This video is taken from the varFDTD Learning Track on Ansys Innovation Courses.

## Transcript

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

profile.

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

these settings.

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

polarizations.

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

mode.

For broadband simulations, material fitting using Multi-coefficient model is performed

for fitting effective materials in broadband simulations.