The rotation and incompatibility phase of the polarization state in monomode optical fibers

Abstract

We have discovered two new types of geometric phases associated with a space curve in motion, considering both the arc length and time parameters, in three different scenarios. By examining the natural Bishop triad (a triad that undergoes parallel transport) and utilizing the concept of Fermi–Walker parallelism, we have identified two distinct phases known as the “Bishop incompatibility” and the “Bishop–Fermi–Walker” phases. These phases arise due to the rotational behavior along the space curve, which exhibits path dependence. We have derived the relationship between these phases for all cases. This classical approach enables us to extend the understanding of geometric rotation of the polarization plane in a monomode optical fiber without birefringence, which is situated on a moving space curve. With this extension, we can calculate the geometric phase of the rotation plane when the optical fiber's space curve possesses an additional degree of freedom. Furthermore, we have established a connection between the Bishop incompatibility phase of the polarization state and the ordinary geometric phase of the rotation plane for the light wave as it propagates through the evolving monomode optical fiber system. © 2023 Elsevier GmbH