First of all, we used and optical spectrometer to determine which proportion of pump and signal is in the injected beam.
the wavelength is THE SAME for the 2nd stage for the beam coming from the core or coming from the clad !
thus, it is impossible to use a spectrometer to obtain this proportion.

Thus, we made the assumption the pump beam (Sp) is unpolarized in contrary to the core beam (Sc) which is almost linearly polarized (Scp, Scs)

with a half waveplate and a PBS, we can define 2 cases in rotating the half waveplate at the output of the PBS :
maximum power : Scp + Sp/2 = a1
minimum power : Scs + Sp/2 = a2
The sum of both power a1 and a2 : a1+a2 = (Scp+Scs) + Sp is the total power of the beam before PBS.
The subtraction of power a1 and a2 : a1-a2 = Scp - Scs is independant of the pump power which can vary for example in opening an iris which normally block the most part of the pump beam.

if the core beam is perfectly linear, Scs=0 => a1-a2=Scp and Sp=2*a2
We did 2 measurements with a1=227mW, a2=67mW => Scp=160mW (Sp=134mW)
and with a1'=277mW, a2'=107mW => Scp=170mW (Sp'=214mW with a wider opened iris)

if these measurements and assumptions are correct, the real power injected to the cavity was 170mW (instead of 300mW).
with a coupling of 75% => Gain ~ 6.3k => Finesse ~ 19.7k !

to be confirmed...