Abstract

As an intrinsic attribute of light, the spin angular momentum (SAM) of photons has aroused considerable attention because of the fascinating properties emerging from light–matter interactions. We show that a diffraction-limited focal field with a steerable photonic spin structure in three dimensions can be produced under a 4π microscopic system. This is achieved by focusing two counter-propagating configurable vector beams produced in the coherent superposition of three different beams with x-polarization, y-polarization, and radial-polarization. By altering the amplitude factors of these resultant beams, the ratios between the three mutually orthogonal polarized components can be freely tuned within the focal plane, thereby allowing dynamic control over the spin orientation and ellipticity of the tightly focused optical field. The results demonstrated in this paper may find applications in spin-controlled nanophotonics.

© 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 (1)

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

2018 (4)

2017 (4)

2016 (2)

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

2015 (8)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2015).
[Crossref]

Y. Lefier and T. Grosjean, “Unidirectional sub-diffraction waveguiding based on optical spin–orbit coupling in subwavelength plasmonic waveguides,” Opt. Lett. 40(12), 2890–2893 (2015).
[Crossref]

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]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (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 and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

2014 (5)

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

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

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

2013 (4)

2012 (3)

Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

2011 (1)

W. Chen and Q. Zhan, “Three-dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

2010 (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

2006 (1)

2004 (1)

M. V. Berry, “Index formulae for singular lines of polarization,” J. Opt. A: Pure Appl. Opt. 6(7), 675–678 (2004).
[Crossref]

2003 (2)

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

2002 (2)

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

2000 (1)

1992 (1)

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]

1959 (1)

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]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

1909 (1)

J. H. Poynting, “The wave-motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly-polarized light,” Proc. R. Soc. London, Ser. A 82(557), 560–567 (1909).
[Crossref]

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]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Allen, L.

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]

Banzer, P.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[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]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[Crossref]

Bauer, T.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[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]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[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]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

Berry, M. V.

M. V. Berry, “Index formulae for singular lines of polarization,” J. Opt. A: Pure Appl. Opt. 6(7), 675–678 (2004).
[Crossref]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

Brown, T.

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]

Cao, Y.

Chen, G.

Chen, J.

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Chen, Z.

Chon, J. W. M.

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Cui, Y.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Eismann, J. S.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

Fu, S.

Gan, X.

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Ganic, D.

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]

Ginzburg, P.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Gong, L.

Grosjean, T.

Gu, B.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

Gu, M.

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Helm, M.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Hu, X.

Hubrich, R.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Karimi, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

Kim, K.-Y.

Kim, S.

Kong, L.

Kozawa, Y.

Krolikowski, W.

Lan, G.

Lefier, Y.

Leger, J. R.

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]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Li, M.

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, X.

Li, Y.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

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

Liang, Y.

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]

Lindlein, N.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Liu, X.

Man, Z.

Marino, G.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Marrucci, L.

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2015).
[Crossref]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

Martínez, A.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Mittendorff, M.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Neugebauer, M.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[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]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (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]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Nie, Z.

Nori, F.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

O’Connor, D.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Orlov, S.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

Poynting, J. H.

J. H. Poynting, “The wave-motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly-polarized light,” Proc. R. Soc. London, Ser. A 82(557), 560–567 (1909).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Rauschenbeutel, A.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

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).
[Crossref]

Rodríguez-Fortuño, F. J.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Rubano, A.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

Rui, G.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

Sato, S.

Schneider, H.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

She, W.

Shvedov, V.

Song, F.

Song, Y.

Spreeuw, R. J. C.

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]

Volz, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

Vyas, S.

Wan, C.

Wang, H.

Wang, S.

Wang, Y.

Wei, G.

Winnerl, S.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Woerdman, J. P.

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]

Wolf, E.

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]

Wurtz, G. A.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Yan, S.

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]

Yan, W.

Yao, B.

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]

Youngworth, K.

Yu, P.

Zayats, A. V.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Zhan, Q.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

J. Chen, C. Wan, L. Kong, and Q. Zhan, “Tightly focused optical field with controllable photonic spin orientation,” Opt. Express 25(16), 19517–19528 (2017).
[Crossref]

W. Chen and Q. Zhan, “Three-dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
[Crossref]

Zhang, P.

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, X.

Zhao, D.

Zhao, Q.

Zhou, S.

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

Zhu, W.

Appl. Phys. Lett. (1)

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

J. Opt. (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

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

M. V. Berry, “Index formulae for singular lines of polarization,” J. Opt. A: Pure Appl. Opt. 6(7), 675–678 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
[Crossref]

Nat. Commun. (1)

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

Nat. Photonics (1)

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

Nat. Phys. (1)

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2015).
[Crossref]

New J. Phys. (1)

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Opt. Commun. (1)

W. Chen and Q. Zhan, “Three-dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

Opt. Express (8)

Opt. Lett. (8)

Photonics Res. (1)

G. Rui, Y. Li, S. Zhou, Y. Wang, B. Gu, Y. Cui, and Q. Zhan, “Optically induced rotation of Rayleigh particles by arbitrary photonic spin,” Photonics Res. 7(1), 69–79 (2019).
[Crossref]

Phys. Rep. (1)

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

Phys. Rev. A (5)

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]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

