Geometric phases in singlemode fiber lightguides and fiber ring interferometers

Abstract

We consider various geometric phases (GPs) in singlemode fiber lightguides (SMFs) and in fiber ring interferometers (FRIs): the Pancharatnam phase stemming from the cyclic evolution of the polarization state of radiation (RP state) in SMF, the Rytov ± Vladimirski|¯phase (RV phase) stemming from the Rytov effect (specifically, rotation of the polarization plane due to noncoplanar winding of SMFs), as well as the nonreciprocal phase difference of counterpropagating waves (NPDCW) and nonreciprocal geometric phase of counterpropagating waves (NGPCW), which are caused by polarization nonreciprocity (PN) in FRIs. We show that in the general case, the Pancharatnam phase for an arbitrary RP state is inconsistent with the real phase change of light fluctuations in media that possess not only circular but also linear birefringence. We show that the RV phase, having a geometric origin, can in principle be considered as a dynamic phase (DP). We also show that the NGPCW can be considered as an effect of the evolution of the RP state mapped on the Poincare sphere in Ginzburg's orthogonal screw polarization modes (GSPMs) of SMFs in the FRI contour. We analyze a number of experiments in which geometric phases were detected in FRIs: changing the RV phase and Rytov's angle (RA) in response to change of the pitch of helicoidal winding of SMFs. Contents 4.1 Kinematic phase in SMFs; 4.2 Linear birefringence of SMFs induced by bending; 4.3 Circular birefringence in SMFs induced by twisting. Ginzburg's screw polarization modes 5. The Rytov effect and Rytov ± Vladimirski|¯phase in SMFs and FRIs in the case of noncoplanar winding 297 5.1 The Rytov effect in a singlemode fiber lightguide of FRIs; 5.2 Similarities between the Rytov effect in polarization optics and the Ishlinski|¯effect in classical mechanics. Parallel vector translation. Noncommutativity of finite rotations; 5.3 The Rytov ± Vladimirski|¯phase and the Pancharatnam phase of the second kind in SMFs with noncoplanar winding 6. Polarization nonreciprocity in FRIs and the nonreciprocal geometric phase of counterpropagating waves 300 6.1 Polarization nonreciprocity in FRIs; 6.2 Nonreciprocal geometric phase of counterpropagating waves in FRIs 7. Analysis of experiments on recording the geometric phase in FRIs 303 7.1 Parameters of fiber ring interferometers on which measurements were conducted; 7.2 Analysis of experimental results 8. Unfounded hypotheses related to geometric phases in FRIs 305 9. Conclusion 305 References 306

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