A non-Newtonian approach to electromagnetic curves in optical fiber

The investigation within this article delves into the non-Newtonian geometric attributes exhibited by a linearly polarized light wave along an optical fiber within the framework of the 3D multiplicative Riemann manifold, employing multiplicative derivative and integral. While conducting this research, the unique arguments of multiplicative analysis (angle, norm, distance, etc.) are used. Within this context, the optical fiber is presumed as a one-dimensional entity embedded in the 3D Riemannian space, establishing a connection between the linearly polarized light wave's evolution and the geometric phase. Consequently, a novel form of the multiplicative geometric phase model is formulated, integrating the principles of multiplicative calculus. Additionally, the concept of multiplicative magnetic curves generated by the electric field $\e$ is introduced. Notably, this study stands out due to its unique utilization of multiplicative derivatives and integrals in the computational processes. The article culminates by presenting illustrative examples consistent with the outlined theoretical framework, accompanied by visual representations. The distinctiveness of this research lies in its departure from conventional methodologies, incorporating multiplicative calculus into the calculations. Remarkably, multiplicative computing demonstrates its applicability across diverse domains including physics, engineering, mathematical biology, fluid mechanics, and signal processing. The pervasive use of multiplicative derivatives and integrals signifies their profound significance as a novel mathematical approach, contributing substantially to problem-solving methodologies across various scientific disciplines.