After connecting the PD with the reflection from the arm to the PDH box, theY arm has been locked on the 01 mode. Maximizing the alignment, we obtained a 00 mode locking, but we couldn't maximize the power.
The size of the reflected beam was different with respect to the size of the incoming beam, so probably a bad mode matching was one of the issues.
Moreover, the reflected beam is very low power. We need to figure out why it is so (bad alignment? related to mode matching?)
After measuring better all the distances, I did a new mode matching calculation. I put the lenses after measuring the beam waist, so the size of the beam on the lenses was the same as expected from the calculation. Nevertheless, the beam size on the beam splitter looks bigger than expected, and also in this case green flashes into the cavity at some HOM (again 01).
I also tried to lock again the cavity and maximize the alignment, but I didn't get any improvement with respect to the previous mode matching.