Time permittivity monitor

[alec-flexcompute]

A permittivity monitor, just in the time domain instead of frequency domain. This should be useful now that our nonlinear capabilities are what they are.

[momchil-flex]

I am not sure this makes sense in general. Maybe for some type of nonlinearities? But generally permittivity is chi-1, and nonlinearities are higher-order-chi-s. I guess when there is no frequency mixing, an effective epsilon can be written, which is maybe what you have in mind?

[alec-flexcompute]

I'm mainly thinking about checking how a nonlinear material's permittivity would be different at different times

[tylerflex]

Maybe one way to do this while still being rigorous could be to consider a method that returns the polarization of a medium as a function of FieldData or FieldTimeData?

https://en.wikipedia.org/wiki/Nonlinear_optics

class Medium(...):
    
     def polarization(field_data: FieldData | FieldTimeData) -> FieldData | FieldTimeData:
         """Compute polarization density of this medium when an electric field is present."""
         # compute all chi terms
         # construct field data with the polarization?

Then the user could add a FieldTimeMonitor to the simulation and call this method if they want to see the effect of the nonlinear medium?