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