We had a quick look at the data we collected yesterday, especially about the decay time of the arms due to induced fast unlocks with only one arm held on resonance at a time.

In the attached plots, the upper graph is about the overall behavior of the signals when we intentionally unlocked the IMC so to cut off the injected power. The IMC decay is quite fast  as expected, then the power measured by the PD on the end bench (transmitted power) has some rebound while decaying, and the PDs looking at the reflected power (B4 and B1p) show the predicted overshoot [1] and then the decay whose time constant is linked to the finesse of the cavity as:

Finesse = pi * tau * FSR *pi/2

We chose to analyse the response measured by B1p_PD1 that is the fastest sampled channel we can use, and also the sensor with a fair amount of power impinging on it. The outcomes are shown in the bottom plots of the attached pictures, semilogy scale to enhance any discrepancy with respect to the simple exponential model. The data stretch for each fit was chosen to start from the overshoot peak and last for 10msec (bottom axis can be misleading: t0 is the peak time of B1p).

Overall, the fit is not bad and gives some 1.77msec for the North arm and 1.80msec for the West. This, in turn, gives a Finesse of 437 for the Nort arm, and 444 for the West arm.

To be noticed that a more refined analysis is needed to take into account the IMC decay time that is possibly non-negligible with respect to the arms. Also, from the same measurements the overshoot can give an indication of matching and losses parameters [1], to be compared with the numbers obtained by the usual measurement of the arm reflectivities on-off resonance.

Work ongoing.

[1] T. Isogai, J. Miller, P. Kwee, L. Barsotti, and M. Evans, "Loss in long-storage-time optical cavities," Opt. Express 21, 30114-30125 (2013)

The measurement of the reflectivities of the arms on and off resonance give a direct way to estimate the round trip losses experienced by the circulating field, and yesterday night we performed it as it has been done many times (see for instance 41555).

In the attached histograms, a distribution of reflectivity values are reported as measured by using B1p_PD1 photodiode, with different conditions (arm on resonance, off resonance, and only ITM correctly aligned). For the West arm (see firs plot), the outcomes are pretty consistent:

when only the WI is aligned we have a nice estimate of the mirror reflectivity that compares well with nominal value (and, by the way, gives a value of Finesse Warm = 454), the reflectivity off resonance is centered around 1 (as expected) and the reflectivity on resonance is comparable with Warm RTL = 60ppm, as reported in many other measurements.

Unfortunately, the same was not true for the North arm measurement. In the second picture it seems that, apart from a wider spread of the values, there is some kind of overall shift towards higher reflectivities (in particular, larger than 1 in the off resonance case that is unfortunately non-physical). We are trying to understand if the problem is in the processing or in the measurement itself.

We had a closer look to the data of this old measurement of rtl of the North arm cavity (entry 42757), and actually found a subtle bug in the script that was used to extract the losses from reflectivity variation during different states of the cavity (on/off resonance and misaligned ETM). The problem was in the normalization and not in the data themselves, and by skipping some 150 initial seconds the normalization of the reflectivity to the off-resonance case worked pretty well.

So in the attached histogram, the ditribution of reflectivity values (bottom axis) and related rtl (top axis) is shown for different configurations of the cavity.

RTL are around 60ppm, reflectivity of NI mirror is slightly larger than the nominal one (purple line) but well within the measurement error and the etalon range.