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–Vladimirskii 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.
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The Berry phase provides a natural geometrical formalism that describes variations of the light polarization along the propagation trajectory.
“The Berry phase provides a natural geometrical formalism that describes variations of the light polarization along the propagation trajectory (see reviews [4 -7] and original papers [8 -20]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [9]
The Berry connection determines the natural parallel transport of the polarization vector e over the unit t-sphere.
“In this manner, polarization vector e is tangent to this sphere, and the Berry connection determines the natural parallel transport of e over the 2 S sphere, Fig. 2 [1 -7,9,13 -15,44,84 -90].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [9]
For a cyclic evolution in momentum space, the Berry phase equals the solid angle cut by the contour Γ.
“For a cyclic evolution in momentum space (which corresponds to a ray trajectory with the coincident input and output directions of propagation), the Berry phase (3.26) equals [4 -20]”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [9]
In the generic case of an elliptical polarization, Eq. (3.28) describes the same turn of the polarization ellipse on angle Φ_B with its eccentricity conserved.
“In the generic case of an elliptical polarization, Eq. (3.28) describes the same turn of the polarization ellipse on angle B Φ with its eccentricity conserved, Fig. 1 [4 -20,59].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [9]
The geometrical phase in this form is equivalent to Rytov's law of the polarization evolution.
“The geometrical phase in this form is equivalent to the Rytov's law of the polarization evolution, which had been invented long before the Berry phase discovery [4,8,9,59].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [9]
Cites
Quantal phase factors accompanying adiabatic changes
Berry, M. V. (1984) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1984.0023 · Cited by 9,252 · see citing works
Theory of Dielectric Optical Waveguides
(1991) · Elsevier eBooks · doi:10.1016/b978-0-12-470951-5.x5001-x · Cited by 2,061 · see citing works
A New Calculus for the Treatment of Optical SystemsI Description and Discussion of the Calculus
Jones, R. C. (1941) · Journal of the Optical Society of America · doi:10.1364/josa.31.000488 · Cited by 1,918 · see citing works
Wiener, N. (1930) · Acta Mathematica · doi:10.1007/bf02546511 · Cited by 1,802 · see citing works
A New Calculus for the Treatment of Optical Systems IV
Jones, R. C. (1942) · Journal of the Optical Society of America · doi:10.1364/josa.32.000486 · Cited by 1,023 · see citing works
Observation of Berry's Topological Phase by Use of an Optical Fiber
Tomita, A., & Chiao, R. Y. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.937 · Cited by 810 · see citing works
Polarization optics of twisted single-mode fibers
Ulrich, R., & Simon, A. (1979) · Applied Optics · doi:10.1364/ao.18.002241 · Cited by 761 · see citing works
Origins and control of polarization effects in single-mode fibers
Rashleigh, S. C. (1983) · Journal of Lightwave Technology · doi:10.1109/jlt.1983.1072121 · Cited by 548 · see citing works
Polarization in optical fibers
Kaminow, I. P. (1981) · IEEE Journal of Quantum Electronics · doi:10.1109/jqe.1981.1070626 · Cited by 536 · see citing works
Vali, V., & Shorthill, R. W. (1976) · Applied Optics · doi:10.1364/ao.15.001099 · Cited by 486 · see citing works
Single-mode fibre fractional wave devices and polarisation controllers
Lefèvre, H. C. (1980) · Electronics Letters · doi:10.1049/el:19800552 · Cited by 467 · see citing works
Mortimore, D. B. (1988) · Journal of Lightwave Technology · doi:10.1109/50.4119 · Cited by 431 · see citing works
A New Calculus for the Treatment of Optical SystemsII Proof of Three General Equivalence Theorems
