Electromagnetic curves and geometric phases of linearly polarized light waves along optical fibers on lightcone in Minkowski 3-space

In this paper, we define Legendre curves and introduce frontals with their associated moving frames on the lightcone in Minkowski 3-space. By treating an optical fiber as a curve on the lightcone, we analyze the geometric phase of linearly polarized light wave propagating along the optical fiber. We examine the transformation of polarization vectors along optical fibers and generate Rytov curves. The singularities of Rytov curves are investigated. Furthermore, we define electromagnetic curves on the lightcone and analyze the motion trajectories of charged particles under the influence of electromagnetic fields. Finally, we demonstrate our results through concrete examples.