Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
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We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.
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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 [28]
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 [28]
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 [28]
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- Authors
- Bliokh, K. Y., & Bliokh, Y. P.
- Affiliations
- Institute of Radio Astronomy (UA)
- Technion – Israel Institute of Technology (IL)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2004-08-23
- Volume
- 70
- Issue
- 2
- Pages
- 026605-026605
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W1972739030
- Cited by
- 129
- References
- 17
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 10 · 2023: 7 · 2022: 10 · 2021: 7 · 2020: 8 · 2019: 9 · 2018: 5 · 2017: 3 · 2016: 4 · 2015: 3 · 2013: 4 · 2012: 7
- FWCI
- 4.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 › Orbital Angular Momentum in Optics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- geometrical optics, Berry phase, Berry curvature, polarization rotation, group velocity, phase velocity, ray equations, ray splitting
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