Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet
Open accessAbstract
We present a solution to the problem of reflection and refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, but, in general, do not satisfy the conservation laws for individual photons as a consequence of the lack of the "which path" information in a two-channel wave scattering. The field structure for the reflected and refracted beams is analyzed. In the scattering of a linearly polarized beam, photons of opposite helicities are accumulated at the opposite edges of the beam: this is the spin Hall effect for photons, which can be registered in the cross-polarized component of the scattered beam.
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The spin-Hall shift at an interface ensures the conservation of the z-component of the total angular momentum between the incident and reflected beams.
“Namely, this shift ensures the conservation of the z -component of the total AM between the incident and reflected beams: S z = ′ S z + Lz ext ′”
From Spin–orbit interactions of light (2015) · cites this paper as [15]
The paper states that transverse shifts satisfy conservation of the z-component of total angular momentum for the beams (p. 3). But it does not generally equate the incident beam’s angular momentum with the reflected beam’s alone: reflection and refraction are two channels, and the separate conservation laws hold only in specified cases, including total internal reflection (pp. 2–3). (LLM, conf=0.88)
Experimental — accuracy not yet measuredA circularly polarized laser beam reflected or refracted at a dielectric interface experiences a tiny transverse spin-dependent shift out of the plane of incidence.
“(i) A circularly polarized laser beam reflected or refracted at a dielectric interface does not propagate in the original plane but experiences a tiny transverse spin-dependent shift out of this plane.”
From Spin–orbit interactions of light (2015) · cites this paper as [15]
In the simplest case of total reflection from an interface, the reflected beam acquires a helicity-dependent shift (the Imbert-Fedorov shift).
“In the simplest case of total reflection from the interface, the reflected beam acquires the helicity-dependent shift”
From Spin–orbit interactions of light (2015) · cites this paper as [15]
Only recently, correct theoretical calculations and definitive measurements have elucidated the Imbert-Fedorov shift's nature as a SOI effect.
“Only recently, correct theoretical calculations 15,72 and definitive measurements 16 have elucidated its nature as a SOI effect.”
From Spin–orbit interactions of light (2015) · cites this paper as [15]
A number of experiments observed spin-orbit coupling and polarization transport of light in complex speckle fields of multimode optical fibers.
“There had been a number of remarkable experiment [120 -123] which observed the spin-orbit coupling and polarization transport of light in complex speckle fields of multimode optical fibers (see also [24]),”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [120]
A number of effects related to the spin-orbit coupling of light take place in multimode optical fibers.
“A number of effects related to the spin-orbit coupling of light take place in multimode optical fibers [24,120 -123,141 -144].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [120]
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Self-citation
- Authors
- Bliokh, K. Y., & Bliokh, Y. P.
- Affiliations
- Bar-Ilan University (IL)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-02-23
- Volume
- 96
- Issue
- 7
- Pages
- 073903-073903
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2026955211
- Cited by
- 753
- References
- 26
- Citations by year
- 2026: 55 · 2025: 69 · 2024: 49 · 2023: 64 · 2022: 59 · 2021: 57 · 2020: 46 · 2019: 49 · 2018: 38 · 2017: 36 · 2016: 29 · 2015: 33 · 2014: 29 · 2013: 28 · 2012: 34
- FWCI
- 9.03
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (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 › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- angular momentum conservation, transverse shift, spin Hall effect, photon spin, reflection and refraction, photon helicity, which-path information, linearly polarized light
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