Hurwitz, H., & Jones, R. C. (1941) · Journal of the Optical Society of America · doi:10.1364/josa.31.000493 · Cited by 368 · see citing works
Anandan, J. (1992) · Nature · doi:10.1038/360307a0 · Cited by 360 · see citing works
The Sagnac effect: correct and incorrect explanations
Malykin, G. B. (2000) · Physics-Uspekhi · doi:10.1070/pu2000v043n12abeh000830 · Cited by 295 · see citing works
Self-citationBirefringence and polarization mode-dispersion in spun single-mode fibers
Barlow, A. J., Ramskov-Hansen, J. J., & Payne, D. N. (1981) · Applied Optics · doi:10.1364/ao.20.002962 · Cited by 286 · see citing works
Ross, J. N. (1984) · Optical and Quantum Electronics · doi:10.1007/bf00619638 · Cited by 260 · see citing works
A New Calculus for the Treatment of Optical SystemsIII The Sohncke Theory of Optical Activity
Jones, R. C. (1941) · Journal of the Optical Society of America · doi:10.1364/josa.31.000500 · Cited by 231 · see citing works
Interpreting the anholonomy of coiled light
Berry, M. (1987) · Nature · doi:10.1038/326277a0 · Cited by 230 · see citing works
Fiber-optic rotation sensing with low drift
Ulrich, R. (1980) · Optics Letters · doi:10.1364/ol.5.000173 · Cited by 224 · see citing works
Anticipations of the Geometric Phase
Berry, M. (1990) · Physics Today · doi:10.1063/1.881219 · Cited by 224 · see citing works
Polarization mode dispersion in single-mode fibers
Rashleigh, S. C., & Ulrich, R. (1978) · Optics Letters · doi:10.1364/ol.3.000060 · Cited by 184 · see citing works
Coupled-Mode Theory for Anisotropic Optical Waveguides
Marcuse, D. (1975) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1975.tb02878.x · Cited by 148 · see citing works
Fiber-ring interferometer: polarization analysis
Ulrich, R., & Johnson, M. F. (1979) · Optics Letters · doi:10.1364/ol.4.000152 · Cited by 130 · see citing works
Simpson, J. R., Stolen, R. H., SEARS, F. M., et al. (1983) · Journal of Lightwave Technology · doi:10.1109/jlt.1983.1072129 · Cited by 128 · see citing works
Path dependence of the geometric rotation of polarization in optical fibers
Haldane, F. D. M. (1986) · Optics Letters · doi:10.1364/ol.11.000730 · Cited by 122 · see citing works
Polarization control in optical-fiber gyroscopes
Kintner, E. C. (1981) · Optics Letters · doi:10.1364/ol.6.000154 · Cited by 121 · see citing works
Sagnac Interferometer for Gravitational-Wave Detection
Sun, K.-X., Fejer, M. M., Gustafson, E. K., et al. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.3053 · Cited by 114 · see citing works
Fiber-Optic Rotation Sensors and Related Technologies
Ezekiel, S., & Arditty, H. J. (1982) · Springer series in optical sciences/SPringer series in optical sciences · doi:10.1007/978-3-540-39490-7 · Cited by 103 · see citing works
Topological phases in quantum mechanics and polarization optics
Vinitskiĭ, S. I., Derbov, V. L., Dubovik, V. M., Markovski, B. L., & Stepanovskiĭ, Y. P. (1990) · Soviet Physics Uspekhi · doi:10.1070/pu1990v033n06abeh002598 · Cited by 101 · see citing works
Physical problems of fiber gyroscopy based on the Sagnac effect
Andronova, I. A., & Malykin, G. B. (2002) · Physics-Uspekhi · doi:10.1070/pu2002v045n08abeh001073 · Cited by 98 · see citing works
Self-citationPerformance of Lyot depolarizers with birefringent single-mode fibers
Bohm, K., Petermann, K., & Weidel, Ε. (1983) · Journal of Lightwave Technology · doi:10.1109/jlt.1983.1072097 · Cited by 94 · see citing works
Low-noise fiber-optic rotation sensing
Böhm, K., Ulrich, R., Russer, P., et al. (1981) · Optics Letters · doi:10.1364/ol.6.000064 · Cited by 90 · see citing works
Birefringence and polarization effects in fiber gyroscopes
Pavlath, G. A., & Shaw, H. J. (1982) · Applied Optics · doi:10.1364/ao.21.001752 · Cited by 87 · see citing works
In-line fiber-optical polarization transformer
Johnson, M. F. (1979) · Applied Optics · doi:10.1364/ao.18.001288 · Cited by 82 · see citing works
Theory of polarization evolution in interferometric fiber-optic depolarized gyros
