I adjusted the mode matching a bit ( changing lenses positions and rotate the lens on the collimator). The coupling efficiency was up to 66%. This should be enough for now.
The power input can go up to ~20mW, so the output is ~12mW which should be enough for gyro. I also adjusted the polarization, so that the polarization of the input beam matched the fast axis of the cable. I tested the polarization of the output beam with a PBS and got the extinction ratio of ~ 670.
The fiber is polarization maintaining fiber, nufern pm980.
It has fast and slow axes, and we have to match the polarization of the input beam to the fast axis. To do that
If the beam polarization matched the fiber axis, the output beam will have linear polarization which gives the maximum extinct ratio. Meanwhile if the beam polarization does not match the fiber axis, the output beam will have elliptic polarization and the extinction ratio will be lower, since certain amount of power will be transmitted and reflected no matter how you rotate the beam.