As some may know, I am a millimeter wave\$^1\$ researcher in my day job.
In said job, I have to work with very low loss (\$ \tan{\delta} < 10^{-3}\$) materials. And these low losses still have a big impact on our applications.
One of the things we work with are foams, but we don't really know how well the foam works - say we have a foam made of PTFE (ptfe has a loss tangent in the ballpark of 0.0002-0.0007, depending on who you ask). Can we just scale the loss tangent by the density of PTFE?
So, I was hoping to do some measurements, but this is where problems come in. Most methods I come up with (measuring transmission loss of a slab between horns, measuring resonators, etc) all end up giving you losses well below the measurement capabilities of most VNAs (which tend to be at best 0.1 dB transmission uncertainty). So how do you measure such low loss tangents?
My frequency of operation is around Ka band on this job, but more general approaches would also be welcome.
\$^1\$ EDIT: for those who don't know, millimeter waves are signals from 30-300 GHz. Above that is usually considered 'sub-millimeter wave' which I also work in, but to a lesser extent.