Angular momentum of focused beams: Beyond the paraxial approximation
Open accessAbstract
We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam [$\ensuremath{\hbar}\ensuremath{\ell}$ orbital angular momentum per photon; $\ensuremath{\sigma}=1(\ensuremath{-}1)$ for left- (right-) handed polarization] by a high-numerical-aperture objective. The diffraction-limited focused beam has unexpected properties resulting from a strong interplay between the angular spatial structure and the local polarization in the nonparaxial regime. In the region near the beam axis, and provided that $|\ensuremath{\ell}|\ensuremath{\ge}2$ and $\ensuremath{\ell}$ and $\ensuremath{\sigma}$ have opposite signs, the energy locally counterpropagates and the projection of the electric field onto the focal plane counter-rotates with respect to the circular polarization of the incident beam. We explicitly show that the total angular momentum flux per unit power is conserved after focusing, as expected by rotational symmetry, but the spin and orbital separate contributions change.
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The SAM-IOAM coupling in nonparaxial optical fields is largely independent of how the field was generated; dipole Rayleigh scattering by a small particle generates a similar conical distribution and spin-to-orbital AM conversion.
“The SAM- IOAM coupling in nonparaxial optical fields is largely independent of how the field was generated. Instead of high-NA focusing, one can consider dipole Rayleigh scattering by a small particle, which generates a similar conical distribution of the outgoing wavevectors, Fig. 2d.”
From Spin–orbit interactions of light (2015) · cites this paper as [108]
Section IV (p. 8) identifies an interplay between spin and orbital angular-momentum fluxes in a nonparaxial focused beam. The paper does not establish that this interplay is independent of how the field is generated or discuss a conical distribution produced by dipole Rayleigh scattering. Section IV (p. 9) also explicitly prefers “interplay” to “interconversion” for local angular momentum. (LLM, conf=0.88)
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References 40 · Cited by 118
Research works printed but not linked: 4
- [6]E. Wolf, Proc. R. Soc. London, Ser. A 253 , 349 (1959).
- [7]B. Richards and E. Wolf, Proc. R. Soc. Lond. A 253 , 358 (1959).
- [9]P. A. Maia Neto and H. M. Nussenzveig, Europhys. Lett. 50 , 702 (2000); A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. London, Ser. A 459 , 3021 (2003); R. S. Dutra, N. B. Viana, P. A. Maia Neto and H. M. Nussenzveig, J. Opt. A: Pure Appl. Opt. 9 , S221 (2007).
- [16]A. Bekshaev, M. Soskin and M. Vasnetsov, arXiv:0801.2309v1 (2008). · arXiv
- Authors
- Monteiro, P. B., Neto, P. A. M., & Nussenzveig, H. M.
- Affiliations
- Universidade Federal do Rio de Janeiro (BR)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2009-03-20
- Volume
- 79
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2075084224
- Cited by
- 118
- References
- 40
- Citations by year
- 2026: 2 · 2025: 14 · 2024: 9 · 2023: 6 · 2022: 6 · 2021: 13 · 2020: 10 · 2019: 10 · 2018: 18 · 2017: 2 · 2016: 2 · 2015: 4 · 2014: 2 · 2013: 3 · 2012: 4
- FWCI
- 3.15
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- 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 › Laser-Matter Interactions and Applications
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- orbital angular momentum, Laguerre-Gaussian beams, circular polarization, high numerical aperture, spin angular momentum, diffraction-limited beam
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