Space-variant geometrical phases in focused cylindrical light beams
Open accessAbstract
We show that the depolarization caused when light is focused with a high-numerical-perture lens is accompanied by a space-variant geometrical phase. This phase results in the formation of modes with helicities and phase singularities that differ from those of the original beam. We show that this effect can be explained as a transverse shift of the rays, which is reminiscent of the recently discovered optical Hall-Magnus effect. Our results show that the asymmetric focal spot associated with the focus of linearly polarized light can be explained through geometrical effects.
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Breaking the cylindrical symmetry of a nonparaxial field produces spin-Hall effect shifts.
“Breaking the cylindrical symmetry of a nonparaxial field also produces spin-Hall effect shifts 28- 33 .”
From Spin–orbit interactions of light (2015) · cites this paper as [28]
The Abstract and the discussion of Fig. 3 describe transverse, helicity-dependent ray shifts during tight focusing, analogous to the optical Hall effect. But the paper studies initially axisymmetric beams and explains an asymmetric focal spot as an outcome; it does not show that breaking cylindrical symmetry of a nonparaxial field produces the shifts. (LLM, conf=0.85)
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 [28]
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 measuredIlluminating 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 [28]
The discussion accompanying Fig. 3 describes a transverse shift of rays with flipped helicity, producing an aberration in the focal plane. It does not describe a shift of the focal spot from illuminating only the x>0 half of the lens; the discussion of Eqs. (1)–(2) explicitly uses the entire aperture. The stated relation Y′ ∝ σ/k is not established for a half-illuminated lens in our copy. (LLM, conf=0.88)
Experimental — accuracy not yet measuredA curvilinear coordinate system based on unit vectors (u1, u2, t) is the only orthogonal coordinate system in the vicinity of the ray trajectory.
“It is worth noticing that a curvilinear coordinate systems based on unit vectors 1 2 ( , , ) u u t is the only orthogonal coordinate system in the vicinity of the ray trajectory [81,87,157].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [157]
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References 1 · Cited by 74
Research works printed but not linked: 10
- L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291.
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- K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. E 70, 026605 (2004).
- B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
- D. Ganic, X. Gan, and M. Gu, Opt. Express 11, 2747 (2003).
- Z. Bomzon, M. Gu, and J. Shamir, Appl. Phys. Lett. 89, 241104 (2006).
- S. M. Barnett, J. Opt. B: Quantum Semiclassical Opt. 4, S7 (2002).
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- Authors
- Bomzon, Z., & Gu, M.
- Affiliations
- Swinburne University of Technology (AU)
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2007-10-10
- Volume
- 32
- Issue
- 20
- Pages
- 3017
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W1996417211
- Cited by
- 74
- References
- 1
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 3 · 2023: 2 · 2022: 2 · 2021: 5 · 2020: 7 · 2019: 6 · 2018: 4 · 2016: 4 · 2015: 2 · 2014: 5 · 2013: 3 · 2012: 3
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- Figshare (submittedVersion, cc-by)
- Swinburne figshare (Swinburne University of Technology) (submittedVersion)
- Swinburne figshare (Swinburne University of Technology)
- Topics
- 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
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Keywords
- Berry phase, depolarization, high numerical aperture lens, helicity, phase singularities, linearly polarized light
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