Daniel, Evan
We looked at the DARM spectrum in the vicinity of the OMC dither line (at 4100 Hz) and its second harmonic (at 8200 Hz) using the OMC DCPD IOP channels.
The spectrum around the line itself appears to be bilinear, perhaps as one would expect (if the OMC is exactly on resonance, there should be no first-order modulation of the transmitted power). The second harmonic of the line is quite clean, with no obvious upconversion. Is this what we should expect?
That's what you expect (when OMC transmission is quadratic to the length).
Power propto L^2 = (L0+dL+dither)^2 = L0^2 + 2L0(dL+dither) + dL^2+ 2dL*dither + dither^2
where L0 and dL are the DC- and AC-ish component of the OMC length and dither is the dither.
dL*dither^2 will only appear in L^3 response, and (dL*dither)^2 in L^4.