Abstract

We generate a new kind of azimuthal-variant vector field with a distribution of states of polarization (SoPs) described by the square of the azimuthal angle. Owing to asymmetrical SoPs distribution of this localized linearly polarized vector field, the tightly focused field exhibits a double half-moon shaped pattern with the localized elliptical polarization in the cross section of field at the focal plane. Moreover, we study the three-dimensional distributions of spin and orbital linear and angular momenta in the focal region. We numerically investigate the gradient force, radiation force, spin torque, and orbital torque on a dielectric Rayleigh particle produced by the tightly focused vector field. It is found that asymmetrical spinning and orbiting motions of trapped Rayleigh particles can be realized by the use of a tight vector field with power-exponent azimuthal-variant SoPs.

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

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References

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2017 (2)

Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
[Crossref]

L. Fang and J. Wang, “Optical angular momentum derivation and evolution from vector field superposition,” Opt. Express 25(19), 23364–23375 (2017).
[Crossref] [PubMed]

2016 (5)

2015 (7)

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

Y. Pan, B. Gu, D. Xu, Q. Zhan, and Y. Cui, “Varying focal fields with asymmetric-sector-shaped vector beams,” J. Opt. 17(1), 015603 (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]

B. Gu, D. Xu, G. Rui, M. Lian, Y. Cui, and Q. Zhan, “Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields,” Appl. Opt. 54(27), 8123–8129 (2015).
[Crossref] [PubMed]

M. Nieto-Vesperinas, “Optical torque: Electromagnetic spin and orbital-angular-momentum conservation laws and their significance,” Phys. Rev. A 92(4), 043843 (2015).
[Crossref]

2014 (5)

H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

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

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

M. I. Marqués, “Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector,” Opt. Lett. 39(17), 5122–5125 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (6)

2011 (5)

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

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]

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

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2010 (3)

2009 (4)

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[Crossref]

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, “Direct observation of the transfer of orbital angular momentum to metal particles from a focused circularly polarized Gaussian beam,” Opt. Express 17(25), 23316–23322 (2009).
[Crossref] [PubMed]

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

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

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2007 (2)

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[Crossref] [PubMed]

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (2)

2003 (1)

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

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] [PubMed]

2000 (1)

1998 (1)

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

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] [PubMed]

1986 (1)

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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[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]

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] [PubMed]

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] [PubMed]

Alonso, M. A.

Anbarasan, P. M.

Ashkin, A.

Banzer, P.

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]

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]

Bautista, G.

Beckley, A. M.

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] [PubMed]

Bekshaev, A. Y.

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

Berry, M. V.

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

Bjorkholm, J. E.

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (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, 3300 (2014).
[Crossref] [PubMed]

Bowman, R.

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

Brown, T.

Brown, T. G.

Canaguier-Durand, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Cao, G. W.

Cao, Y.

Chen, H.

H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

Chen, J.

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[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), 253602 (2010).
[Crossref] [PubMed]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[Crossref]

Chen, Z.

H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

K. Hu, Z. Chen, and J. Pu, “Tight focusing properties of hybridly polarized vector beams,” J. Opt. Soc. Am. A 29(6), 1099–1104 (2012).
[Crossref] [PubMed]

Chiu, D. T.

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, “Direct observation of the transfer of orbital angular momentum to metal particles from a focused circularly polarized Gaussian beam,” Opt. Express 17(25), 23316–23322 (2009).
[Crossref] [PubMed]

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

Chong, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Chu, S.

Cuche, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Cui, Y.

D. Xu, B. Gu, G. Rui, Q. Zhan, and Y. Cui, “Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors,” Opt. Express 24(4), 4177–4186 (2016).
[Crossref] [PubMed]

B. Gu, D. Xu, G. Rui, M. Lian, Y. Cui, and Q. Zhan, “Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields,” Appl. Opt. 54(27), 8123–8129 (2015).
[Crossref] [PubMed]

Y. Pan, B. Gu, D. Xu, Q. Zhan, and Y. Cui, “Varying focal fields with asymmetric-sector-shaped vector beams,” J. Opt. 17(1), 015603 (2015).
[Crossref]

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
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Dholakia, K.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[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), 253602 (2010).
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H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[Crossref]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
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Du, L.

Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
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V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
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X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
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Feng, B.

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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Alignment or spinning of laser trapped microscopic waveplates,” Nature 394(6691), 348–350 (1998).
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Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
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V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
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D. B. Ruffner and D. G. Grier, “Optical forces and torques in nonuniform beams of light,” Phys. Rev. Lett. 108(17), 173602 (2012).
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D. Xu, B. Gu, G. Rui, Q. Zhan, and Y. Cui, “Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors,” Opt. Express 24(4), 4177–4186 (2016).
[Crossref] [PubMed]

B. Gu, D. Xu, G. Rui, M. Lian, Y. Cui, and Q. