Soliton propagation of electromagnetic field vectors of polarized light ray traveling along with coiled optical fiber on the unit 2-sphereS²

Abstract

In this paper, we relate the evolution equation of the electric field and magnetic field vectors of the polarized light ray traveling along with a coiled optical fiber on the unit 2-sphere S² into the nonlinear Schrödinger'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 spherical equations that is defined along with the coiled optical fiber lying on the unit 2-sphere S². We also propose perturbed solutions of the nonlinear Schrödinger's evolution equation that governs the propagation of solitons through electric field (E) and magnetic field (M) vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes.

Geometric phase for timelike spherical normal magnetic charged particles optical ferromagnetic model

“…In the physical context, it has a key role in the theory of general relativity since it is one of the vacuum solutions of field equations. In the cosmological sight, solutions of formulas of Einstein by a positive cosmological constant are constructed in de Sitter metric, which models an expanding universe [26][27][28].…”

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