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

Ceyhan H., zdemir Z. O., KAYA S., GÜRGİL İ.

Revista Mexicana de Fisica, vol.70, no.6, pp.1-12, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.31349/revmexfis.70.061301
  • Journal Name: Revista Mexicana de Fisica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, DIALNET
  • Page Numbers: pp.1-12
  • Keywords: electromagnetic theory, magnetic flows, Multiplicative calculus, non-newtonian calculus, ordinary differential equations
  • Uşak University Affiliated: Yes

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. Usingthe quaternionic approaches, we were able to derive the magnetic curve equations and theorems. Then, three particular instances have beenillustrated with examples of electromagnetic curves and magnetic field equations. Lastly, we provided an interpretation of the findings. Withthe 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.