Abstract-A complete analysis of the eigenstate of polarization (ESOP's) in a Brillouin fiber ring laser using fibers with a high circular birefringence is proposed in this paper. Conditions to obtain circular ESOP's for application in a Brillouin fiber optic current sensor are highlighted as well as conditions to have stable ESOP's for applications in other passive or active sensors. Measurements are performed on a Brillouin laser using a mechanically twisted fiber ring resonator confirming the theoretical predictions. Ring resonator configurations using linearly birefringent fibers are compared to configurations using circularly birefringent fibers.Index Terms-Brillouin scattering, optical fiber birefringence, optical fiber devices, optical fiber lasers, optical fiber polarization, optical resonators, optical scattering.