Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space

In this paper, we relate the evolution equations of the electric field and magnetic field vectors of the polarized light ray traveling in a coiled optical fiber in the ordinary space into the nonlinear Schrodinger's equation by proposing new kinds of binormal motions and new kinds of Hasimoto functions in addition to commonly known formula of the binormal motion and Hasimoto function. All these operations have been conducted by using the orthonormal frame of Bishop equations that is defined along with the coiled optical fiber. We also propose perturbed solutions of the nonlinear Schrodinger'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.