculate the effective index for these methods are shown here.
In the equations, eps_r is the reference slab permittivity profile, M is the selected slab
mode profile, and Beta_r is the slab mode propagation constant.
For more detailed information, see the references for the two effective index calculation approaches
listed below this video.
The variational approach is the default.
There is also an additional option in the settings to clamp effective index values to
physical material properties, which sets the minimum and maximum allowable effective index
values to the minimum and maximum refractive index of the materials of the 3D structure.
This option is enabled by default.
The default settings are typically good for most types of devices, so we don't often change
You can verify the results by comparing with 3D FDTD or EME simulations, like we did in
the My First Simulation section.
Both methods use the key assumption that there is negligible coupling between slab modes
of the device.
This is a good assumption for most silicon-on-insulator based devices which support 2 modes with different
Because the effective materials depend on the selected slab mode, the source that is
injected in the simulation will need to have the same polarization as the selected slab
For broadband simulations, material fitting using Multi-coefficient model is performed
for fitting effective materials in broadband simulations.