Szafraniec, B., & Sanders, G. A. (1999) · Journal of Lightwave Technology · doi:10.1109/50.754787 · Cited by 81 · see citing works
Rotation of the polarization plane in optical fibers
Frins, E. M., & Dultz, W. (1997) · Journal of Lightwave Technology · doi:10.1109/50.552122 · Cited by 69 · see citing works
Polarizer requirements for fiber gyroscopes with high-birefringence fiber and broad-band sources
Burns, W., & Moeller, R. (1984) · Journal of Lightwave Technology · doi:10.1109/jlt.1984.1073627 · Cited by 67 · see citing works
Linear coupling of electromagnetic waves in inhomogeneous weakly-ionized media
Zheleznyakov, V. V., Kocharovskiĭ, V. V., & Kocharovskiĭ, V. V. (1983) · Soviet Physics Uspekhi · doi:10.1070/pu1983v026n10abeh004518 · Cited by 66 · see citing works
Reciprocity of birefringent single-mode fibers for optical gyros
Schiffner, G., Leeb, W. R., Krammer, H., et al. (1979) · Applied Optics · doi:10.1364/ao.18.002096 · Cited by 55 · see citing works
Comment on ‘‘Observation of Berry’s topological phase by use of an optical fiber’’
Kitano, M., Yabuzaki, T., & Ogawa, T. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.523 · Cited by 51 · see citing works
Earlier studies of the Sagnac effect
Malykin, G. B. (1997) · Physics-Uspekhi · doi:10.1070/pu1997v040n03abeh000218 · Cited by 49 · see citing works
Self-citationJones calculus analysis of single-mode fiber Sagnac reflector
Birks, T. A., & Morkel, P. R. (1988) · Applied Optics · doi:10.1364/ao.27.003107 · Cited by 47 · see citing works
Special theory of relativity and the Sagnac effect
Логунов, А. А., & Chugreev, Y. V. (1988) · Soviet Physics Uspekhi · doi:10.1070/pu1988v031n09abeh005624 · Cited by 47 · see citing works
Fiber-optic gyroscopes with depolarized light
Burns, W. K., & Kersey, A. D. (1992) · Journal of Lightwave Technology · doi:10.1109/50.144925 · Cited by 46 · see citing works
Martinelli, M., & Vavassori, P. (1990) · Optics Communications · doi:10.1016/0030-4018(90)90380-c · Cited by 45 · see citing works
Sagnac effect in a rotating frame of reference. Relativistic Zeno paradox
Malykin, G. B. (2002) · Physics-Uspekhi · doi:10.1070/pu2002v045n08abeh001225 · Cited by 41 · see citing works
Self-citationPhase error bounds of fibre gyro with imperfect polariser/depolariser
Fredricks, R. J., & Ulrich, R. (1984) · Electronics Letters · doi:10.1049/el:19840224 · Cited by 39 · see citing works
Berry geometric phase in oscillatory processes
Клышко, Д. Н. (1993) · Physics-Uspekhi · doi:10.1070/pu1993v036n11abeh002178 · Cited by 37 · see citing works
Ring interferometer 950 m long
Vali, V., & Shorthill, R. W. (1977) · Applied Optics · doi:10.1364/ao.16.000290 · Cited by 35 · see citing works
Bias reduction by polarisation dispersion in the fibre-optic gyroscope
Jones, E., & Parker, J. W. (1986) · Electronics Letters · doi:10.1049/el:19860037 · Cited by 34 · see citing works
Polarization Sagnac interferometer with postmodulation for gravitational-wave detection
Beyersdorf, P. T., Fejer, M. M., & Byer, R. L. (1999) · Optics Letters · doi:10.1364/ol.24.001112 · Cited by 32 · see citing works
Polarization Sagnac interferometer with a common-path local oscillator for heterodyne detection
Beyersdorf, P. T., Fejer, M. M., & Byer, R. L. (1999) · Journal of the Optical Society of America B · doi:10.1364/josab.16.001354 · Cited by 27 · see citing works
Direct observation of Berry's topological phase by using an optical fiber ring interferometer
Frins, E. M., & Dultz, W. (1997) · Optics Communications · doi:10.1016/s0030-4018(96)00702-x · Cited by 23 · see citing works
Fiber-optic Sagnac interferometer for the observation of Berry's topological phase
Senthilkumaran, P., Culshaw, B., & Thursby, G. (2000) · Journal of the Optical Society of America B · doi:10.1364/josab.17.001914 · Cited by 21 · see citing works
Optical rotation sensing by the geometric effect of fiber-loop twisting
