The latest measurements of 1/f^{2/3} between SR aligned and misaligned seems to confirm that the level of noise depends on the recycling by SR https://logbook.virgo-gw.eu/virgo/?r=66178. This would mean that the noise could be carried over by a higher order mode, and be higher when SR is aligned, as then the higher order mode amplitude is higher due to signal recycling.
If we consider order 2 modes there are two degrees of freedom:
- One has been explored by changing differentially the radius of curvature of the end mirrors. This had shown that there was no change in noise level when changing the power of the order 2 mode by a factor ~5, see for example section 2.1 of https://git.ligo.org/virgo/commissioning/mystery_one_over_f_two_thirds_noise . Changing the end mirrors radius of curvature changes the radius of the beam on the input mirrors, but it doesn't change the curvature of the beam on the input mirrors, as it has to remain parallel to the input mirror curvature.
- The changes in curvature of the input mirror have never been explored to my knowledge. Changing the lenses in the compensation plates has a similar effect, it changes the wavefront curvature of the beam, but outside of the cavity instead of inside. This equivalent when looking from the point of view of the destructive interference at the beam splitter, that is not perfect and send some higher order modes toward SR.
Analytical computations of the field reflected from a mismatch with the arms have been done a few years ago https://tds.virgo-gw.eu/?r=21578, (VIR-0117A-23). In slide 6 one can see that a difference in end mirror radius of curvature creates an order 2 mode that is in phase with the carrier, while on slide 16 that a difference in CP lenses creates an order 2 mode that is in quadrature with the carrier. The mode that is in quadrature with the carrier at the input of the arms is in the quadrature used for the local oscillator for measuring DARM. So differential CP lenses create a static order 2 mode that is in the right quadrature to transport noise to the dark port.
On Feb 7 2024, https://logbook.virgo-gw.eu/virgo/?r=63200, there were two steps of the DAS correction on NI and WI, following the increase of input power from 15W to 18W. There were difference in 1/f^{2/3} noise level observed during that time, VIR-0159A-24.
Figure 1 shows the noise level after the change in DAS power while figure 2 is during the night before the change in DAS power (but already at 18W of input power). The fit of the 1/f^{2/3} noise requires a 20% improvement in noise level. This improvement is in addition to any changes in double cavity pole frequency and DARM optical gain. In both cases the detector is in LN3, and the frequency noise projection is sufficiently low to be negligible.
/users/mwas/detchar/toySensitivity_20240207/toySensitivity.m
