Hi Peter,
I think I'm on top of it, but discussion is always fun and educational.
Your loop filter is exactly as I described it in my original post, and I understand exactly how such filters behave. I can draw you a Bode plot for that (or any other combination of R and C) in a matter of seconds.
At sufficiently low frequencies this loop filter behaves identically as an integrator, with 90 degrees phase lag, giving 180 degrees total lag around the loop. However, as I pointed out in my second post, this does not actually matter, because the loop gain is not one at these low frequencies, but actually much greater than one.
Agreed that provided C1 is significantly less than C2, that it look resistive over a range of intermediate frequencies. This does not give a 'phase lead' though, it gives a small phase lag which, as you say, is arranged to be near unity gain frequency so as to guarantee stability, as per the correct version of Barkhausen stability criterion.
In my case I also need to consider the low-pass-filter characteristic (several hundred Hz 3dB point) of the laser frequency-control input. No problems. This is all simple stuff that I can draw Bode plots for and design the loop filter accordingly.
I'm actually reasonably experienced at designing control loops, except that none of the systems I have designed in the past (eg temperature control or electronic circuits) were attempting to control something that looks like a 'pure integrator', with no zero order term, which is what a VCO looks like. That initially had me scratching my head, because I was not really thinking about it and incorrectly interpreting the Barkhausen stability criterion. Now I've figured that out, I'm completely comfortable and 'in control'.
I'm quite familiar with 'natural frequency' and 'damping factor', which are easily calculated (at least for a 2nd order system) and another way of looking at things. But I'm one of those really fussy guys that needs to be able to draw the same conclusion no matter what angle the problem is viewed from, and initially I could not reconcile what I knew was stable with what Barkhausen appeared to predict. But now all is well and I can sleep at night.
Thanks and cheers, Col