Summary
Daniel points out that the behavior of REFL LF during the 9 MHz modulation depth reduction does not make sense:
- The measurement implies that during lock acquisition, at 50 W of PSL power there is 0.76 mW of 9 MHz light on the REFL diode.
- On the other hand, assuming a 9 MHz modulation depth of 0.22 rad, and a splitting ratio of 0.0066 W/W for the diode, and assuming 100% of the 9 MHz light is reflected out of the interferometer, we should instead expect 8.0 mW of 9 MHz light on the REFL diode.
- Additionally, AS_C sum indicates that we have about 100 mW of 9 MHz light leaking out the dark port at 50 W of PSL power, compared to 1.2 W of 9 MHz light being sent into the interferometer (assuming 0.22 rad of modulation depth). So we are not losing a significant amount of 9 MHz light through the dark port.
One possible explanation is that the 9 MHz depth is a factor of 3 lower than we think it is. However, based on single-bounce OMC tests (described below), this seems to not be the case. So the discrepancy remains unexplained.
Details
For the OMC test, I first turned up the modulation depth by 3 dB (the slider value is normally 16.8 dB during lock acquisition, so I turned it to 19.8 dB).
Then I locked the OMC on the carrier, and then each of the 9 MHz sidebands, and recorded the following data:
| Frequency |
PSL power (W) |
OMCR A sum (ct) |
OMC trans sum(mA) |
| Carrier | 9.8 | 600 | <0.01 |
| 82 | 14.6 | ||
| USB 9 | 47.2 | 2930 | 0.01 |
| 2860 | 1.07 | ||
| LSB 9 | 47.7 | 2920 | 0.01 |
| 2880 | 1.07 |
I assign an uncertainty of 10% to the OMCR and OMC trans sum values. The OMC visibility is not perfect here, but we can nonetheless roughly infer the modulation index. If the carrier measurement had been done at 47 W, we would have seen 70.6 mA of sum photocurrent. Since Psb/Pc ≈ Γ2/4, this implies Γ = 0.25 rad during this measurement. This implies a value of Γ = 0.17 rad during normal lock acquisition. This is within 30% of the old value measured with the PSL OSA (0.22 rad). In other words, we are not missing a factor of 3 in the modulation depth, so the behavior of REFL LF during lock acquisition does not make sense.
I am attaching more time series for what happens during 9 MHz modulation depth reduction.
The ~0.8% increase in the transmitted arm powers suggests a modulation depth during lock acquisition of about 0.13 rad. With this modulation depth, we'd expect a change of 2.0 mW on REFL LF during the reduction (instead we see 0.54 mW).
I made the following power measurements at 1.9 W:
I made the following measurements at 44 W, after reaching some kind of thermal equilibrium:
Note that (somewhat confusingly) REFL LF is calibrated into milliwatts on the diode itself, while AS LF appears to be calibrated into milliwatts exiting the AS port (i.e., before OM1).
We can use the REFL LF measurements to infer the carrier and sideband content both at 1.9 W and at 44 W. Here we assume the modulation depths have their nominal lock-acquisition values (16.8 dB for 9 MHz and 23.2 dB for 45 MHz, which based on old OSA measurements correspond to 0.22 rad and 0.28 rad of modulation depth). Additionally, we can scale the 1.9 W measurements to infer what we should see at 44 W, all other things being equal.
7.30
Note the large 9 MHz discrepancy from the power-up.
I copied the RF slider values for the 44 W measurement wrong out of my lab notebook, so here is the corrected table:
The algebra and resulting numerical values for the PD sideband content were done correctly, though.