Itoh, K., Saitoh, T., & Ohtsuka, Y. (1987) · Journal of Lightwave Technology · doi:10.1109/jlt.1987.1075584 · Cited by 21 · see citing works
All-fibre gyroscope using depolarised superluminescent diode
Tai, S., Kojima, K., Noda, S., et al. (1986) · Electronics Letters · doi:10.1049/el:19860372 · Cited by 20 · see citing works
Fiber-optic tunable loop mirror using Berry’s geometric phase
Senthilkumaran, P., Thursby, G., & Culshaw, B. (2000) · Optics Letters · doi:10.1364/ol.25.000533 · Cited by 20 · see citing works
Partially polarized fiber-optic gyro
Blake, J. N., Szafraniec, B., & Feth, J. R. (1996) · Optics Letters · doi:10.1364/ol.21.001192 · Cited by 19 · see citing works
Geometrical phase effects in neutron optics
Bodnarchuk, V. I., Davtyan, L. S., & Korneev, D. A. (1996) · Physics-Uspekhi · doi:10.1070/pu1996v039n02abeh000133 · Cited by 19 · see citing works
Topological phase in classical mechanics
Malykin, G. B., & Kharlamov, S. A. (2003) · Physics-Uspekhi · doi:10.1070/pu2003v046n09abeh001635 · Cited by 17 · see citing works
Self-citationMalykin, G. B. (1999) · Physics-Uspekhi · doi:10.1070/pu1999v042n05abeh000495 · Cited by 17 · see citing works
Self-citationRuffin, P. B., Baeder, J., & Sung, C. C. (2001) · Optical Engineering · doi:10.1117/1.1354630 · Cited by 14 · see citing works
Effects of polarization nonreciprocity in fiber ring interferometers
Andronova, I. A., Gelikonov, G. V., & Malykin, G. B. (1999) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.340149 · Cited by 14 · see citing works
Self-citationKatsnel'son, A. A., Olemskoĭ, A. I., Sukhorukova, I. V., et al. (1995) · Physics-Uspekhi · doi:10.1070/pu1995v038n03abeh000077 · Cited by 13 · see citing works
Polarization Sagnac interferometer with a reflective grating beam splitter
Traeger, S., Beyersdorf, P. T., Goddard, L. C., et al. (2000) · Optics Letters · doi:10.1364/ol.25.000722 · Cited by 12 · see citing works
Boson- and fermion-like resonances in frozen-polarization media sensitive to Berry's phase rotation
Ривлин, Л. А. (1998) · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · doi:10.1088/1355-5111/10/1/033 · Cited by 5 · see citing works
Solid State Science: Past, Present and Predicted
Firth, W. J. (1987) · Journal of Modern Optics · doi:10.1080/09500348714551311 · Cited by 5 · see citing works
Space-time geometry with nonholonomic time field
Башков, В. И., & Sintsova, Y. V. (2001) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(01)80094-x · Cited by 5 · see citing works
Improved Response of Pyroelectric Millimeter Wave Detectors (Correspondence)
Alday, J. R., Everett, G. E., & White, D. J. (1966) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.1966.1126180 · Cited by 4 · see citing works
Connections in Principal Bundles and the Sagnac Effect
Башков, В. И., & Sintsova, Y. V. (1999) · Gravitation and Cosmology · Cited by 2 · see citing works
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Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
Spin-orbit interactions of light in isotropic media
Bliokh, K. Y., Aiello, A., & Alonso, M. A. (2012) · The Angular Momentum of Light · doi:10.1017/cbo9780511795213.009 · Cited by 20 · see citing works
- Authors
- Malykin, G. B., & Pozdnyakova, V. I.
- Affiliations
- Russian Academy of Sciences (RU)
- ORCID
- Pozdnyakova, Vera I
- Venue
- Physics-Uspekhi
- Published
- 2004-03-31
- Volume
- 47
- Issue
- 3
- Pages
- 289-308
- ISSN
- 1063-7869 (ISSN-L)
- 1468-4780
- OpenAlex
- W2002840123
- Cited by
- 28
- References
- 71
- Citations by year
- 2026: 1 · 2025: 1 · 2023: 2 · 2019: 1 · 2018: 2 · 2017: 1 · 2016: 2 · 2014: 1 · 2012: 1
- FWCI
- 1.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physics-Uspekhi (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Fiber Optic Sensors
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
- Keywords
- Berry phase, Pancharatnam phase, counterpropagating waves, dynamic phase, birefringence, Poincaré sphere, polarization evolution
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