Abstract

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

2018 (6)

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
[Crossref]

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
[Crossref]

P. Shi, L. Du, and X. Yuan, “Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation,” Opt. Express 26(18), 23449–23459 (2018).
[Crossref]

P. Meng, S. Pereira, and P. Urbach, “Confocal microscopy with a radially polarized focused beam,” Opt. Express 26(23), 29600–29613 (2018).
[Crossref]

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams,” Opt. Lett. 43(22), 5677–5680 (2018).
[Crossref]

2017 (2)

2016 (2)

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

K. Y. Kim and S. Kim, “Spinning of a submicron sphere by airy beams,” Opt. Lett. 41(1), 135–138 (2016).
[Crossref]

2015 (4)

W. Zhu, V. Shvedov, W. She, and W. Krolikowski, “Transverse spin angular momentum of tightly focused full poincaré beams,” Opt. Express 23(26), 34029–34041 (2015).
[Crossref]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

2014 (1)

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

2013 (2)

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

S. N. Khonina, “Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions,” Opt. Eng. 52(9), 091711 (2013).
[Crossref]

2012 (1)

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

2011 (2)

2010 (3)

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref]

J. Pu and Z. Zhang, “Tight focusing of spirally polarized vortex beams,” Opt. Laser Technol. 42(1), 186–191 (2010).
[Crossref]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt. 11(6), 065204 (2009).
[Crossref]

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Z. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89(24), 241104 (2006).
[Crossref]

2004 (1)

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

2000 (2)

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

1992 (2)

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems-i. an integral representation of the image field,” Proc. R. Soc. Lond. A 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

1919 (1)

V. S. Ignatowsky, “Diffraction by a lens of arbitrary aperture,” Trans. Opt. Inst. 1, 1–36 (1919).

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Alfano, R. R.

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Chemical Rubber Company, 2016).

Alonso, M. A.

Ambrosio, A.

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

Andrews, D. L.

D. L. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2012).

Aoki, N.

Babiker, M.

D. L. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2012).

Banzer, P.

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Chemical Rubber Company, 2016).

Bauer, T.

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bliokh, K. Y.

Bomzon, Z.

Z. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89(24), 241104 (2006).
[Crossref]

Borbone, F.

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Brown, T. G.

Cai, Y.

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
[Crossref]

Canaguier-Durand, A.

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref]

Chaumet, P. C.

Cheng, H.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

Chujo, K.

Dainty, C.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Du, L.

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

Genet, C.

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

Golub, I.

Gong, L.

Gschneidtner, T.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Gu, M.

Z. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89(24), 241104 (2006).
[Crossref]

Han, L.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

Hu, X.

Ignatowsky, V. S.

V. S. Ignatowsky, “Diffraction by a lens of arbitrary aperture,” Trans. Opt. Inst. 1, 1–36 (1919).

Johansson, P.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Jones, P. H.

M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt. 11(6), 065204 (2009).
[Crossref]

Käll, M.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Karpeev, S. V.

Khonina, S.

Khonina, S. N.

Kim, K. Y.

Kim, S.

Krolikowski, W.

Kuchmizhak, A.

Kudryashov, S.

Kulchin, Y.

Lara, D.

Leach, J.

Lehmuskero, A.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Leuchs, G.

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Li, M.

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
[Crossref]

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
[Crossref]

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
[Crossref]

Li, P.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

Li, Y.

Liang, Y.

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
[Crossref]

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
[Crossref]

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
[Crossref]

Liberman, V. S.

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref]

Liu, S.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

Maddalena, P.

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[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Maragò, O. M.

M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt. 11(6), 065204 (2009).
[Crossref]

Marrucci, L.

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Meng, P.

Milione, G.

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M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
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Neugebauer, M.

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

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J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref]

Nguyen, T. A.

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Nolan, D. A.

Nori, F.

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

Ogier, R.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Okida, M.

Omatsu, T.

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M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
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Ostrovskaya, E. A.

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Chemical Rubber Company, 2016).

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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Pereira, S.

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Porfirev, A. P.

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J. Pu and Z. Zhang, “Tight focusing of spirally polarized vortex beams,” Opt. Laser Technol. 42(1), 186–191 (2010).
[Crossref]

Pustovalov, E.

Rashid, M.

M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt. 11(6), 065204 (2009).
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Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
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K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Z. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89(24), 241104 (2006).
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Shi, P.

Shvedov, V.

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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Vitrik, O.

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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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E. Wolf, “Electromagnetic diffraction in optical systems-i. an integral representation of the image field,” Proc. R. Soc. Lond. A 253(1274), 349–357 (1959).
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B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
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Yan, S.

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
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M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
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M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
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Yao, B.

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
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M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
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M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
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Yu, P.

Yuan, X.

Zayats, A. V.

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
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Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
[Crossref]

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
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M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
[Crossref]

Zhang, Y.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

Zhang, Z.

J. Pu and Z. Zhang, “Tight focusing of spirally polarized vortex beams,” Opt. Laser Technol. 42(1), 186–191 (2010).
[Crossref]

Zhao, J.

