Geometric interpretation of polarization plane movement in optical fiber

In this thesis study, the polarization states of the polarized light wave moving along the optical fiber associated with a curve are examined. In this research, quaternions, one of the fundamental tools of kinematic geometry, Plücker coordinates and Rodrigues formula are used. In addition, these polarization states are shown with Stokes parameters by using the relationship between quaternions and Stokes vectors. Some polarization states have been investigated using the surface-dependent curve associated with the optical fiber, along with the surface on which the curve is located. All polarization states are exemplified and visualized with the help of mathematical programs, thanks to the obtained formulations. The first chapter of the thesis, which consists of seven chapters, consists of an introduction where the studies on the subject mentioned in the thesis and the motivation of what is done in this thesis are explained. In the second chapter, mathematical and physical definitions and theorems used in preparing the thesis are included. In the third chapter, elliptical and circular polarization cases, which are taken as examples in the creation of other chapters of the thesis, are introduced. In the fourth which constitutes the original part of the thesis, the polarization states of the polarized light wave along the optical fiber are investigated with the help of hyperbolic split quaternions and dual split quaternions. Polarization states are examined according to Rodrigues formula, Plücker coordinates and screw motions, and thus polarization state formulations are obtained. All investigated polarization states are calculated with the help of Stokes parameters, with the help of the relationship of Stokes vectors with quaternions. Finally, examples confirming the results are given and visualized with the help of mathematical programs. In the fifth chapter, which is the last part of the thesis, the results obtained are interpreted geometrically and physically.