Propagation of the polarized light along an optical fiber via Rodrigues formula and Lorentzian screw motion

Abstract

In this study, we investigate the propagation of polarized light along an optical fiber with the help of screw motion and Clifford's algebra of hyperbolic split dual quaternion in R sigma 1,sigma 2,sigma 31,2 . The importance of this study is that hyperbolic screw motion allows to us characterize four types of polarization states of polarized light waves in an optical fiber. These are elliptical polarization ((E)-polarization), circular polarization ((C)-polarization), Lorentzian circular polarization ((LC)-polarization), and linear polarization ((L)-polarization). In addition, we determine the parametric equations of the four types of trajectories drawn by the end-points of the polarization vector while propagating in space that are called elliptical-Rytov curves (ER), circular-Rytov curves (CR), hyperbolic-Rytov curves (HR) and linear-Rytov curves (LR). Moreover, we visualize the polarization states and the related Rytov curves via mathematical programs. Furthermore, we use the four Stokes parameters and their matrix formulas to explain polarization states in R sigma 1,sigma 2,sigma 31,2 .