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
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Zhao, Q.

Zhizhchenko, A.

Zhu, W.

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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Appl. Phys. B: Lasers Opt. (1)

S. N. Khonina, “Vortex beams with high-order cylindrical polarization: features of focal distributions,” Appl. Phys. B: Lasers Opt. 125(6), 100 (2019).
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Appl. Phys. Lett. (1)

Z. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89(24), 241104 (2006).
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Astrophys. J. (1)

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J. Opt. (1)

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Spinning of particles in optical double-vortex beams,” J. Opt. 20(2), 025401 (2018).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

M. Rashid, O. M. Maragò, and P. H. Jones, “Focusing of high order cylindrical vector beams,” J. Opt. A: Pure Appl. Opt. 11(6), 065204 (2009).
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J. Opt. Soc. Am. B (1)

Nano Lett. (1)

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref]

Nat. Commun. (1)

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3(1), 989 (2012).
[Crossref]

Nat. Photonics (3)

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Nature (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Opt. Eng. (1)

S. N. Khonina, “Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions,” Opt. Eng. 52(9), 091711 (2013).
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Opt. Express (8)

W. Zhu, V. Shvedov, W. She, and W. Krolikowski, “Transverse spin angular momentum of tightly focused full poincaré beams,” Opt. Express 23(26), 34029–34041 (2015).
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K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
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P. Meng, S. Pereira, and P. Urbach, “Confocal microscopy with a radially polarized focused beam,” Opt. Express 26(23), 29600–29613 (2018).
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S. Syubaev, A. Zhizhchenko, A. Kuchmizhak, A. Porfirev, E. Pustovalov, O. Vitrik, Y. Kulchin, S. Khonina, and S. Kudryashov, “Direct laser printing of chiral plasmonic nanojets by vortex beams,” Opt. Express 25(9), 10214–10223 (2017).
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K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
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S. N. Khonina, A. P. Porfirev, and S. V. Karpeev, “Recognition of polarization and phase states of light based on the interaction of non-uniformly polarized laser beams with singular phase structures,” Opt. Express 27(13), 18484–18492 (2019).
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T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
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P. Shi, L. Du, and X. Yuan, “Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation,” Opt. Express 26(18), 23449–23459 (2018).
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Opt. Laser Technol. (1)

J. Pu and Z. Zhang, “Tight focusing of spirally polarized vortex beams,” Opt. Laser Technol. 42(1), 186–191 (2010).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (6)

M. Li, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Transverse spinning of particles in highly focused vector vortex beams,” Phys. Rev. A 95(5), 053802 (2017).
[Crossref]

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

V. S. Liberman and B. Y. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

L. Han, S. Liu, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams,” Phys. Rev. A 97(5), 053802 (2018).
[Crossref]

M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, and B. Yao, “Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams,” Phys. Rev. A 97(5), 053842 (2018).
[Crossref]

Phys. Rev. Lett. (5)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, “Optical polarization möbius strips and points of purely transverse spin density,” Phys. Rev. Lett. 117(1), 013601 (2016).
[Crossref]

Proc. R. Soc. Lond. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems-i. an integral representation of the image field,” Proc. R. Soc. Lond. A 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

Trans. Opt. Inst. (1)

V. S. Ignatowsky, “Diffraction by a lens of arbitrary aperture,” Trans. Opt. Inst. 1, 1–36 (1919).

Other (2)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Chemical Rubber Company, 2016).

D. L. Andrews and M. Babiker, The angular momentum of light (Cambridge University, 2012).

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Figures (9)

