Geometric Phase, Fermi–Walker Transport, and Polarization in Optical Fibers via Framed Curve Kinematics

The polarization dynamics of light in optical fibers are strongly influenced by the geometry of the propagation path. While experimental optics often employs Jones matrices or Mueller calculus to describe polarization transformations, such formalisms do not explicitly capture the geometric and topological features of curved trajectories. In this work, we propose a purely geometric framework by modelling an optical fiber as a framed curve in three-dimensional space. Using Berry phase analysis and Fermi–Walker transport, we establish explicit relations between curvature–torsion invariants of the curve and the evolution of the polarization vector. This approach leads to the definition of electromagnetic curves, providing a consistent mathematical formalism to interpret polarization transport in structured fibers. Theoretical results are illustrated through case studies and symbolic computations in MAPLE, which demonstrate how singularities in the framed curve influence the polarization state. Although our study is primarily mathematical, it offers a complementary theoretical perspective to standard optical methods and highlights how geometric invariants can serve as tools for understanding polarization in non-planar fiber geometries.