Using my model for the propagation from OM2 to the OMC I discussed in alog #84255, I made a contour plot for the mode overlap (O(q1,q2 ))c between the mode propagated through cold OM2 to the OMC, q1 and the fundamental mode of the OMC, q2 divided by the mode propagated through hot OM2 overlapped with the OMC mode, (O(q1,q2 ))h .
This is so I could comnpare it to measurements I made of the drop in optical gain, G when the curvature of OM2 was changed. Its hard to predict how much loss in total there is with the full interferomter locked but the optical gain change can tell us the change in optical loss between these two states which we assume to be due to mode-mis-match.
O' / O = (G' / G)2
In the plot I have used overlap ratio percentage, O % on the z axis, the real part of of the q I started with between OM1 and OM2 on the x-axis, and the imaginary part of this q on the y-axis.
O % = (O(q1,q2 ))h / (O(q1,q2 ))c × 100
The white line gives the square ratio of the optical gains measured in full-lock (alog #82559) for each of these states. The code to run this is in OM2_to_OMC_comp_full_IFO.m found at this respository on ligo gitlab.
The white line contains a contour of possible values of the q parameter between OM1 and OM2 for the full-locked state of the interferometer bar any changes since the end of January 2025 when I took these measurements.
The limit on mode-matching to the OMC with OM2 hot is 96.2% of the mode-matching to the OMC with OM2 cold. This means in full-lock our mode-matching should be better with a cold OM2.
The q value before OM2 should lie somewhere on this white curve in full-lock but we don't have any direct mode measurements with the interferometer in full-lock to constrain this yet.