This video is taken from the FDTD 100 course on Lumerical University.

## Transcript

Before running a simulation, it’s important to check the material fit in the Material

Explorer to make sure that the simulated material properties for sampled data materials will

accurately represent the physical material.

Open the Material Explorer from the “Check” menu.

The Material menu can be used to select a material.

Click the “Fit and plot” button to generate the plots of the data points for the real

and imaginary parts of the material data, and the material fit curve which is labeled

“FDTD model” in the legend.

The Material settings portion of the Material Explorer window includes the fit tolerance

setting and the max coefficients setting.

The fit tolerance setting specifies the target RMS (root mean squared) error between the

generated material fit and the material data.

You can see the RMS error displayed in the Fit analysis below.

It’s typically safe to set the fit tolerance to 0.

The max coefficients setting sets the maximum number of coefficients of the equation used

for the material fit.

The more coefficients, the more inflection points there can be in the fit curve.

The material fit with the lowest error will be chosen, so the fit may use fewer coefficients

than the number of max coefficients if using more coefficients doesn’t result in a better

fit.

For example here max coefficients is set to 3, but the number of coefficients used is

2.

If the number of max coefficients is too high, it’s possible to get a material fit which

has a lower RMS error, but actually doesn’t generate a better fit, as you can see here

when I change max coefficients to 5, as it leads to extraneous peaks in the fit.

This is one reason why it’s good to visually inspect the fit.

Clicking on the "Show advanced" button exposes additional advanced fitting parameters.

The imaginary weight is the relative weighting placed on the fit of the imaginary part of

the permittivity or conductivity compared to the real part.

By default this is set to 1 to give equal consideration to the real and imaginary part.

A value of 2 will give twice the weight to fit of the imaginary part of the data compared

to the real part and a value of 0.5 will give twice the weight to the real part compared

to the imaginary part.

The weighted RMS error displayed in the Fit analysis is the RMS error with imaginary weight

applied.

The improve stability and make fit passive options are selected by default.

These settings are used to improve the numerical stability of the material and ensure that

there is no gain introduced by the fit.

Unchecking these options could result in a fit with smaller RMS error but could lead

to instability causing the fields to diverge when you run the simulation, so keeping these

options checked is recommended.

Specify fit range allows you to set the wavelength or frequency range of the fit.

By default, the fit range will be set to the wavelength range of your source.

You might want the fit to consider data points outside of the source range in the fit, for

example, if you are going to run several simulations with different source wavelength ranges and

you want to make sure the material fit used does not change when you change the source

bandwidth, or if you are simulating a nonlinear effect such as harmonic generation where there

will be light generated at wavelengths outside of the source wavelength range.

Next, we’ll go through some examples of material fits discuss how to modify the settings

in each case to obtain a better fit, as well as some fitting tips.

In the first example, we can see the fit is not very good.

The quality of the fit can be improved by increasing the number of coefficients from

4 to 10.

Next, suppose we want a better fit for the imaginary part of the permittivity.

Currently, we can see the fit to the real part is much better than the imaginary part.

This is simply because the real part is larger, so it contributes more to the RMS.

To improve the fit to the imaginary part, click Show advanced and increase the Imaginary

weight from 1 to 30.

This will put more emphasis on getting a good fit to the imaginary part, possibly at the

expense of a slightly worse fit to the real part.

The fit is now much closer to the imaginary data.

In this example, the fit initially looks fine, but a careful inspection shows some extra

peaks in the fit.

The experimental data has contains some noise, and the fitting routine is attempting to fit

that noise.

Assuming this feature is noise and not the real material property, it is best not to

include this feature in the material fit.

This feature can be removed by reducing the number of coefficients from 10 to 4.

The response of some devices such as plasmonic devices can be sensitive to the material properties.

To test the sensitivity of the results to the material fit, re-run the simulation with

several different fits.

Another option is to run a series of single frequency simulations, which avoids the need

for broadband material fitting.