Anholonomic co-ordinates and electromagnetic curves with alternative moving frame via Maxwell evolution

Year 2023, Volume: 72 Issue: 4, 1094 - 1109, 29.12.2023

Hazal Ceyhan , Ebru Yanık , Zehra Ozdemir

https://doi.org/10.31801/cfsuasmas.1247095

Cited By: 1

Abstract

In this study, we examine the Berry’s phase equation for E-M curves in the C − direction and W − direction throughout an optic fiber via alternative moving frame in three dimensional space. Moreover, electromagnetic curve’s C − direction and W − direction Rytov parallel transportation laws are defined. Finally, we examine the electromagnetic curve with anholonomic co-ordinates for Maxwellian evolution by Maxwell’s equation.

Keywords

Applications to physics, magnetic curves, vector fields, Maxwell equations, electromagnetic theory, anholonomic co-ordinates, alternative moving frame

References

• Marris, A., Passman, S., Vector fields and flows on developable surfaces, Arch. Ration. Mech. Anal., 32(1) (1969), 29-86.
• Mukhopadhyay, A., Vyas, V., Panigrahi, P., Rogue waves and breathers in Heisenberg spin chain, Eur. Phys. J. B., 88 (2015), 188. https://doi.org/10.1140/epjb/e2015-60229-8
• Uzunoglu, B., Gök, I., Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput., 27 (2016), 317-323.
• Frins, E. M., Dultz, W., Rotation of the polarization plane in optical fibers, J. Lightwave Tech., 15 (1997), 144-147.
• Haldane, F. D. M., Path dependence of the geometric rotation of polarization in optical fibers, Opt. Lett., 11 (1986), 730-732.
• Ceyhan, H., Özdemir, Z., Gök I., Ekmekci, F. N., Electromagnetic curves and rotation of the polarization plane through alternative moving frame, Eur. Phys. J. Plus., 135(867) (2020). https://doi.org/10.1140/epjp/s13360-020-00881-z
• Satija, I. I., Balakrishnan, R., Geometric phases in twisted strips, Arch. Phys. Lett. A., 373 (2009), 3582-3585. https://doi.org/10.1016/j.physleta.2009.07.083
• Amor, J., Gimenez, A., Lucas, P., Integrability aspects of the vortex filaments equation for pseudo-null curves, Int. J. Geom. Methods Mod. Phys., 14 (2017), 1750090. https://doi.org/10.1142/S0219887817500906
• Cabrerizo, J. L., Fernandez, M., Gomez, J. S., The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A: Math. Theor., 42 (2009), 195201. doi 10.1088/1751-8113/42/19/195201
• Cabrerizo, J. L., Magnetic fields in 2D and 3D sphere, J. Nonlinear. Math. Phys., 20 (2013), 440-450. https://doi.org/10.1080/14029251.2013.855052
• Ross, J. N., The rotation of the polarization in low briefrigence monomode optical fibres due to geometric effects, Opt. Quantum Electron., 16 (1984), 455-461.
• Barros, M., Romero, A., Cabrerizo, J. L., Fernandez, M., The Gauss-Landau-Hall problem on Riemannian surfaces, J. Math. Phys., 46 (2005), 112905. https://doi.org/10.1063/1.2136215
• Barros, M., Cabrerizo, J. L., Fernandez, M., Romero, A., Magnetic vortex filament flows, J. Math. Phys., 48 (2007), 082904. https://doi.org/10.1063/1.2767535
• Grbovic, M., Nesovic, E., On Backlund transformation and vortex filament equation for pseudo-null curves in Minkowski 3-space, Int. J. Geom. Methods Mod. Phys., 13 (2016), 1650077. doi 10.1142/S0219887816500778
• Ungs, M., Ungs, L.P., Giz´e, A., The Theory of Quantum Torus Knots: Its Foundation in Differential Geometry - Volume II, Lulu, USA, 2020.
• Berry, M. V., Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A., 392 (1984), 45-57.
• Gürbüz, N., The pseudo-null geometric phase along optical fiber, Int. J. Geom. Methods Mod. Phys., 18(14) (2021), 2150230. doi 10.1142/S0219887821502303
• Yamashita, O., Geometrical phase shift of the extrinsic orbital momentum density of light propagating in a helically wound optical fiber, Opt. Commun., 285 (2012), 3061-3065. https://doi.org/10.1016/j.optcom.2012.02.041
• Dandoloff, R., Zakrzewski, W. J., Parallel transport along a space curve and related phases, J. Phys. A: Math. Gen., 22 (1989), L461-L466.
• Rytov, S. M., Dokl. Akad. Nauk. SSSR 18 (1938) 263; Topological Phases in Quantum Theory, eds. B. Markovski and S. I. Vinitsky (World Scientific, Singapore, 1989) (reprinted).
• Körpinar, T., Demirkol, R. C., Körpinar, Z., Asil, V., Maxwellian evolution equations along the uniform optical fiber in Minkowski space, Rev. Mex. de Fis., 66 (2020), 431-439. https://doi.org/10.31349/RevMexFis.66.431
• Körpinar, T., Optical directional binormal magnetic flows with geometric phase: Heisenberg ferromagnetic model, Optik 219 (2020), 165134. https://doi.org/10.1016/j.ijleo.2020.165134
• Körpinar, T., Körpinar, Z., Demirkol, R. C., Binormal schrodinger system of wave propagation field of light radiate in the normal direction with q-HATM approach, Optik, 235 (2021), 166444. https://doi.org/10.1016/j.ijleo.2021.166444
• Körpinar, T., Demirkol, R. C., Körpinar, Z., Approximate solutions for the inextensible Heisenberg antiferromagnetic flow and solitonic magnetic flux surfaces in the normal direction in Minkowski space. Optik, 238 (2021), 166403. https://doi.org/10.1016/j.ijleo.2021.166403
• Körpinar, T., Demirkol, R. C., Körpinar, Z., Binormal schrodinger system of Heisenberg ferromagnetic equation in the normal direction with Q-HATM approach, Int. J. Geom. Methods Mod. Phys., 18(6) (2021), 2150082. doi 10.1142/S0219887821500821
• Banica, V., Miot, E., Evolution, interaction and collisions of vortex filaments, Differential Integral Equations, 26(3/4) (2013), 355.
• Özdemir, Z., A new calculus for the treatment of Rytov’s law in the optical fiber, Int. J. Light Electr. Opt., 216 (2020), 164892. https://doi.org/10.1016/j.ijleo.2020.164892