I measured the waist of the input beam to the PMC after putting the mode matching lenses back. In the process of this, I noticed some problems with the beamscan.
I played with the beamscan axis until I found something that looked gaussian to the eye, and took a series of measurements, and fit the data (see attached).
I calculated the expected power loss from mode mismatch a la Dana Anderson's paper on cavity (mis)alignment and got some results:
I get estimates for power losses of:
6% due to waist position mismatch
12% due to waist size mismatch
NOTA BENE: The formulas in the Anderson paper start to break down as the linear approximations break down, which is happening for us...
If b is my mismatch parameter in waist position, my condition for the linear approximation is:
lambda*b/(pi*waist^2) <<1 but the LHS quantity is .492
and if w0' and w0 are my input beam and cavity waists, respectively, my condition is:
w0'/w0  1 <<1 but the LHS is .34 here
Summary: I don't know how bad the Anderson formulas are in this regime of mismatch, but I can clearly do better in my mode matching. Next step: mode match/fix lens positions
Attached Image:
RED is roughly the PMC waist and position (based on the 40m PMC's waist  we have no measurement of this PMC's waist size yet afaik: put this on to do list)
GREEN is weighted least squares fit
BLUE is the data
