When cavity mirror alignment changes, the optical axis of cavity will change. This makes intra-cavity beam hits on different points on cavity mirrors. For example, when a pitch pertubation 'x' is introduced to cavity end mirror, according to cavity geometry, the intra-cavity beam will change beam hitting position on end mirror by 'x*(R-L)/2' while change beam hitting position on input mirror by 'x*(R+L)/2'. In our case, R~440m and L~300m.

When FC is locked with GR both in length and alignment, we can introduce the pertubation for input\end pitch\yaw. The detuning change is taken simulatenously. However, it is noticed that only small amount of misalignment can be introduced (about 5urad), otherwise, cavity get unlock. This introduced misalignment corresponds to a beam position change on the other cavity mirror by about 2mm.

The misalignment and detuning change is attached. We can see that the input mirror misalignment introduce more detuning change. This can be reasonable since the end mirror has more layers of coatings, which is more probably to have difference for phase error between GR and IR.

Michael and Yuhang

It was found that the detuning change is highly related with the correction signal sent to main laser when filter cavity is controlled with GR (elog2636).

To confirm this effect, we sent a sinusoidal signal to main laser temperature which can change main laser frequency up to few GHZ. After that, we collected the data of filter cavity end mirror z_corr, fc__ir_tra, and fc_ir_detuning.

Using the same method as elog2636 but the calibration factor from correction signal to length is from elog2606 because the control loop gain needs to be considered.  Then we get cavity correction signal and detuning change as attached figures. This proves again the detuning change caused by the presence of AOM.

OPO automatic lock recovered by itself.

Due to the presence of AOM, the length/frequency change influence GR and IR resonance in a different way. But if GR is always kept on resonance, IR detuning should have a change of 1.83e5 * cavity length correction.

In elog2611, I took a 24 hours monitor of detuning change and correction signal change. I checked the pointing loop is always kept around the good point. I used the simple above equation and compared the calculation and observed detuning change. To calibrate the observed correction to length change, the calibration method in elog2629 is used. Discrepancy between calculation and observation was found in the attached figure, but I think it is not surprising bacause the input and end mirror may have horizontal and vertical translational motion. By hitting on different position of mirror with 100um, detuning can change by few Hz.

To see if there is frequency drift effect from RF source, I tried to use DDS. I took DDS3 CH0 for the time being.

1. I removed 12dB attenuator connected to the output of DDS3 CH0.

2. I put 8dB attenuator (2*3+2).

3. Amplify with 13.6dB.

4. Goes to the amplifier which was used for old AOM RF source.

The frequency in DDS3 was found to be 109.541930MHz to make IR TEM00 on resonance.

First I optimized the p pol PLL frequency to maximize the amplitude of CCFC error signal. The optimized p pol PLL frequency was 200 MHz for OPO temperature of 7.163 kOhm and the CCFC calibration amplitude was 134mVpp.

Then I checked the nonlinear gain. The nonlinear gain was 4.4, which corresponds to the generated squeezing of 10.1dB.

I used a red LEMO cable between DDS output and mixer for CCFC LO to have larger detuning. The figure 1 shows CCFC FDS. The 50Hz bump somehow disappeared today. The detuning fluctuation is 51-69Hz. Note that the detuning fluctuation is not bad (51-57 Hz) other than the anti-squeezing quadrature.

I found that the 50Hz and its harmonics are already very large in shot noise (figure 2). The DC balance or ground condition is not good?

Degradation parameters:

sqz_dB = 10.1;                 % generated squeezing (dB)

L_rt = 120e-6;                 % FC losses

L = 0.49;                      % Propagation losses

A0 = 0.06;                     % Squeezer/filter cavity mode mismatch

C0 = 0.02;                     % Squeezer/local oscillator mode mismatch

ERR_L =   1.5e-12;             % Lock accuracy (m)

ERR_csi = 30e-3;               % Phase noise (rad)

[Aritomi, Yuhang]

Today we found that FC green error signal was noisy due to SHG oscillation. The figure 1 and 2 show the FC error signal with SHG gain of 1.4 and 1.6. We decreased the SHG gain from 1.6 to 1.4. The SHG OLTF with gain of 1.4 is shown in figure 3. The UGF is 4.7 kHz and phase margin is 10 deg.

We also found that the FC green injection power was reduced. We changed the SHG temperature and the green injection power increased from 18.8 mW to 23.7 mW.

Yuhang and Michael fitted this data with mcmc. However, the detuning fluctuation is larger than that with least square... In this fit, the fit has been started from 60Hz and the detuning fluctuation could be smaller with higher fit starting frequency.

Left: mcmc (detuning: 50-68 Hz)

Right: least square (detuning: 49-61 Hz)

In the last calibration calculation, I didn't consider the loop gain. Therefore, the calibration factor must have some error.

Nevertheless, we can use another way to do this calibration without considering the loop gain. 

