Multiplicative calculus in optical fiber analysis: an alternative frame perspective
DOI:
https://doi.org/10.31349/RevMexFis.72.011301Keywords:
Optical fiber, non-Newtonian calculus, electromagnetic curves, polarized light wave, alternative moving frameAbstract
This work uses the techniques of a non-Newtonian calculus (or multiplicative calculus) in the 3D Riemannian manifold to investigate the geometric features of linearly polarized light waves along optical fibers using the alternative moving frame. The evolution of a linearly polarized light wave is linked to a geometric phase since the optical fiber is thought to be a one-dimensional object embedded in a 3D Riemannian manifold. Thus, we produce a novel kind of multiplicative derivative geometric phase model. Furthermore, we present magnetic curves that are produced by the electric field E, defined by the electromagnetic curve. Then we define the Rytov curve, which consists of the combination of the space curve and the electromagnetic curve. In conclusion, we gave examples that match the theory and visualized them using the MATLAB program and analyzed the results using multiplicative calculus, which allows us to interpret the results proportionally.
References
M. Grossman and R. Katz, Non-Newtonian Calculus, (Lee Press, Pigeon Cove, MA, 1972)
E. A. Bashirov, E. M. Kurpinar and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (2008) 36, https://doi.org/10.1016/j.jmaa.2007.03.081
S. G. Georgiev, Multiplicative Differential Geometry (Chapman and Hall/CRC, New York, 2022)
S. G. Georgiev, K. Zennir and A. Boukarou, Multiplicative Analytic Geometry (Chapman and Hall/CRC, New York, 2022)
Z. Ma, X. Yao, J. Li, and H. Liu, Non-Newtonian caustics and wavefronts in multiplicative Euclidean 2-space, Modern Physics Letters A (2025) 2550093
K. C. Wilson and A. D. Thomas, A new analysis of the turbulent flow of non-newtonian fluids, The Canadian Journal of Chemical Engineering 63 (1985) 539-546
Z. Li, L. Zheng and W. Huang, Rheological analysis of Newtonian and non-Newtonian fluids using Marsh funnel: experimental study and computational fluid dynamics modeling, Energy Science and Engineering 8 (2020) 2054-2072
M. M. Rashidi, M. T. Rastegari, M. Asadi and O. A. Bég, A study of non-Newtonian flow and heat transfer over a nonisothermal wedge using the homotopy analysis method, Chemical Engineering Communications 199 (2012) 231-256
G. Bohme and L. Rubart, Non-Newtonian flow analysis by fi- ¨ nite elements, Fluid dynamics research, 5 (1989) 147
T. Körpinar and R. C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semiRiemannian manifold, J. Mod. Opt. 66 (2019) 857
T. Körpinar and R. C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D Riemannian manifold with Bishop equations, Optik 200 (2020) 163384
H. Ceyhan, Z. Özdemir, I. Gok and F. N. Ekmekci, Electromagnetic curves of the polarized light wave along the optical fiber in De-Sitter 2-space, Eur. Phys. J. Plus 135 (2020) 867
Z. Özdemir, A new calculus for the treatment of Rytov’s law in the optical fiber, Optik 216 (2020) 164892
T. Körpinar, R. C. Demirkol and Z. Körpinar, Polarization of propagated light with optical solitons along the fiber in de-sitter space S 2 1 , Optik 226 (2021) 165872
T. Körpinar and R. C. Demirkol, Electromagnetic curves of the polarized light wave along the optical fiber in De-Sitter 2-space, Indian J. Phys. 95 (2021) 147
B. Yilmaz, A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus, Optik 247 (2021) 168026
B. Yilmaz and A. Has, Obtaining fractional electromagnetic curves in optical fiber using fractional alternative moving frame, Optik 260 (2022) 169067
S. G. Georgiev and K. Zennir, Multiplicative Differential Calculus (Chapman and Hall/CRC, New York, 2022)
A. Has and B. Yilmaz, A non-Newtonian conics in multiplicative analytic geometry, Turk. J. Math. 48 (2024) 976
A. Has, B. Yilmaz and H. Yildirim, A non-Newtonian perspective on multiplicative Lorentz-Minkowski space L 3 ∗, Math. Meth. Appl. Sci. 47 (2024) 1
Z. Özdemir and H. Ceyhan, Multiplicative hyperbolic split quaternions and generating geometric hyperbolical rotation matrices, Appl. Math. Comput. 479 (2024) 128862
H. Ceyhan, Z. Özdemir and I. Gok, Multiplicative generalized tube surfaces with multiplicative quaternions algebra, Math. Meth. Appl. Sci. 47 (2024) 9157
M. E. Aydin, A. Has and B. Yilmaz, Multiplicative rectifying submanifolds of multiplicative Euclidean space, Math. Meth. Appl. Sci. 48 (2024) 329
H. Ceyhan, Z. Özdemir, S. Kaya and I. Gurgil, A nonnewtonian approach to geometric phase through optic fiber via multiplicative quaternions, Rev. Mex. Fis. 70 (2024) 1
Z. Bozkurt, I. Gok, Y. Yayli and F. N. Ekmekci, A new approach for magnetic curves in 3D Riemannian manifolds, J. Math. Phys. 55 (2014) 053501
H. Ceyhan, Z. Özdemir, ˙I. Gok and F. Nejat Ekmekci, Electromagnetic curves and rotation of the polarization plane through alternative moving frame, Eur. Phys. J. Plus. 135 (2020) 867
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