I have now taken 3 measurements with s polarization at the input that saturated the lockin amplifier..
It seems that we can really easily saturates the p polarization.
Indeed, it is connected to the old lockin amplifier where the range (0 to 1 V) is changed depending on the sensitivity setting we are using.
Now I'm injecting about 160 uW of power but when doing the measurement with s polarization it seems that the p polarization power changes by more than a factor 14...
I'm starting hopefully the last measurement with s polarization at the input where the sensitivity of the old lockin is set to 100 mV despite the value at the center being 0.2 mV.
It would be convenient to have a new lockin amplifier to avoid this issue...