Earlier studies of the Sagnac effect

Malykin, G. B.

doi:10.3367/ufnr.0167.199703i.0337

Cited by 23 publications

(6 citation statements)

References 2 publications

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“…(6) In media possessing no magnetic activity or possessing simultaneous natural activity and linear birefringence, the Pancharatnam phase PP2 and the Rytov ± Vladimirski|¯phase are reciprocal and can be observed within a segment of the SMF or in Michelson and Mach ± Zender fiber interferometers; in fiber ring interferometers, they can be observed only in two-channel situations that arise if a monochromatic radiation source is used, that is, as a manifestation of a change in PN2. (7) The NGPCW can be regarded as a consequence of the difference between the excitation and evolution condition for GSPMs in the singlemode fiber lightguide of the fiber ring interferometer, corresponding to different arcs on the PoincareÂ sphere. If the FRI contour is made of a singlepolarization SMF, then the NGPCW and NPDCW are identical.…”

Section: Resultsmentioning

confidence: 99%

“…8 This is the reason why this phenomenon is known as noncommutativity of finite rotations. This effect, caused by the conical motion of a solid (referred to as`coning' in the American literature) was already discussed by W R Hamilton [13] and later, in more detail, by A Yu Ishlinski|¯ [14,15] (see also review [7]). Incidentally, as we showed in our publications [134,135], this classic effect has a relativistic analog: the Thomas precession.…”

Section: 2mentioning

confidence: 91%

“…Obviously, even if the above condition is satisfied, it is no longer possible to neglect the linear interaction of normal modes (polarization modes) if there are a large number of inhomogeneities over a considerable length of the optical medium (such as the SMF). 7 Ginzburg's results [101], just like those of Rytov [8,9] and Vladimirski|¯ [10], went unused for a long time. It was only in 1972 that E V Suvorov [116] applied the results of [101] to describe the propagation of electromagnetic waves through a plasma in the presence of a shear of force lines of a magnetic field.…”

Section: Circular Birefringence In Smfs Induced By Twistingmentioning

confidence: 99%

“…Presently, the term`Berry's phase' is often used not only in quantum mechanics but also in other fields (see reviews [2 ± 7]). It must be mentioned that the main manifestations of the geometric phase in polarization optics were discussed in detail in the 1930s ± 1950s by S M Rytov [8,9], V V Vladimirski|¯ [10], and S Pancharatnam [11,12] and even earlier in classical mechanics: 150 years ago by W R Hamilton [13] and 50 years ago by A Yu Ishlinski|¯ [14,15] (see review [7]). …”

Section: Introductionmentioning

confidence: 99%

“…Paper[101] treated a linear phase plate with torsion stresses 7. The condition that is violated in this case is hL 5 1, where L is the length of the SMF.…”

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Geometric phases in singlemode fiber lightguides and fiber ring interferometers

Malykin¹,

Pozdnyakova²

2004

Phys.-Usp.

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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 PoincareÂ 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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Section: Resultsmentioning

confidence: 99%

Section: 2mentioning

confidence: 91%

Section: Circular Birefringence In Smfs Induced By Twistingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Paper[101] treated a linear phase plate with torsion stresses 7. The condition that is violated in this case is hL 5 1, where L is the length of the SMF.…”

mentioning

confidence: 99%

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