In the past few weeks and months it has been becoming increasingly clear that we are limited by beam jitter when going to higher power. The beam jitter requirements were derived assuming an rms misalignment of the test masses of 10^-9 rad rms in units of divergence angle or beam radius; see T0900142. The coupling mechanism is through the symmetric alignment matrix which mixes TEM₀₀ and TEM₁₀ modes. This transforms jitter in the first order mode back to zeroth order where it beats against the carrier field to produce an intensity fluctuation. This mechanism is independent of the OMC, since the intensity noise is generated in the interferometer. The jitter requirement into the input mode cleaner is:

We can compare this with the measurement from alog 30237 in the attached pdf. The solid olive curve represents the requirement which is a factor of 10 below the level (dashed olive line) one would expect the noise to be visible in the gravitational wave readout at full power and assuming a 10^-9 rms misalignment.

The following observations can be made:

• Even during O1 we have observed the periscope peak to be a factor of a few above the noise level. This would indicate the the assumption of a 10^-9 rms misalignment is about right for a cold interferometer. Keep in mind that the rms includes any static offset errors.
• In the current laser configuration (HPO on with ~5 l/m cooling flow) we are above the requirement for all frequencies between 50 Hz and ~1 kHz; typically by a factor of a few and a factor of ~40 in the worst case.
• The first order jitter out of the HPO meets the requirements. We would need a close to 2 orders of magnitude larger coupling to see the HPO jitter around 500 Hz.
• At high power with thermal loading the coupling typically gets worse—presumably because of higher order modes introducing a larger misalignment.
• It is basically impossible to explain the observed jitter coupling from the HPO using the exact same mechanism.

Possible alternative explanations to the visible HPO jitter in the gravitational wave readout at 50 W input:

• An unlikely Gouy phase conspiracy where the jitter after the PMC couples much weaker than the HPO jitter. In principle, the rms misalignment angle and spot position could be far different from each other. However, this would require two orders of magnitude difference and a required Gouy phase accuracy of ~1°.
• The HPO might also generate second order jitter at the TEM₂₀, TEM₁₁ and TEM₀₂ modes. This second order jitter would couple with arm cavity curvature and beam size mismatch back into the zeroth order mode. Under thermal load it is unlikely that we have a match at the 10^-9 level of beam size and curvature. It could be 100 times larger easily.
• Some other unknown mechanism—even so direct coupling through intensity noise, frequency noise or error point offset in the reflection port have essentially been ruled out.