I set the laser current at 200mA.
I used the PM100D power meter with the S145C power meter head to check the laser power fluctuations in several conditions.
I connected the analog output of the PM100D to the oscilloscope, and took some videos
I set the bandwidth of the PM to HI. I swithed OFF the auto range and set the range to 370mW.

PM right after the fiber output
display power: 61.3mW
analog out DC: 365mW
AC: video1 oscilloscope

PM after the first PBS
display power: 58.3mW
DC 350mW
AC: video2 

Then I rotated the half-wave plate to change the  PBS-HWP-PBS system transmitted power 

after PBS-HWP-PBS max transmission
display power: 54.3mW
DC: 327mV
AC: video3 
 

after PBS-HWP-PBS min transmission
display power: 0.0mW
DC: 10mV
AC: video4 

after PBS-HWP-PBS half transmission
display power: 25mW
DC: 150mV
AC:video5 

Changed the PM range to 370uW
after PBS-HWP-PBS min transmission
display power: 27uW
DC: 160mV
AC: video6 

Conclusion: looks like the fluctuations increase when the polarization rotates toward the minimum transmission.
I can't recognize the same jumps I saw in the DET10N