A non-Newtonian approach to electromagnetic curves in optical fiber

Authors

  • Aykut Has Kahramanmaras Sutcu Imam University
  • Beyhan Yılmaz Kahramanmaras Sutcu Imam University

DOI:

https://doi.org/10.31349/RevMexFis.71.051306

Keywords:

Non-Newtonian calculus; optical fiber; electromagnetic theory; multiplicative Riemann manifolds; berry phase

Abstract

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.

References

Volterra V., Hostinsky B., Operations Infinitesimales Lineares, Herman, Paris, 1938.

Grossman M., Katz R., Non-Newtonian Calculus, 1st ed., Lee Press, Pigeon Cove Massachussets, 1972.

Grossman M., Bigeometric Calculus: A System with a Scale-Free Derivative, Archimedes Foundation, Massachusetts, 1983.

Rybaczuk M., Stoppel P., The fractal growth of fatigue defects in materials, International Journal of Fracture, 103 (2000), 71-94.

Rybaczuk M., Zielinski W., The concept of physical and fractal dimension I. The projective dimensions, Chaos, Solitons and Fractals, 12(13) (2001), 2517-2535.

Samuelson W.F. , Mark S.G., Managerial Economics, Wiley, New York, 2012.

Afrouzi H. H., Ahmadian M., Moshfegh A., Toghraie D., Javadzadegan A., Statistical analysis of pulsating non-Newtonian flow in a corrugated channel using Lattice-Boltzmann method. Physica A: Statistical Mechanics and its Applications, 535 (2019), 122486

Othman G.M., Yurtkan K., Özyapıcı A., Improved digital image interpolation technique based on multiplicative calculus and Lagrange interpolation. SIViP, 17 (2023), 3953–3961.

Uzer A., Multiplicative type complex calculus as an alternative to the classical calculus, Computers and Mathematics with Applications, 60 (2010) 2725–2737.

Bashirov A., Riza M., On complex multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics, 1(1) (2011), 75-85.

Yazici M., Selvitopi H., Numerical methods for the multiplicative partial differential equations, Open Math., 15 (2017), 1344–1350.

K. Boruah, B. Hazarika, Some basic properties of bigeometric calculus and its applications in numerical analysis, Afrika Matematica, 32 (2021), 211-227.

Aniszewska, D., Multiplicative Runge-Kutta methods. Nonlinear Dynamics, 50 (2007), 262-272.

Bashirov A., Mısırlı E., Tandogdu Y., Ozyapıcı A., On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ., 26(4) (2011), 425-438.

Yalçın N., Celik E., Solution of multiplicative homogeneous linear differential equations with constant exponentials, New Trends in Mathematical Sciences, 6(2) (2018), 58-67.

Waseem M., Noor M.A., Shah F.A., Noor K.I., An efficient technique to solve nonlinear equations using multiplicative calculus, Turkish Journal of Mathematics, 42 (2018), 679-691.

Bashirov A.E., Kurpınar E.M., Özyapıcı A., Multiplicative calculus and its applications. J. Math. Anal. Appl., 337 (2008), 36–48.

Gulsen T., Yilmaz E., Goktas S., Multiplicative Dirac system. Kuwait J.Sci., 49(3) (2022), 1-11.

Goktas S., Kemaloglu H., Yilmaz E., Multiplicative conformable fractional Dirac system. Turk. J. Math., 46 (2022), 973–990.

Goktas S., Yilmaz E., Yar A.C., Multiplicative derivative and its basic properties on time scales. Math. Meth. Appl. Sci., 45 (2022), 2097-2109.

Georgiev S.G., Zennir K., Multiplicative Differential Calculus (1st ed.), Chapman and Hall/CRC., New York, 2022.

Georgiev S.G., Multiplicative Differential Geometry (1st ed.), Chapman and Hall/CRC., New York, 2022.

Georgiev S.G., Zennir K., Boukarou A., Multiplicative Analytic Geometry (1st ed.), Chapman and Hall/CRC., New York, 2022.

Nurkan S.K., Gurgil I., Karacan M.K., Vector properties of geometric calculus. Math. Meth. Appl. Sci., (2023), 1–20.

Aydin M.E., Has A., Yilmaz B., A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves. ArXiv, (2023). https://doi.org/10.48550/arXiv.2307.16782

A. Has, B. Yılmaz, On helices in multiplicative differential geometry, Preprint arxiv: 2403.11282 (2024)

A. Has, B. Yılmaz, A non-Newtonian magnetic curves in multiplicative Riemann manifolds, Physica Scripta, 99 (2024) 045239

A. Has, B. Yılmaz, A non-Newtonian conics in multiplicative analytic geometry, Turkish Journal of Mathematics 48 (2024) 976

Y.A. Kravtsov, Y.I. Orlov, Geometrical Optics of Inhomogeneous Medium. Springer-Verlag, Berlin, 1990.

Kugler M., Shtrikman S., Berry’s phase, locally inertial frames, and classical analogues, Phys. Rev. D 37(4) (1988), 934.

Ross J.N., The rotation of the polarization in low briefrigence monomode optical fibres due to geometric effects, Opt. Quantum Electron. 16(5) (1984), 455.

Özdemir Z., A new calculus for the treatment of Rytov’s law in the optical fiber, Optik Int. J. Light Electr. Opt., 216 (2020), 164892.

Bozkurt Z., Gok I., Yaylı Y., Ekmekçi F.N., A new approach for magnetic curves in 3D Riemannian manifolds, Journal of Mathematical Physics, 55 (2014) 053501.

S.K. Nurkan, Ceyhan H., Özdemir Z., Gök İ., Electromagnetic curves and Rytov's law in the optical fiber with Maxwellian evolution via alternative moving frame, Revista Mexicana de Fisica, 69(6) (2023), 061301.

Körpınar T., Demirkol R.C. KörpınarZ., On the new conformable optical ferromagnetic and antiferromagnetic magnetically driven waves, Optical and Quantum Electronics, 55 (2023), 496.

Has A., Yılmaz B., Effect of fractional analysis on magnetic curves. Rev. Mex. Fís., 68(4) (2022),041401.

Yılmaz B., A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus, Optik - International Journal for Light and Electron Optics, 247 (2021), 168026.

Yılmaz B., Has A., A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus, Optik - International Journal for Light and Electron Optics, 260 (2022), 169067.

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Published

2025-09-01

How to Cite

[1]
aykut has and B. Yılmaz, “A non-Newtonian approach to electromagnetic curves in optical fiber”, Rev. Mex. Fís., vol. 71, no. 5 Sep-Oct, pp. 051306 1–, Sep. 2025.