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

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Phys. Rev. Lett. (3)

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[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]

Phys. Rev. X (2)

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

Proc. R. Soc. Lond. A (1)

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]

Proc. R. Soc. London, Ser. A (1)

J. H. Poynting, “The wave-motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly-polarized light,” Proc. R. Soc. London, Ser. A 82(557), 560–567 (1909).
[Crossref]

Science (3)

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electro-magnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Schematic illustration of the optical scheme for achieving a diffraction-limited focal field with arbitrary controlled photonic spin. P, polarizer; RPC, radial polarization convertor; BS, beam splitter; HWP, half-wave plate; M, mirror; Obj, objective.
Fig. 2.
Fig. 2. Focal behaviors of the two counter-propagating configurable vector beams with (ξ, η, ζ; δx, δy) = (1, 1, 1; –π/4, π/4). (a) Normalized intensity distributions of the focal electric field, as well as the polarization projections in three orthogonal planes. The white contour encloses the area defined by the full-width at half-maximum (FWHM). (b) Line scans of the intensity distributions along the x-, y-, and z-axes. (c) Ellipticity of the 3D polarization ellipses in the x-y plane.
Fig. 3.
Fig. 3. Polarization and spin characteristics in the x-y plane of the highly confined optical field depicted in Fig. 2(a): (a1)–(a3) normalized Stokes parameters; (b1)–(b3) spin density components; (c1)–(c3) direction angles used to quantify the orientation of the spin axis.
Fig. 4.
Fig. 4. 3D polarization distributions in the x-y plane and their projections in the three orthogonal planes with (ξ, η, ζ) = (a) (0, 1, 1), (b) (1, 0, 1), and (c) (1, 1, 0). The black arrows indicate the orientation of the spin axis. (d1)–(d3) Spin density components with (ξ, η, ζ) = (0, 1, 1). (e1)–(e3) Spin density components with (ξ, η, ζ) = (1, 0, 1). (f1)–(f3) Spin density components with (ξ, η, ζ) = (1, 1, 0). For all calculations, (δx, δy) = (–π/4, π/4) is chosen.
Fig. 5.
Fig. 5. Evolutions of the spin orientation and ellipticity in the x-y plane versus the amplitude factors of the incident beams. In (a) and (b), η = ζ= 1. In (c) and (d), ξ = ζ = 1. In (e) and (f), ξ = η = 1. For all calculations, (δx, δy) = (–π/4, π/4) is chosen.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

[ E L 1 ( ρ Q , ϕ Q , z Q ) E L 2 ( ρ Q , ϕ Q , z Q ) E L 3 ( ρ Q , ϕ Q , z Q ) ] = i A 0 2 π 0 θ max l ( θ ) co s 1 / 2 θ M [ p 1 p 2 p 3 ] e i k [ ρ Q sin θ cos ( φ ϕ Q )  +  z Q cos θ ] sin θ d θ d φ ,
[ E R 1 ( ρ Q , ϕ Q , z Q ) E R 2 ( ρ Q , ϕ Q , z Q ) E R 3 ( ρ Q , ϕ Q , z Q ) ] = i A 0 2 π 0 θ max l ( θ ) co s 1 / 2 θ M [ q 1 q 2 q 3 ] e i k [ ρ Q sin θ cos ( φ ϕ Q ) z Q cos θ ] sin θ d θ d φ ,
l ( θ ) = exp [ β 0 2 ( sin θ NA / n ) 2 ] J m ( 2 β 0 sin θ NA / n ) ,
M = [ ξ exp ( i δ x ) 0 0 0 η exp ( i δ y ) 0 0 0 ζ ] ,
[ p 1 x p 1 y p 1 z ]  =  [ si n 2 φ  + cos θ co s 2 φ (cos θ 1 ) sin φ cos φ sin θ cos φ ] ,
[ p 2 x p 2 y p 2 z ]  =  [ (cos θ 1 ) sin φ cos φ si n 2 φ  + cos θ co s 2 φ sin θ sin φ ] ,
[ p 3 x p 3 y p 3 z ]  =  [ cos θ cos φ cos θ sin φ sin θ ] ,
[ q 1 x q 1 y q 1 z ]  =  [ 1 0 0 0 1 0 0 0 1 ] [ p 1 x p 1 y p 1 z ] ,
[ q 2 x q 2 y q 2 z ]  =  [ 1 0 0 0 1 0 0 0 1 ] [ p 2 x p 2 y p 2 z ] ,
[ q 3 x q 3 y q 3 z ]  =  [ 1 0 0 0 1 0 0 0 1 ] [ p 3 x p 3 y p 3 z ] .
E ( ρ Q , ϕ Q , z Q ) = E L ( ρ Q , ϕ Q , z Q ) + E R ( ρ Q , ϕ Q , z Q ) .
Λ 1  =  1 | E E | Re ( E E E ) ,
Λ 2  =  1 | E E | Im ( E E E ) ,
ε  =  ± ta n 1 ( Λ 2 / Λ 1 ) ,
S Im ( E × E ) .
{ α  = co s 1 ( S x / S x 2 + S y 2  +  S z 2 ) β  = co s 1 ( S y / S x 2 + S y 2  +  S z 2 ) . γ  = co s 1 ( S z / S x 2 + S y 2  +  S z 2 )

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