The Adiabatic Phase and Pancharatnam's Phase for Polarized Light
Abstract
In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincaré sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).
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This polarization-dependent shift is known as the spin Hall effect of light or optical Magnus effect.
“This effect is known as the spin Hall effect of light or optical Magnus effect [24 -35]”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
The Berry phase induces an additional term in the equations of motion (ray equations) which describes a polarization-dependent shift of the wave trajectory.
“In particular, it induces an additional term in the equations of motion (ray equations) which describes a polarization-dependent shift of the wave trajectory.”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
The spin Hall effect can be treated as an effective circular birefringence of the inhomogeneous medium, but in fact it arises because of the intrinsic property (spin) of light coupled to a curved ray trajectory.
“It can be treated as an effective circular birefringence of the inhomogeneous medium [25,26], but, in fact, it arises because of the intrinsic property (spin) of light coupled to a curved ray trajectory.”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
The spin Hall displacement is accumulated for repeating, cyclical trajectories in p space, e.g., for circular or helical trajectories in real space.
“Furthermore, the displacement is accumulated for repeating, cyclical trajectories in the p space - e.g., for circular or helical trajectories in the real space, Fig. 4 [25,35].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
The magnitude of the displacement δr can be estimated from Eq. (3.46) as the wavelength λ for a complete 2π turn of the direction of propagation, e.g., for a circular trajectory.
“The magnitude of the displacement δ r can be estimated from Eq. (3.46) as the wavelength λ for a complete 2 π turn of the direction of propagation (e.g., for a circular trajectory) [25].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
The spin Hall effect appears due to the transverse momentum gradient of the Berry phase.
“In other words, the spin Hall effect appears due to the transverse momentum gradient of the Berry phase [25] (see also [67]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [25]
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- Authors
- Berry, M. V.
- Corresponding author
- Berry, M.V.
- ORCID
- Berry, M.V.
- Venue
- Journal of Modern Optics
- Publisher
- Informa UK Limited
- Published
- 1987-11
- Volume
- 34
- Issue
- 11
- Pages
- 1401-1407
- ISSN
- 0950-0340 (ISSN-L)
- 1362-3044
- OpenAlex
- W2062830522
- Cited by
- 1,068
- References
- 20
- Citations by year
- 2026: 46 · 2025: 73 · 2024: 54 · 2023: 64 · 2022: 80 · 2021: 69 · 2020: 65 · 2019: 76 · 2018: 82 · 2017: 53 · 2016: 50 · 2015: 37 · 2014: 26 · 2013: 27 · 2012: 13
- FWCI
- 5.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Modern Optics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- Pancharatnam phase, adiabatic phase, Poincaré sphere, cyclic polarization, spinor algebra, Hermitian matrices, Aharonov-Bohm effect, circularly polarized light, optical fibers, Berry phase
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