Fermat principle for spinning light
Open accessAbstract
Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' for polarized light (alias the ``Optical Magnus Effect'').
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Spin-Hall effects are ubiquitous to any optical interfaces and have been measured for interfaces with metals, uniaxial crystals, semiconductors, nanometal films, graphene layers, and metasurfaces.
“Spin-Hall effects are ubiquitous to any optical interfaces. They have been measured for interfaces with metals 81 , uniaxial crystals 82 , and semiconductors 83 , as well as at nanometal films 84 , graphene layers 85 , and metasurfaces 86 .”
From Spin–orbit interactions of light (2015) · cites this paper as [81]
In “Fermat Principle for spinning light” (p. 4), the paper describes an optical spin-Hall-related transverse shift at an interface between two homogeneous media with different refractive indices. It does not establish that the effect occurs at any optical interface or report measurements for the listed materials and structures. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe polarization rotation corresponding to the Berry phase has been measured experimentally in single-mode optical fibers coiled in a helix and for helical rays in a multimode rectilinear waveguide.
“The polarization rotation corresponding to the Berry phase (3.33) and (3.34) has been measured experimentally in single-mode optical fibers coiled in a helix similar to Fig. 1 [10,11] and for helical rays in a multimode rectilinear waveguide [20,35], cf. Section 4.”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
The Stokes vector obeys a precession equation.
“By differentiating expression (3.36) and using Eq. (3.29) we find that the Stokes vector obeys the following precession equation [34,35]:”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
The topological monopole affects the wave motion as a rather real physical entity.
“As it will be shown, the topological monopole affects the wave motion as a rather real physical entity (see Section 3.5) [35].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
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 [35]
The spin Hall effect of light and the ray equations (3.40) were verified by direct measurements for helical trajectories as in Fig. 4.
“Recently, the spin Hall effect of light and the ray equations (3.40) were verified by direct measurements for a helical trajectories as in Fig. 4 [35].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
The topological term in equations (3.40) can be written as Eq. (A12).
“Indeed, the topological term in equations (3.40) can be written as [35]”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
The geometrodynamical description of the propagation of light in gradient-index media can be extended to the case of weakly anisotropic media.
“The geometrodynamical description of the propagation of light in gradient-index media can be extended to the case of weakly anisotropic media [34,35,136 -138].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [35]
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- Authors
- Duval, C., Horváth, Z., & Horváthy, P. A.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- Université de Tours (FR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2006-07-07
- Volume
- 74
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2000278653
- Cited by
- 107
- References
- 20
- Citations by year
- 2026: 3 · 2024: 4 · 2023: 6 · 2022: 10 · 2021: 7 · 2020: 4 · 2019: 6 · 2018: 6 · 2017: 3 · 2016: 3 · 2015: 6 · 2014: 3 · 2013: 4 · 2012: 2
- FWCI
- 5.79
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Keywords
- Fermat's principle, Papapetrou equations, semiclassical model, optical Hall effect, polarized light
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