A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus

Abstract

In the present paper, the geometric properties of the linearly polarized light wave are researched along an optical fiber using the conformable fractional derivative and integral in 3D Riemannian manifold. Since the optical fiber is supposed to be a one-dimensional object imbedded in a 3D Riemannian manifold, the evolution of a linearly polarized light wave is associated with geometric phase. So, we generate a new type of geometric phase model with fractional derivative. Also, we introduce a magnetic curves which are generated by the electric field E. Finally, examples consistent with the theory are examined and visualized for different values of the conformable fractional derivative. The difference of this study from others is the use of conformal fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics, signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.