Kinematic modeling of Rytov's law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra

Abstract

In this paper, we aim a kinematic method to investigate the behavior of polarized light in an optical fiber. Geometric phase equations are obtained using elliptic quaternions. The behavior of polarized light is studied for three conditions where the angle between the polarization vector (electric field) and the Darboux frame fields are constant on the ellipsoid. For these conditions, the polarization vector experiences a homothetic motion on the ellipsoid. Moreover, this motion can be defined by the Fermi Walker parallelism rule. Also, the traced curves of the polarization vector (Rytov curves) are calculated by homothetic motions and Elliptic quaternions. Additionally, the magnetic vector field related to the polarization vector is derived. Then the characterizations of the electromagnetic curve are obtained. To reinforce the theory, the homothetic motions of the polarization vector on the ellipsoid are visualized by giving examples for each case.