Nishino,

I measured the Open loop trandfer function (OLTF) and other properties of the green locking path. When locking the cavity with mass feedback, there was instability in transmission power at the frequency of 670 Hz. This oscillation cannot be suppressed just by increasing the UGF; the locking was lost. 

To investigate the reason, I measured the OLTF. It is weird that the phase of A*H decreases above ~1 kHz, while its gain is flat (oltfotherplot.png). The dip structure at 670 Hz can also be seen. I also plotted the optical gain (H) in opticalgain.png.

I also measured the power spectrum density of the error and feedback signal. From the error spectrum, one can infer the spectrum of the disturbance out of loop (m/rHz). displacementoutofloop.png shows the ASD and the accumulated RMS noise. At 10 Hz, RMS is ~3 nm. When it is locked, the transmission light oscillates across the full resonance curve. From this phenomena, one can estimate the amplitude of oscillation as:

30 cm (cavity length) * 500 MHz (cavity FSR) / 80 (Finesse) / 600 THz (GR frequency) ~ 3 nm.

which is almost consistent with the plot.

This instability might be caused by a bad bonding of the mirror with piezo.