A non-newtonian approach to geometric phase through optic fiber via multiplicative quaternions

Abstract

In this paper, we researched magnetic and electromagnetic curves in multiplicative Euclidean 3-space via multiplicative quaternion algebra. Firstly, we examined the geometric phase representation of the polarized light wave in the optic fiber by multiplying Frenet frame. Using the quaternionic approaches, we were able to derive the magnetic curve equations and theorems. Then, three particular instances have been illustrated with examples of electromagnetic curves and magnetic field equations. Lastly, we provided an interpretation of the findings. With the help of the results, we were able to present an alternative viewpoint on the construction of trajectories (such as circular or spiral-like ones) that do not exist uniquely in the realm of physics.