Summary

• Lowering the CHRoCC power seems to improve the 56MHz mode matching by 40% for the USB and LSB from the point of view of the OMC
• The mode shape is very bad in any case with ~30% of order 1 mode and ~50% of order 2 mode, and many bright higher order modes

I have looked at the scans for 3 powers of the PR CHRoCC. Note that the USB (as described by the phase camera) is at lower OMC temperature, so that is why it appears first and is marked at negative frequency in the figures below.

Figure 7 is the overview, with the time roughly rescaled into MHz. The black line is for 0.43V, purple for 0.41V and grey for 0.39V. Also the position of the LSB/USB order 0, 1 and 2 are marked as a guide for the eye. The order mode has roughly 1/3 of the power of the TEM00, and the order 2 mode has roughly 1/2 of the power of the TEM00. This is a lot of misalignment and mode-mismatch. But I don't know what our expectation should be. Note that there is quite of higher order modes to. For example the USB order 3 mode has also 50% of the power of the TEM00.

Figure 1, 2 and 3 show respectively the oder 0, 1 and 2 mode for the 56MHz USB. Figure 4, 5 and 6 show the order 0, 1 and 2 mode for the 56MHz LSB.

The USB TEM00 seems to increase in power by ~20% for each step of reduction in CHRoCC power. The order 1 and 2 modes stay roughly the same, changing by less than 10%.

The LSB TEM00 stays the same within 10%. While the order 1 mode is reduced by 30%, and the order 2 mode is reduced by 40%.

So for both the 56MHz LSB and USB the mode shape improves as the CHRoCC power is reduced, as the ratio of TEM00 to order 1 and 2 modes is improving by 40%. The balancing of the sideband TEM00 remains roughly the same but changes signs. For 0.43V, the USB TEM00 was 30% lower than the LSB TEM00, while at 0.39V the USB TEM00 is 30% more powerful than the LSB TEM00.

When I look at the mode shapes during the scan at 0.43V the USB order 1 mode is ~80% a vertical misalignment, and the order 2 mode is completely vertical. For the LSB the order 1 mode is also ~80% vertical, while the order 2 mode is unclear as the camera shows a vertical mode, then a cross shaped mode, then a bull-eye mode, and there is only one image per second, so it is unclear what is corresponding to the peak, the order 2 mode in the time series does look like it is double with one peak half the size of the other, so it is reasonable to think that the horizontal and vertical order 2 mode contribute, with power ratio of a factor 2 between them.

When I look at the scan at 0.39V. The USB shows the same pattern, and the LSB as well, with also an ambiguous order 2 mode shape, that happens to be the brightesst for the horizontal order 2 mode, but this is somewhat random due to the sampling of 1Hz for the camera image.

Code used for these figures is in /users/mwas/OMC/OMC_scan_20220812

Figure 1 show the phace camera 56MHz powers during the three steps of 0.43V, 0.41V and 0.39V on the CHRoCC. The situation is consistent with what is observed with the OMC. The 56MHz LSB power is decreasing, and the OMC sees the reduction in power in HOM of the 56MHz LSB. The 56MHz USB power is increasing, and the OMC sees the increase of the TEM00 power with lower CHRoCC voltage.  The first step in decrease of CHRoCC voltage also improves the 56MHz LSB vs USB overlap, both on B1p and on B4.

Figure 2, 3 and 4 shows the B4/B1p PC images for respectively 0.43V, 0.41V and 0.39V. On B4 the beam is getting clearly more round with lower voltage on the CHRoCC. But is hard to draw a conclusion from the B1p image shape, it doesn't significantly get better or worse. So the OMC provides some information here by doing a mode decompostion, but that mode decomposition could in prinicple be done directly on the B1p PC image, and skip the 20min OMC scan, and 30min of analyzing the scan to figure which mode is which.

A question is what we expect for the 56MHz on the anti-symmetric (B1p) port. It is not clear to me if we expect the 56MHz to be on the dark fringe, or to have a bright TEM00 due to the Schnupp asymmetry. And whether this depends on which sideband is used to control the MICH degree of freedom (if 56MHz is used would we expect the 56MHz to be on the dark fringe, or that remains of dark fringe due to the Schnupp asymmetry, as the error signal still corresponds to a beat with the carrier light). This could actually be different for the 1f and 3f locks. I don't have a clear view here.

Overall the situation seems to improve with lower CHRoCC correction. The checks of arm cavities shows a worse matching between the CITF mode and the arms. But could it be due to the input beam matching? As the PR CHRoCC power is changed, the input beam is no longer well matched with the arms as the POP lens is changing, and to have a true view whether the CHRoCC tuning is improving things one would need to retune the input telescope to match well the arms on the carrier input beam (CITF not locked)