A Geometric Interpretation of Polarized Light and Electromagnetic Curves Along an Optical Fiber with Surface Kinematics

In this study, we research the behavior of a linearly polarized light wave coupling into an optical fiber on a surface in 𝔼^3 via geometric phase equations. The geometric phase has applications in many areas from condensed-matter physics and optics to high-energy and particle physics and from fluid mechanics to gravity and cosmology. In this paper, we discuss in detail the motion of the polarization plane, and realizations of the geometric phase, using the Darboux frame fields. Moreover, we examine the rotation of the polarization plane of a light wave traveling in an optical fiber that lies on the surface based on the Fermi Walker parallel transportation rule. Furthermore, we visualize some motivated examples to support the theoretical results in the article using the MAPLE program.