IIR filters for dispersive media

[stevengj]

Rather than using a sum of Lorentzians to represent dispersive media, we might want to support general rational functions (ratios p(ω)/q(ω) of polynomials) via IIR filters. There are lots of papers on this, e.g.

https://link.springer.com/article/10.1007/s11741-000-0068-z

The goal here would be to be able to take the output of IIR filter design tools (there are lots of these) as-is, so people could just use one of those tools to fit the filter coefficients to experimental ε(ω) data in a given frequency range and then input those coefficients directly into Meep.

Essentially, this would involve implementing a new type of susceptibility class that represented an IIR filter, much like the Lorentzian class but keeping a longer "history" (proportional to the filter order). Actually, vaguely recall that Alex Rodriguez and I may have implemented something like this already at some point for generating colored noise in FDTD (https://arxiv.org/abs/physics/0703152) for nonlinear thermal simulations (https://arxiv.org/abs/1406.4074). I'm not sure what happened to that code.