Photon Berry’s phase as a classical topological effect
Abstract
We discuss Berry's phase rotation for electromagnetic radiation propagating in an optical fiber as a classical effect. We show that the evolution of the polarization vector is determined by a connection on the tangent bundle of the two-dimensional sphere. We use a topological argument to show that there exists only one rotationally invariant connection on the tangent bundle of the two sphere. The arguments apply to any classical transverse wave: for example, transverse vibrations propagating in a bent solid rod. The analogous effect in quantum electrodynamics, namely, Berry's phase for a single photon propagating in an optical fiber, is a simple consequence of the classical effect described. We argue that this should be viewed as a classical, rather than a quantum, effect. We also comment on recent related work of Haldane and of Berry.
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This effective magnetic field takes the form of a 'magnetic monopole' located at the origin of p-space.
“Remarkably, this field takes the form of a ' magnetic monopole ' located at the origin of p -space [12,17 -19,26 -35] (cf. [38,39]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [17]
This evidences an adiabatic regime of the wave evolution, i.e., independence of the right- and left-hand circular polarizations.
“This evidences adiabatic regime of the wave evolution [4,12,14,17], i.e., independence of the right- and left-hand circular polarizations.”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [17]
Cites
The Large Scale Structure of Space-Time
Hawking, S. W., & Ellis, G. F. R. (1973) · doi:10.1017/cbo9780511524646 · Cited by 10,624 · see citing works
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
Differential Forms in Algebraic Topology
Bott, R., & Tu, L. W. (1982) · Graduate texts in mathematics · doi:10.1007/978-1-4757-3951-0 · Cited by 2,860 · see citing works
Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
Simon, B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.2167 · Cited by 1,884 · see citing works
Gravitation, gauge theories and differential geometry
Eguchi, T., Gilkey, P., & Hanson, A. J. (1980) · Physics Reports · doi:10.1016/0370-1573(80)90130-1 · Cited by 1,833 · see citing works
Characteristic Classes. (AM-76)
Milnor, J., & Stasheff, J. D. (1974) · Princeton University Press eBooks · doi:10.1515/9781400881826 · Cited by 1,230 · 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
Manifestations of Berry's Topological Phase for the Photon
Chiao, R. Y., & Wu, Y.-S. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.933 · Cited by 482 · see citing works
Foundations of Differential Geometry.
Rickey, F. (1935) · doi:10.31390/gradschool_disstheses.7772 · Cited by 420 · see citing works
Ross, J. N. (1984) · Optical and Quantum Electronics · doi:10.1007/bf00619638 · Cited by 260 · see citing works
Interpreting the anholonomy of coiled light
Berry, M. (1987) · Nature · doi:10.1038/326277a0 · Cited by 230 · 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
Schwabl, F. (1999) · Advanced texts in physics · doi:10.1007/978-3-662-03929-8 · Cited by 91 · see citing works
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The Adiabatic Phase and Pancharatnam's Phase for Polarized Light
Berry, M. V. (1987) · Journal of Modern Optics · doi:10.1080/09500348714551321 · Cited by 1,068 · see citing works
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
Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
Bliokh, K. Y., Frolov, D. Y., & Kravtsov, Y. A. (2007) · Physical Review A · doi:10.1103/physreva.75.053821 · Cited by 67 · see citing works
Polarization transport of transverse acoustic waves: Berry phase and spin Hall effect of phonons
Bliokh, K. Y., & Freilikher, V. D. (2006) · Physical Review B · doi:10.1103/physrevb.74.174302 · Cited by 55 · see citing works
Geometric phase of optical rotators
Galvez, E. J., & Holmes, C. D. (1999) · Journal of the Optical Society of America A · doi:10.1364/josaa.16.001981 · Cited by 46 · 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
- Segert, J.
- Affiliations
- Princeton University (US)
- Corresponding author
- Segert, Jan
- ORCID
- Segert, Jan
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1987-07-01
- Volume
- 36
- Issue
- 1
- Pages
- 10-15
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W1989506700
- Cited by
- 53
- References
- 13
- Citations by year
- 2024: 4 · 2023: 1 · 2021: 3 · 2020: 1 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2014: 1 · 2013: 1 · 2012: 3
- FWCI
- 3.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Keywords
- Berry phase, optical fibers, polarization rotation, transverse waves, quantum electrodynamics, topological phases
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