  A high-finesse Fabry-Perot cavity with a frequency-doubled continuous wave
green laser (532~nm) has been built and installed in Hall A of Jefferson Lab
for high precision Compton polarimetry. The infrared (1064~nm) beam from a
ytterbium-doped fiber amplifier seeded by a Nd:YAG nonplanar ring oscillator
laser is frequency doubled in a single-pass periodically poled MgO:LiNbO$_{3}$
crystal. The maximum achieved green power at 5 W IR pump power is 1.74 W with a
total conversion efficiency of 34.8\%. The green beam is injected into the
optical resonant cavity and enhanced up to 3.7~kW with a corresponding
enhancement of 3800. The polarization transfer function has been measured in
order to determine the intra-cavity circular laser polarization within a
measurement uncertainty of 0.7\%. The PREx experiment at Jefferson Lab used
this system for the first time and achieved 1.0\% precision in polarization
measurements of an electron beam with energy and current of 1.0~GeV and
50~$\mu$A.
