Sheila, Elenna, Craig

Motivation: we are struggling to power up past 55 watts of input power.  
This is partially because the corner degrees of freedom are behaving strangely as we go up, with LSC sensing matrices which are strongly dependent on the power in the interferometer.
Rotation in the sensing matrix generally causes loss of gain and lockloss, unless we hold the hand of the loops (measure, adjust, step the power up).
Even so, we are hitting a hard limit at around 60 watts, beyond which we get a "fast" lockloss.

Idea: We thought that our RF sidebands may become imbalanced, causing some of our corner locking issues.  
To test this idea, we took several OMC scans at low and high power, in single bounce and full lock,  with moving the 9 MHz modulation depth.

Although we have all the data in the can, to simplify the discussion we will focus on the below scan, taken at 55 watts input with no DARM offset, but with the 9 MHz modulation depth increased by 3 dB.

Summary: 
1) The first thing that sticks out is the upper 9 MHz 20 mode.  It is higher than the 45 MHz 00 mode.
This is extreme, since the 9 MHz modes should not be making it through the SRC in huge amounts.  The upper 9 MHz 02 should not resonate anywhere in the interferometer.  Likely, some horrible scattering must be happening somewhere in the PRC.

2) The lower 9 MHz 20 mode (4.5 mA) is 20 times lower than the 9 MHz 20 mode.  Unfortunately, our code does not identify which of the double peaks is the lower 9 MHz 20, so it's not identified in the legend.
But from the plot it's clear that the scattering for the upper and lower 9 MHz modes is not equal.  From our 10W scan (second PDF attached), the ratio of (upper 9 20 / lower 9 20) = 3, not 20.

3) The 00 modes of both sidebands don't seem to suffer from this level of imbalance.  The 45 00s are very well balanced, but the 9 00s are apparently a factor of 3.4 off from one another.

4) Increasing power may be slowly exacerbating the power.  Plotted in PDF 4 is a comparison between a 50 and 55 W scan with normal mod depths.  There seems to be a big change in the upper 9 MHz 20, but none in the lower 9 MHz 20.  

5) I am not sure if we are correctly identifying the upper 9 MHz 00 mode.  Many of these mode identifications can be called into question, in fact.  The PZT voltage to frequency calibration was done with a third order polynomial fit using the 45 00 peaks as references.




The implications of this could mean we are introducing significant optical offsets into our corner due to HOM's polluting the normal error signal.
Now that we have this tool, we may try scanning more at high power, or during a TCS tuning session or ITM spot move to see if we can reduce/balance out these HOMs a bit.


The code for this analysis lives in labutils/omc_scan: https://git.ligo.org/aligo_commissioning/labutils/-/tree/master/omc_scan
Our code is in python.
Elenna has also copied Koji's MATLAB analysis code to this repo, fixed it up, and written instructions for how to use it.  The MATLAB analysis coded is focused on the single bounce scan only for now.