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.