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Cited by 80Orbital Angular Momentum in OpticsQuantum and Classical ElectrodynamicsLaser-Matter Interactions and Applications

Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization

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Li, Chun-Fang·2009·Physical Review A
DOI 10.1103/physreva.80.063814
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Abstract

It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that originates from the former part is spin, and the angular momentum that originates from the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxial beams that are described in a recently published paper [Phys. Rev. A 78, 063831 (2008)]. It is found that the orbital angular momentum depends, apart from an $l$-dependent term, on two global quantities, the polarization represented by a generalized Jones vector and another characteristic represented by a unit vector $\mathbf{I}$, though the spin depends only on the polarization. The polarization dependence of orbital angular momentum through the effect of $\mathbf{I}$ is obtained and discussed. Some applications of the result obtained here are also made. The fact that the spin originates from the part of momentum density that has no contribution to the net momentum is used to show that there does not exist the paradox on the spin of circularly polarized plane wave. The polarization dependence of both spin and orbital angular momentum is shown to be the origin of conversion from the spin of a paraxial Laguerre-Gaussian beam into the orbital angular momentum of the focused beam through a high numerical aperture.

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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 [107]

    Section III.B (p. 9) says its orbital-angular-momentum results hold for any physically allowed angular-spectrum function within the class of beams studied. Section IV.B (p. 16) explains spin-to-orbital conversion for high-NA focusing, but the paper does not establish that the coupling is independent of generation method or discuss dipole Rayleigh scattering and its proposed conical distribution. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

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References 43 · Cited by 80

Research works printed but not linked: 34

  1. [1]E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, Phys. Rev. Lett. 57, 2423 (1986).
  2. [4]S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
  3. [5]J. Leach et. al., Phys. Rev. Lett. 88, 257901 (2002).
  4. [6]G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
  5. [7]N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
  6. [8]M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature (London) 394, 348 (1998).
  7. [9]H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
  8. [10]L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
  9. [11]B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
  10. [12]B. Piccirillo, A. Vella, and E. Santamato, J. Opt. B: Quantum Semiclass. Opt. 4, S20 (2002).
  11. [13]A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
  12. [14]V. Garc´ es-Ch´ avez et al., Phys. Rev. Lett. 91, 093602 (2003).
  13. [15]Y. Zhao et. al., Phys. Rev. Lett. 99, 073901 (2007).
  14. [16]S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).
  15. [17]M. V. Berry, Proc. SPIE 3487, 6 (1998).
  16. [18]S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
  17. [19]L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics 39, 291 (1999).
  18. [20]S. M. Barnett, J. Opt. B: Quantum Semiclass. Opt. 4, S7 (2002).
  19. [22]C.-F. Li, Phys. Rev. A 78, 063831 (2008).
  20. [23]C.-F. Li, Phys. Rev. A 79, 053819 (2009).
  21. [26]J. Humblet, Physica 10, 585 (1943).
  22. [28]S. J. van Enk and G. Nienhuis, Europhys. Lett. 25, 497 (1994).
  23. [30]L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
  24. [31]Paula B. Monteiro, Paulo A. Maia Neto, and H. Moyses Nussenzveig, Phys. Rev. A 79, 033830 (2009).
  25. [32]D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
  26. [33]K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
  27. [34]C.-F. Li, Opt. Lett. 32, 3543 (2007).
  28. [36]J. W. Simmons and M. J. Guttmann, States, Waves and Photons (Addison-Wesley, MA, 1970).
  29. [37]R. Beth, Phys. Rev. 50, 115 (1936).
  30. [38]R. I. Khrapko, Am. J. Phys. 69, 405 (2001).
  31. [39]L. Allen and M. J. Padgett, Am. J. Phys. 70, 567 (2002).
  32. [40]A. Stewart, Eur. J. Phys. 26, 635 (2005).
  33. [41]M. Mansuripur, Opt. Express 13, 5315 (2005).
  34. [42]D. Lenstra and L. Mandel, Phys. Rev. A 26, 3428 (1982).

Authors
Li, C.-F.
Affiliations
Shanghai University (CN)
Corresponding author
Li, Chun-Fang
ORCID
Li, Chun-Fang
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2009-12-08
Volume
80
Issue
6
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.80.063814
OpenAlex
W1661933417
Cited by
80
References
43
Citations by year
2026: 2 · 2025: 6 · 2024: 1 · 2023: 1 · 2022: 1 · 2021: 6 · 2020: 4 · 2019: 5 · 2018: 4 · 2017: 1 · 2016: 7 · 2015: 6 · 2014: 8 · 2013: 9 · 2012: 5
FWCI
3.53
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • arXiv (Cornell University)
Funders
  • University of Rochester
  • National Natural Science Foundation of China
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 › Laser-Matter Interactions and Applications
Keywords
spin angular momentum, orbital angular momentum, momentum density, transversality conditions, circularly polarized plane waves, Laguerre-Gaussian beams, high numerical aperture focusing

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