Abstract

We investigate the spin properties of a family of cylindrical vector vortex beams under a focusing condition. The spin-orbit interaction is demonstrated by comparing the energy flow and spin flow density of the focused field to those of the incident field. This spin-orbit interaction is analyzed to construct the desired distribution of spin angular momentum for optical manipulation. The structured spin angular momentum of the focused field can transfer to the optical torque for the non-magnetic absorptive particle. The influences of polarization topological charge, vortex topological charge and wavelength on optical torque in the hot-spot of focused field are summarized for three typical particles. Such results may be exploited in practical optical manipulation, particularly for optically induced rotations.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (2)

Y. Zhang, J. Shen, Z. Xie, X. Dou, C. Min, T. Lei, J. Liu, S. Zhu, and X. Yuan, “Dynamic plasmonic nano-traps for single molecule surface-enhanced Raman scattering,” Nanoscale 9(30), 10694–10700 (2017).
[Crossref] [PubMed]

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]

2016 (2)

P. Woźniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

L. Zhang, X. Dou, C. Min, Y. Zhang, L. Du, Z. Xie, J. Shen, Y. Zeng, and X. Yuan, “In-plane trapping and manipulation of ZnO nanowires by a hybrid plasmonic field,” Nanoscale 8(18), 9756–9763 (2016).
[Crossref] [PubMed]

2015 (5)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (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]

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]

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

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

2014 (6)

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] [PubMed]

D. O’Connor, P. Ginzburg, F. J. Rodríguez-Fortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 53271 (2014).
[Crossref] [PubMed]

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

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 33001 (2014).
[Crossref] [PubMed]

M. Li, S. Yan, B. Yao, M. Lei, Y. Yang, J. Min, and D. Dan, “Intrinsic optical torque of cylindrical vector beams on Rayleigh absorptive spherical particles,” J. Opt. Soc. Am. A 31(8), 1710–1715 (2014).
[Crossref] [PubMed]

2013 (2)

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4(1), 2891–2897 (2013).
[Crossref] [PubMed]

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] [PubMed]

2012 (2)

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

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

2011 (5)

K. Dholakia and T. Cižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

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

A. Bekshaev, K. Y Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

K. Huang, P. Shi, G. W. Cao, K. Li, X. B. Zhang, and Y. P. Li, “Vector-vortex Bessel-Gauss beams and their tightly focusing properties,” Opt. Lett. 36(6), 888–890 (2011).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

2010 (2)

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

X.-L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 2536021 (2010).
[Crossref] [PubMed]

2009 (4)

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

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express 17(4), 2224–2234 (2009).
[Crossref] [PubMed]

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation detection in light-driven nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2001 (1)

P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78(2), 249–251 (2001).
[Crossref]

2000 (1)

1998 (1)

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

1995 (1)

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. 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] [PubMed]

1986 (1)

S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys. 58(3), 699–739 (1986).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[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. 253(1274), 358–379 (1959).
[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 polarised light,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 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] [PubMed]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. 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] [PubMed]

Alonso, M. A.

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).
[Crossref] [PubMed]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Banzer, P.

P. Woźniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (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] [PubMed]

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

Bauer, T.

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

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. 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] [PubMed]

Bekshaev, A.

A. Bekshaev, K. Y Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[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), 33001 (2014).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

Bliokh, K. Y

A. Bekshaev, K. Y Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (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 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), 33001 (2014).
[Crossref] [PubMed]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref] [PubMed]

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

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).
[Crossref] [PubMed]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

Bonaccorso, F.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation detection in light-driven nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Bouchard, F.

P. Woźniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Bowman, R.

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

Boyd, R. W.

P. Woźniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Calogero, G.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation detection in light-driven nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Canaguier-Durand, A.

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

Cao, G. W.

Chaumet, P. C.

