Naoki, Vicky, Dhruva

With the FC locked in green with the red VCO locking, we observed that that the effective cavity length noise in red was much lower than how when we're using mass feedback. This made it possible to take ringdown measurments and estimate the finesse and cavity pole.

What is a ringdown measurement?

When the input beam to a cavity is turned off or moved off resonance, the circulating power in the cavity decays with a time constant (known as the storage time), which depends on the finesse/cavity pole/losses. This allows us to see transients in transmission and reflection from the FC. 

In order to make this measurement, we locked the OPO using dither lock on seed and moved the FCGS VCO offsets to make the seed resonant in the FC. Once on resonance, we brought the OPO to down, effectively turning off IR. This allowed us to see a transient exponential decay in the powers on REFL and TRANS. These were fit to the function -

P = P0 exp(-2t/tau)

where tau is the storage time of the cavity. 

It is related to the finesse as 

F = tau*pi*FSR

and cavity pole as 

f_pole = 1/(2*pi*tau)

See this paper for reference. 

There seemed to be a lot of variation between the 5 measurements that we took, however. The average storage time was around 4.2ms, corresponding to a finesse of ~6700. The range of cavity poles estimated by these measurements are between 30 and 50 Hz. We may retry these measurements in the future if we are stably able to lock the seed in the FC with a dither lock like LLO used for this measurment. 

EDIT : The design cavity pole of the FC is 40Hz (Finesse~6200)  so the measured value is quite close and does not indicate any obvious loss.

Looking at the fits carefully, it looks like the first measurement (which looks like an outlier) seems to have started a bit off resonance, with the trans being much lower than the rest (refl being higher).  Maybe a stable seed lock in the FC will help us get more consistent measurments