Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations

In this paper, we firstly obtain the evolution equations of the magnetic field and electric field vectors of polarized light ray propagating along a coiled optical fiber in Minkowski space. Then we define new kinds of binormal motions and new kinds of Hasimoto transformations to relate these evolution equations into the nonlinear Schrodinger’s equation. During this procedure, we use a parallel adapted frame or more commonly known as Bishop frame to characterize the coiled optical fiber geometrically. We also propose perturbed solutions of the nonlinear Schrödinger’s evolution equation that governs the propagation of solitons through the electric field ( E ) and magnetic field ( M ) vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes. Graphical abstract