Multiplicative calculus in optical fiber analysis: an alternative frame perspective

This work uses the techniques of a non-Newtonian calculus (or multiplicative calculus) in the 3D Riemannian manifold to investigate the geometric features of linearly polarized light waves along optical fibers using the alternative moving frame. The evolution of a linearly polarized light wave is linked to a geometric phase since the optical fiber is thought to be a one-dimensional object embedded in a 3D Riemannian manifold. Thus, we produce a novel kind of multiplicative derivative geometric phase model. Furthermore, we present magnetic curves that are produced by the electric field E, defined by the electromagnetic curve. Then we define the Rytov curve, which consists of the combination of the space curve and the electromagnetic curve. In conclusion, we gave examples that match the theory and visualized them using the MATLAB program and analyzed the results using multiplicative calculus, which allows us to interpret the results proportionally.