Edwige pointed that my quick analytical computation are not correct. One obvious mistake was that I did not take into account the amplification by SR. In any case, Oscar simulation of this have been done in the past several time, and a 2m difference in curvature between the two arms should create ~100mW of order 2 mode (see for example VIR-0892A-23). And we clearly have not seen that. One reason is that we haven't done 2m of steps yet. The two steps characterized correspond to 1m in total, and the additional 0.5m have not been characterized yet. The characterization of that point hopefully will give us a clearer answer, but it is likely we haven't seen any effect with the previous two steps, because we have crossed zero average delta RoC while doing the steps. Looking at the shape of the order 2 mode in the different scan might give us more information, as there is also some astigmatism in the arms, so we could have moved from a zero difference in horizontal direction to zero in vertical direction (or vice versa).

The latest OMC scan on Jun 6 has finally provided some useful information. https://logbook.virgo-gw.eu/virgo/?r=64449

Figure 1 shows the scan from Jun 6, the order 2 mode power is around 150mW

Figure 2 superposes it with the other OMC scans done in the past few weeks. The order 2 mode power is about 3-4 times higher than in the previous scans, while the other HOM are not very different.

One important reason for that large difference is that the OMC scan on Tuesday Jun 4 was not done due lack of time, so there were in fact two steps of the EM RH since the last scan.

Figure 3 is an interpretation of what we have measured so far. On the x-axis are the steps of EM RH differential tuning, we have been doing steps of 0.5m in differential radius of curvautre, on the y axis is the order 2 mode power. From arm FSR scans we know the arms are astigmatic with ~2m in RoC difference between the horizontal and vertical direction. The model of figure 3 is just P = A*((dRoc-1)^2 + (dRoc+1)^2) with adjusted to get reasonably looking power. So the explanation of our measurements would be that the first three EM RH states with have OMC scans for would correspond to -0.5, 0 and 0.5 on that curve, and the last measurement is 1.5m on that curve (as it is after 2 steps). This would give 3 times more power in the last step, and roughly the same power in the other 3 steps.

Figure 4 Playing a bit more with parameters, and using an astigmatism of 1.5m instead of 2m one can get the measurement points close to a quadratic curve.

This would suggest that we need to do between 2 and 4 steps backwards (it can be done as a single larger step) to get back to the optimum. But that OMC scans are not informative if it should 2, 3 or 4 steps, and probably it doesn't matter because of the arm astigmatism. We could just try to go back to the state from March when the BNS range was close to 60Mpc, as that is somewhere in that range, and there is a chance that for some reasons we currently don't understand that particular setting was better.

/users/mwas/OMC/OMC_scan_demod_20240507/OMC_SCAN.m

  30.500   41.200   19.000   29.500
   25.800   29.900   38.200   41.700
   43.500   37.700   36.300   44.550
   19.000   57.200   20.500   23.300
   150        160         162      180