Abstract
This study investigates the behavior of a linearly polarized light wave in optical fiber and the rotation of the polarization plane through an alternative moving frame \(\{{\mathbf {n}},{\mathbf {c}},{\mathbf {w}}\}\) in 3D Riemannian space. It is known that the geometric evolution of a polarized light wave is associated with the Berry phase (geometric phase). Thus, a new kind of geometric phase model has been generated in 3D Riemannian space. Moreover, the rotation of the polarization plane has been described using the Fermi–Walker parallel transportation law. Then, this was reviewed with the Rytov parallel transportation along with the direction of the state of the polarization plane in an optical fiber by means of the \(\{n, c, w\}\) frame. Furthermore, the electromagnetic trajectories (\({\mathbf {E}}\)M-trajectories) obtained by the electric field \({\mathbf {E}}\) along the polarization plane of a light wave traveling in an optical fiber were characterized. Finally, various examples to support the theoretical background were visualized.
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References
Y.A. Kravtsov, Y.I. Orlov, Geometrical Optics of Inhomogeneous Medium (Nauka, Moscow, 1980 (Springer-Verlag, Berlin, 1990)
S.M. Rytov, Dokl. Akad. Nauk. SSSR 18, 263 (1938), reprinted, in Topological Phases in Quantum Theory, ed. by B. Markovski, S.I. Vinitsky (World Scientific, Singapore, 1989)
V.V. Vladimirski, Dokl. Akad. Nauk. SSSR 31, 222 (1941); reprinted, in Topological Phases in Quantum Theory, ed. by B. Markovski, S.I. Vinitsky (World Scientific, Singapore, 1989)
M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45 (1984)
M. Kugler, S. Shtrikman, Berry’s phase, locally inertial frames, and classical analogues. Phys. Rev. D 37(4), 934 (1988)
J.N. Ross, The rotation of the polarization in low briefrigence monomode optical fibres due to geometric effects. Opt. Quantum Electron. 16(5), 455 (1984)
R. Dandoloff, W.J. Zakrzewski, Parallel transport along a space curve and related phases. J. Phys. A Math. Gen. 22(11), L461 (1989)
R. Dandoloff, Berry’s phase and Fermi–Walker parallel transport. Phys. Lett. A 139(12), 19 (1989)
I.I. Satija, R. Balakrishnan, Geometric phases in twisted strips. Phys. Lett. A 373(39), 3582 (2009)
O. Yamashita, Effect of the geometrical phase shift on the spin and orbital angular momenta of light traveling in a coiled optical fiber with optical activity. Opt. Commun. 285, 3740 (2012)
O. Yamashita, Geometrical phase shift of the extrinsic orbital angular momentum d ensity of light propagating in a helically wound optical fiber. Opt. Commun. 285, 3061 (2012)
E.M. Frins, W. Dultz, Rotation of the polarization plane in optical fibers. J. Lightwave Technol. 15(1), 144 (1997)
T. Körpinar, R.C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi- Riemannian manifold. J. Mod. Opt. (2019) https://doi.org/10.1080/09500340.2019.1579930
T. Körpinar, R.C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D Riemannian manifold with Bishop equations. Optik Int. J. Light Electr. Opt. 200, 163334 (2020)
Z. Özdemir, A new calculus for the treatment of Rytov’s law in the optical fiber. Optik Int. J. Light Electr. Opt. 216, 164892 (2020)
A. Comtet, On the Landau Hall levels on the hyperbolic plane. Ann. Phys. 173, 185 (1987)
T. Adachi, Kahler magnetic flow for a manifold of constant holomorphic sectional curvature. Tokyo J. Math. 18, 473 (1995)
T. Adachi, Kahler magnetic on a complex projective space. Proc. Jpn. Acad. Ser. A Math. Sci. 70, 12 (1994)
J.L. Cabrerizo, M. Fernandez, J.S. Gomez, The contact magnetic flow in 3D Sasakian manifolds. J. Phys. A Math. Theor. 42, 195201 (2009)
M. Barros, J.L. Cabrerizo, M. Fernández, A. Romero, Magnetic vortex flament flows. J. Math. Phys. 48, 1–27 (2007)
M. Barros, A. Romero, J.L. Cabrerizo, M. Fernández, The Gauss-Landau-Hall problem on Riemanniansurfaces. J. Math. Phys. 46, 112905 (2005)
M. Barros, Magnetic helices and a theorem of Lancret. Proc. Am. Math. Soc. 125(5), 1503–1509 (1997)
T. Sunada, (1993) Magnetic flows on a Riemann surface. In Proceedings of the KAIST Mathematics Workshop:Analysis and Geometry, Taejeon, Korea, 3–6 August 1993; KAIST: Daejeon, Korea
Z. Bozkurt, İ. Gök, Y. Yaylı, F.N. Ekmekci, A new approach for magnetic curves in 3D Riemannian manifolds. J. Math. Phys. 55, 053501 (2014)
J.L. Cabrerizo, Magnetic fields in 2D and 3D sphere. J. Nonlinear Math. Phys. 20, 440–450 (2013)
S.L. Druta-Romaniuc, M.I. Munteanu, Magnetic curves corresponding to killing magnetic fields in E3. J. Math. Phys. 52, 113506 (2011)
S.L. Druta-Romaniuc, M.I. Munteanu, Killing magnetic curves in a Minkowski 3-space. Nonlinear Anal. Real World Appl. 14, 383–396 (2013)
Z. Özdemir, İ. Gök, Y. Yaylı, F.N. Ekmekci, Notes on magnetic curves in 3D semi-Riemannian manifolds. Turk. J. Math. 39, 412–426 (2015)
B. Uzunoğlu, İ. Gök, Y. Yaylı, A new approach on curves of constant precession. Appl. Math. Comput. 275, 317–323 (2016)
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Ceyhan, H., Özdemir, Z., Gök, İ. et al. 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
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DOI: https://doi.org/10.1140/epjp/s13360-020-00881-z