Reciprocity of birefringent single-mode fibers for optical gyros

Optical fiber ring interferometers are considered as sensors of rotation rate. Upon rotation of the fiber coil, a small nonreciprocal phase shift is introduced due to the Sagnac effect, and the interferometer senses this nonreciprocal behavior. To measure the rotation rate with high accuracy, it is important to exclude all nonreciprocal effects except the Sagnac effect. The paper presents mathematical evidence that birefringent single-mode fibers at rest in the absence of magnetic fields are reciprocal in the sense of the Lorentz reciprocity theorem. It is shown that placing polarizers in front of the fiber ends can suppress fringe shifts caused by changing reciprocal fiber properties.