Chen, J.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 2536021 (2010).
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Figures (6)

Fig. 1
Fig. 1 Longitudinal components of (a) energy flow and (b) SFD when n = 5 and m = 0. The transverse components of the energy flow and the SFD vanish. Longitudinal components of (c) energy flow and (d) SFD when n = 5 and m = 1. All physical quantities are real numbers and are normalized by the maximum. The NA of the objective is 0.9.
Fig. 2
Fig. 2 Intensities of σ ^ + and σ ^ components of focused field are presented in (a) and (b) and the corresponding phases are shown in (c) and (d), respectively. The topological charges of incident CVVB are set to n = 5, m = 0. It is obvious that the distributions of these two components are identical with the exception of the opposing phase. When the topological charges of incident CVVB are set to n = 5 and m = 1, respectively, the intensities of σ ^ + and σ ^ components of focused field are presented in (e), (f) with the corresponding phases shown in (g) and (h), respectively. The difference between the absolute value of the orders of the vortex phases is equal to 2m. All intensities are normalized and the NA of the objective is 0.9.
Fig. 3
Fig. 3 The azimuthal (a) and longitudinal (b) components of SAM for the PTC n = 5 and VTC m = 0; the azimuthal (c) and longitudinal (d) components of SAM for the PTC n = 5 and VTC m = 1. The radial component of SAM vanish for each case. All quantities are normalized.
Fig. 4
Fig. 4 The radial (a), azimuthal (b) and longitudinal (c) components of SAM as the PTC and VTC are 5 and 0, respectively; the radial (d), azimuthal (e) and longitudinal (f) components of SAM as the PTC and VTC are 5 and 1, respectively. All quantities are normalized.
Fig. 5
Fig. 5 Variations of (a) transverse and (d) longitudinal torques versus VTC for silver particles. Variation of (b) transverse and (e) longitudinal torques versus VTC for gold particles. Variation of (c) transverse and (f) longitudinal torques versus VTC for silicon particles. The red, blue, black, magenta, green and cyan lines represent the calculated torques for PTCs of n = 1, n = 2, n = 3, n = 4, n = 5 and n = 6, respectively. The calculated wavelength is 0.532μm. In Ref [41], P. C. Chaumet et al. gave the materials properties of the gold and silver. In Ref [42], P. B. Johnson et al. gave the material property of the silicon.
Fig. 6
Fig. 6 Variation of the transverse torques as PTC = 5 and VTC = 0 and the longitudinal torques when PTC = 5 and VTC = 5 versus the wavelengths are investigated for (a) Ag particle, (b) Au particle and (c) Si particle.

Equations (11)

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E ˜ t c ( r ) = A r e i m φ [ cos [ ( n 1 ) φ + φ 0 ] e ^ r , sin [ ( n 1 ) φ + φ 0 ] e ^ φ ] Τ ,
E z c 1 i k A r r cos [ ( n 1 ) φ ] e i m φ .
E ˜ t σ = A r e i m φ / 2 [ e σ i [ n φ + φ 0 ] σ ^ + , e σ i [ n φ + φ 0 ] σ ^ ] Τ
E ˜ l e n s σ cos θ U ^ ( θ , φ ) E ˜ σ ,
E ˜ l e n s σ A r cos θ 2 ( [ cos 2 θ 2 e σ i n φ sin 2 θ 2 e σ i ( n 2 ) φ sin θ 2 e σ i ( n 1 ) φ ] e i m φ + [ sin 2 θ 2 e σ i ( n 2 ) φ cos 2 θ 2 e σ i n φ sin θ 2 e σ i ( n 1 ) φ ] e i m φ ) .
H ˜ c ( r ) = k ω μ e i m φ [ A r sin [ ( n 1 ) φ ] , A r cos [ ( n 1 ) φ ] , 1 i k A r r sin [ ( n 1 ) φ ] ] Τ
P ˜ c = ε μ Re ( E c × H c ) ε k | A r | 2 ω [ 0 , 0 , 1 ] Τ .
p ˜ i , s c = 1 4 ω Im [ × ( ε E c × E c + μ H c × H c ) ] ε 8 k ω 2 2 | A r | 2 r 2 [ 0 , 0 , cos [ 2 ( n 1 ) φ ] ] Τ .
S ˜ = 1 4 ω Im { ε E f × E f + μ H f × H f }
E ˜ l e n s σ A r cos θ 2 ( [ cos 2 θ 2 e i σ φ sin 2 θ 2 e i σ ϕ sin θ 2 ] E i σ + [ sin 2 θ 2 e i σ ϕ cos 2 θ 2 e i σ φ sin θ 2 ] E i + σ ) ,
Γ = 1 2 | α | 2 Re [ 1 α 0 E × E ] ,

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