Fig. 1.
Fig. 1. Polarization distributions of CVV beams with $\varphi _0=\textrm{(a)}\;0,\;\textrm{(b)}\; \pi /6,\; \textrm{(c)}\;\pi /4,\; \textrm{(d)}\;\pi /3,\;$ and $\textrm{(e)}\;\pi /2$, respectively, when the topological charge $m=0$.
Fig. 2.
Fig. 2. Electric field intensity distributions in the focal plane of CVV beams with $\varphi _0=0$, $\pi /4$, $\pi /3$, $\pi /2$ and $-\pi /4\,$ (rows 1-5, respectively), when the topological charge $m=0$. All the intensities are normalized to the maximum intensities near focus for each illumination mode.
Fig. 3.
Fig. 3. Normalized SAM density distributions in the focal plane for CVV beams in Fig. 2 with $\varphi _0=0$, $\pi /4$, $\pi /3$, $\pi /2$ and $-\pi /4$  from left column to right, respectively. Rows $1$-$3$ are radial, azimuthal and longitudinal components of SAM density.
Fig. 4.
Fig. 4. Electric field intensity distribution in the focal plane of CVV beams with $\varphi _0=0$, $\pi /4$, $\pi /3$, $\pi /2$ and $-\pi /4\,$ (rows 1-5, respectively), when the topological charge $m=1$. All the intensities are normalized to the maximum intensities near focus for each illumination mode.
Fig. 5.
Fig. 5. Normalized SAM density distributions in the focal plane for CVV beams in Fig. 4 with $\varphi _0=0$, $\pi /4$, $\pi /3$, $\pi /2$ and $-\pi /4$  from left column to right, respectively. Rows $1$-$3$ are radial, azimuthal and longitudinal components of SAM density.
Fig. 6.
Fig. 6. Normalized cross-sectional electric spin densities in the focal plane of strongly focused input CVV beams with $\varphi _0=0$, $\pi /6$, $\pi /4$, $\pi /3$, $\pi /2$ and $-\pi /4$ and topological charge $m=0$ (Figs. 6$(\textrm{a}_1)$6$(\textrm{c}_1)$), $m=1$ (Figs. 6 $(\textrm{a}_2)$6$(\textrm{c}_2)$) and $m=-1$ (Figs. 6 $(\textrm{a}_3)$6$(\textrm{c}_3)$), respectively. The distributions in all plots are normalized to their maximum values.
Fig. 7.
Fig. 7. Normalized cross-sectional electric spin densities $\textrm{(a)}$ radial SAM density $S_r$, $\textrm{(b)}$ azimuthal SAM density $S_\phi$ and $\textrm{(c)}$ longitudinal SAM density $S_z$ in the focal plane of strongly focused input CVV beams with $\varphi _0=\pi /4$ and topological charge changes from 0 to 4. The distributions in all plots are normalized to their maximum values.
Fig. 8.
Fig. 8. Three-dimensional optical torque $\mathbf {\Gamma }$ distributions in the focused fields of general CVV beams with $\varphi _0=\pi /4$ and topological charges (a) m=4 and (b) m=-4. The corresponding spin and orbital motions of trapped absorptive spheres illuminated by the same focal beams with (c) m=4 and (d) m=-4.
Fig. 9.
Fig. 9. Three components of local maximum optical torques $\mathbf {\Gamma }$ at the hot-spots in the focused fields of CVV beams with topological charges (a) m=1, (b) m=2 and (c) m=3 versus the angle $\varphi _0$ changes from 0 to 2$\pi$. Different colors refers to different components: blue-the radial torque, red-the azimuthal torque and yellow-longitudinal torque. For comparison, (d)-(f) show the variations of each maximal optical torque components at the hot-spot as the topological charge changes from 1 to 5 and $\varphi _0$ changes from 0 to 2$\pi$. Different line styles represent different topological charges.

Equations (12)

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E 0 = A 0 e i m φ ( cos φ 0 e ^ r + sin φ 0 e ^ φ ) = A 0 e i m φ [ cos ( φ + φ 0 ) e ^ x + sin ( φ + φ 0 ) e ^ y ] ,
E ( r , ϕ , z ) = i k f 2 π 0 2 π 0 θ max cos θ l ( θ ) sin θ e i m φ M e exp ( i k r ) d θ d φ , H ( r , ϕ , z ) = i k f 2 π 0 2 π 0 θ max cos θ l ( θ ) sin θ e i m φ k × M e exp ( i k r ) d θ d φ ,
l ( θ ) = exp [ β 2 ( sin θ sin θ max ) 2 ] J 1 ( 2 β sin θ sin θ max ) ,
M e = [ sin φ 0 sin φ + cos φ 0 cos θ cos φ sin φ 0 cos φ + cos φ 0 cos θ sin φ cos φ 0 sin θ ] ,
k × M e = [ cos φ 0 sin φ sin φ 0 cos θ cos φ cos φ 0 cos φ sin φ 0 cos θ sin φ sin φ 0 sin θ ] ,
E ( r , ϕ , z ) = i k f 2 0 θ max l ( θ ) P m cos θ sin θ exp ( i k z s sin θ ) d θ ,
P m = i m e i m ϕ s [ i [ J m + 1 ( ξ ) J m 1 ( ξ ) ] cos φ 0 cos θ [ J m + 1 ( ξ ) + J m 1 ( ξ ) ] sin φ 0 [ J m + 1 ( ξ ) + J m 1 ( ξ ) ] cos φ 0 cos θ i [ J m + 1 ( ξ ) J m 1 ( ξ ) ] sin φ 0 2 J m ( ξ ) cos φ 0 ] .
S = Im [ ϵ ( E × E ) + μ ( H × H ) ] 4 ω ,
S r = ϵ 4 ω Im ( E ϕ E z E ϕ E z ) , S ϕ = ϵ 4 ω Im ( E z E r E z E r ) , S z = ϵ 4 ω Im ( E r E ϕ E r E ϕ ) .
α = α 0 1 i ( 2 / 3 ) k 3 α 0 , α 0 = 4 π ϵ 1 a 3 ϵ 2 / ϵ 1 1 ϵ 2 / ϵ 1 + 2 ,
Γ = 1 2 | α | 2 Re [ 1 α 0 E × E ] ,
Γ r = 1 2 | α | 2 Re [ 1 α 0 ( E ϕ E z E z E ϕ ) ] , Γ ϕ = 1 2 | α | 2 Re [ 1 α 0 ( E z E r E r E z ) ] , Γ z = 1 2 | α | 2 Re [ 1 α 0 ( E r E ϕ E ϕ E r ) ] .