0. Lock filter cavity.

1. Change slightly the temperature of main laser.

2. Read how much main laser frequency is changed.

3. Check how much length correction is sent to end mirror.

I did these procedures. The frequency change is read from the attached two figures. The correction signal change is in the attached figure three.

And get calibration factor (frequency difference)/(correction signal) = (248.6-235.2) [MHz]/ (5200) [counts] = 2.56 [MHz] / 1000 [counts]

Since 1pm = 1Hz, we can calibrate the factor above as 2.56 [um]/[kcounts].

The mcmc fit result of four parameters from published FDS data

[Aritomi, Yuhang]

Today we found that OPO automatic lock doesn't work. The reason was that OPO somehow cannot be scanned automatically with servo. For the moment, we locked OPO manually. We checked the UGF of the manual OPO lock and it was 4kHz.

We also found that current of p pol laser was not optimal value and the mode hop appeared in the OPO p pol transmission. We brought the current to the optimal value and the mode hop disappeared.

Yesterday, I took a new mixer (not the old TAMA one) and monitor its IF channel with two identical frequency RF signals as RF/LO.

The result is attached. Comparing this monitoring with elog2616, we can see much smaller drift.

To investigate the origin of bumps at 50 and 100 Hz in FDS measurement, I removed a phase shifter for CCFC LO and directly connected the DDS output for CCFC LO to the mixer with brown+green LEMO cables.

I tuned the CCFC demodulation phase by changing the LEMO cable length between DDS and mixer for CCFC so that time difference between center and 0 crossing point of the CCFC error signal becomes 44.4 ms, which corresponds to 44.4 ms*1.2 kHz/s = 53.3 Hz detuning. By using brown+green LEMO cables, I could realize the time difference of 44.4 ms. The sign of CCFC error signal is opposite compared with the one with the phase shifter.

The attached figure shows CCFC FDS without the phase shifter. The 100Hz bump becomes better without the phase shifter, but the 50Hz bump is still present. Also the 50Hz harmonics become larger without the phase shifter.

The detuning drift is 36-52 Hz, but this will be better with mcmc fit. The detuning is a bit smaller than the optimal value, so I will change the LEMO cable length for CCFC LO.

To compare least square fit and mcmc fit in a fair way, it is necessary to make both of them have both four parameters free with the four parameters defined in elog2618.

The information of mcmc fit has been already summarized in elog2618. The fit of least square information is summarized in the attached four figures.

Figure 1 and 2 are FDS with detuning ~200Hz. Figure 3 and 4 are FDS with detuning ~70Hz.

The least square fit gives similar result with mcmc if detuning is around 200Hz. However, the least square fit gives not-expected and seems-unresonable result as figure 3 and 4. By just changing the fitting method from least square to mcmc, we extract information more precisely and more reasonably.

For detuning around 200Hz data, the fit result of generated squeezing level and optical losses are

For detuning around 70Hz data, the fit result of generated squeezing level and optical losses are

Michael and Yuhang

In this elog, we compare the published FDS fit result and the new mcmc method we are using.

Interesting result! By the way, how is the fitting result of generated squeezing and optical loss for each curve? Are they consistent with each other?

Michael and Yuhang

We took FDS with filter cavity GR control about two weeks ago. The measurement contains 12 effective data with 6 for detuning around 200Hz and 6 for detuning around 70Hz. The data below around 70Hz is contaminated by back scattered noise. To have some margin from back scattered noise, we start fit from 100Hz.

The mcmc code needs a good enough initial value and corresponding range. We start with a least square fit with detuning, homodyne angles free and other parameters fixed. The fit result was used as initial value for mcmc code. The least square fit results are attached as figure 1 and 2.

We used the result of least square for mcmc and set four parameters to be free, including homodyne angle, detuning, optical losses, generated squeezing level. The result is attached as figure 3 and 4. The FDS with 200Hz detuning has more information about the squeezing quadrature rotation. Therefore, the error of fitting result is more precise. But the FDS with 70Hz detuning has less information, which makes the fit result has larger error on detuning.

The mcmc result gives more stabilized detuning, which means data favors a more stable detuning. The least square mothod gives larger detuning change may just comes from the fact that we are fixing other parameters but leave only two free.

First I checked IR injection alignment. There was yaw misalignment and the mode matching was 89%. 

After the alignment of yaw, the mode matching became 92% as follows. The injected BAB was 447uW. The misalignment is more or less fine, but LG is a bit larger than before.

By the way, during the alignment work, I noticed that the injection BAB power drifted a lot between 435uW and 465uW within a few minutes.

Then I locked CCFC and measured FDS (attached figure). CCFC calibration amplitude was 124mVpp, which is somehow lower than before. CCFC gain was 1000 and CC2 mass feedback gain was 3. The CCFC was stable and it kept locking during FDS measurement other than the squeezing quadrature. The 50, 100Hz bumps and detuning drift still exist.

Finally, I checked the nonlinear gain as follows. The nonlinear gain was 4.5 which corresponds to the generated squeezing of 10.2dB.

I will replace the electronics for CCFC to investigate the 50 and 100 Hz bumps.