Spin-orbit interaction of a photon in an inhomogeneous medium
Abstract
As light propagates in an optically inhomogeneous medium, bending and twisting of the beam cause the rotation of the polarization plane. This is the well-known Rytov-Vladimirsky effect or Berry phase. Considering this effect as the result of an interaction between the spin of the photon (polarization) and its orbital motion, one can expect the reverse effect. In fact, the additional angular shift of a trajectory of the circularly polarized beam (CPB) was recently studied for the particular case of an optical fiber. In this paper the spin-orbit interaction Hamiltonian is obtained both in geometrical optics and in wave optics. We have calculated also the effect of the transverse shift of CPB under refraction on the boundary of two media. The expressions for the angular shift of a trajectory of CPB in optical fibers with two types of refractive-index profiles have been obtained. Geometrical optics expressions can be applied for the typical waveguides only at lengths less than 0.05 cm. However, using the geometric optical picture we can successfully describe statistical properties of speckle patterns of laser radiation as it propagates at a considerable distance.
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In a gradient-index medium, the trajectory of light is described by equations of motion whose last term describes the transverse spin-dependent displacement (spin-Hall effect of light).
“The last term in Eq. (1) describes the transverse spin-dependent displacement of the trajectory, i.e., the spin-Hall effect of light (Fig. 1a).”
From Spin–orbit interactions of light (2015) · cites this paper as [3]
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 [27]
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 [27]
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 [27]
In a spherically-symmetric medium with n = n(r), the ray equations (3.40) possess an integral of motion J.
“Indeed, in a spherically-symmetric medium, ( ) ( ) n n r = r , the ray equations (3.40) possess the following integral of motion [27]:”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [27]
The conservation of total angular momentum, Eq. (3.42), links the spin Hall effect of light to the transverse Imbert-Fedorov shift.
“The conservation of the total angular momentum, Eq. (3.42), links the spin Hall effect of light to another remarkable phenomenon - the transverse Imbert-Fedorov shift [24,27,99 -118].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [27]
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Spin–orbit interactions of light
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“Comparing the phases of circularly polarized waves propagating in different directions involves SO(3) rotations of coordinates and generates helicity-dependent geometric phases, which are described by the Berry connection and curvature on the sphere of directions in wavevector space4,7,8,75,76,79 (Box 2).”
BackgroundMethodInfluential
- Authors
- Liberman, V. S., & Zel’dovich, B. Y.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1992-10-01
- Volume
- 46
- Issue
- 8
- Pages
- 5199-5207
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2158793546
- Cited by
- 424
- References
- 13
- Citations by year
- 2026: 12 · 2025: 11 · 2024: 28 · 2023: 28 · 2022: 30 · 2021: 26 · 2020: 20 · 2019: 23 · 2018: 22 · 2017: 19 · 2016: 22 · 2015: 23 · 2014: 9 · 2013: 23 · 2012: 10
- FWCI
- 1.15
- 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 › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Keywords
- spin-orbit coupling, photon polarization, Berry phase, circularly polarized light, optical fibers, refractive index profile, speckle patterns, geometrical optics, physical optics
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