Electromagnetic curves and rotation of the polarization plane through alternative moving frame

Abstract

This study investigates the behavior of a linearly polarized light wave in optical fiber and the rotation of the polarization plane through an alternative moving frame $$\{{\mathbf {n}},{\mathbf {c}},{\mathbf {w}}\}$$ in 3D Riemannian space. It is known that the geometric evolution of a polarized light wave is associated with the Berry phase (geometric phase). Thus, a new kind of geometric phase model has been generated in 3D Riemannian space. Moreover, the rotation of the polarization plane has been described using the Fermi–Walker parallel transportation law. Then, this was reviewed with the Rytov parallel transportation along with the direction of the state of the polarization plane in an optical fiber by means of the $$\{n, c, w\}$$ frame. Furthermore, the electromagnetic trajectories ( $${\mathbf {E}}$$ M-trajectories) obtained by the electric field $${\mathbf {E}}$$ along the polarization plane of a light wave traveling in an optical fiber were characterized. Finally, various examples to support the theoretical background were visualized.