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

## Transcript

In this unit, we'll cover why we need to generate broadband material fits in the first place.

For dispersive materials we have the frequency-domain relation D=epsilon*E where D is the displacement

field, epsilon is the material permittivity and E is the electric field.

Since FDTD is a time-domain solver, we need to convert this relationship to the time domain

where the multiplication from the frequency domain becomes a convolution product in the

time domain which is an integration over all previous time.

The permittivity over time is what gets simulated.

To perform this integration by brute force at each time step in the simulation would

require more time and memory than would be practically feasible, but it turns out that

for a certain set of functions there are known solutions that doesn't require performing

the integration so it’s much more computationally efficient.

However, there are some restrictions to the types of functions that can be solved, and

these include restrictions due to stability and causality – for example, you can’t

have the result at a point in time depend on an electric field from a future time.

This places some restrictions on the relationship between the real and imaginary part of the

permittivity known as the Kramers-Kronig relations.

Similar restrictions apply to conductive material models.

Before running broadband simulations, a broadband material fit is generated which meets these

restrictions for dispersive materials.

For imported data in sampled data materials, the broadband fits that are generated use

the Multi-Coefficient Model or MCM which meets the required restrictions.

The Multi-Coefficient Model is able to generate good fits for a broad range of dispersive

materials like the ones shown here, and the material fits data often better represent

the real material properties compared to simpler models like the Drude model (also known as

the plasma model) for metals.