Angular momenta and spin-orbit interaction of nonparaxial light in free space
Open accessAbstract
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observedexperimentally.
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The mean radius of a focused vortex beam is determined by its σ-dependent IOAM value: R ~ L_z / k sin θ; thus a beam with parallel SAM and IOAM becomes more strongly focused than a similar beam with anti-parallel SAM and IOAM.
“Namely, the mean radius of a focused vortex beam is determined by its σ -dependent IOAM value: R ~ Lz / k sin θ 8,27 . Due to this effect, a beam with parallel SAM and IOAM becomes more strongly focused than a similar beam with anti-parallel SAM and IOAM.”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
Section IV (pp. 4–5) relates the Bessel-beam caustic radius to σ-dependent OAM, but its quantization condition implies a larger radius when helicity σ and vortex charge ℓ have the same sign. That is the opposite of the claim that parallel SAM and IOAM produce stronger focusing. The paper discusses a caustic underlying an intensity maximum, not a beam’s mean radius. (LLM, conf=0.85)
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Experimental — accuracy not yet measuredThe Berry connection and Berry curvature immediately appear in all intrinsic SOI phenomena, such as the spin-Hall effect.
“Therefore, the Berry connection and Berry curvature immediately appear in all intrinsic SOI phenomena, such as the spin-Hall effect.”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
The Operator Formalism (p. 2) identifies a Berry connection and its curvature, and the Conclusion (p. 6) says Berry terms in the position operator describe the spin-Hall effect of light. The paper establishes this connection for the optical SOI phenomena it studies—nonparaxial light in free space—but does not support the claim about all intrinsic SOI phenomena. (LLM, conf=0.85)
Experimental — accuracy not yet measuredDue to the off-diagonal elements, incoming circularly-polarized light with helicity σ acquires an oppositely-polarized component with helicity -σ and vortex factor, and also a longitudinal z-component with vortex; for small apertures, the longitudinal component plays the leading role in AM conversion.
“Due to these elements, the incoming circularly-polarized light with helicity σ acquires an oppositely-polarized component with helicity -σ and vortex factor b exp 2 i σφ ( ) , and also a longitudinal z -component with the vortex 2 ab exp i ( σφ ) . For small apertures, the longitudinal component plays the leading role in the AM conversion.”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe spin-to-orbital AM conversion can be interpreted as an azimuthal spin-Hall effect in cylindrically-symmetric fields; breaking this symmetry results in a pronounced spin-Hall effect in the direction orthogonal to the symmetry-breaking axis.
“The spin-to-orbital AM conversion can be interpreted as an azimuthal spin-Hall effect in cylindrically-symmetric fields 24,26,112 . Breaking this symmetry results in a pronounced spin-Hall effect in the direction orthogonal to the symmetry-breaking axis 8,28- 33 .”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe intrinsic SOI of light originate from fundamental properties of the Maxwell equations and are analogous to the spin-orbit interactions of relativistic quantum particles and electrons in solids.
“The intrinsic SOI of light originate from fundamental properties of the Maxwell equations 7,8 and are analogous to the spin-orbit interactions of relativistic quantum particles 2,9,10 and electrons in solids 11,12 .”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
For nonparaxial beams, the simple association of SAM and IOAM with polarization and vortex is not valid; the SAM and IOAM become (3), and the total intrinsic AM is preserved, so part of the SAM is transferred to the IOAM (spin-to-orbital AM conversion).
“For nonparaxial beams, consisting of circularly-polarized plane waves with the wavevectors forming a cone with an opening angle θ (like in Fig. B2b), the SAM and IOAM become 8,27,96- 98”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
The spin-to-orbital AM conversion is closely related to the geometric phase between azimuthally-distributed wavevectors in the beam spectrum.
“Importantly, this effect is closely related to the geometric phase between the azimuthally-distributed wavevectors k in the beam spectrum (Fig. B2b) 8,27 .”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
Illuminating only the x>0 half of a high-NA lens results in a subwavelength transverse shift of the focal spot: Y' ∝ σ/k.
“For example, illuminating only the x > 0 half of a high-NA lens results in the subwavelength transverse shift of the focal spot 8,28- 30 : ′ Y ∝σ / k .”
From Spin–orbit interactions of light (2015) · cites this paper as [8]
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References 59 · Cited by 319
Research works printed but not linked: 1
- [31]B. Richards and E. Wolf, Proc. R. Soc. London A 253 , 358 (1959).
- Authors
- Bliokh, K. Y., Alonso, M. A., Ostrovskaya, E. A., & Aiello, A.
- Affiliations
- Ollscoil na Gaillimhe – University of Galway (IE)
- University of Rochester (US)
- Australian National University (AU)
- Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2010-12-21
- Volume
- 82
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2133796920
- Cited by
- 319
- References
- 59
- Citations by year
- 2026: 12 · 2025: 24 · 2024: 31 · 2023: 17 · 2022: 27 · 2021: 23 · 2020: 20 · 2019: 22 · 2018: 23 · 2017: 18 · 2016: 18 · 2015: 17 · 2014: 10 · 2013: 22 · 2012: 18
- FWCI
- 9.76
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ANU Open Research (Australian National University) (submittedVersion)
- MPG.PuRe (Max Planck Society) (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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- spin angular momentum, orbital angular momentum, spin-orbit coupling, Bessel beams, Berry phase, caustics, energy flow
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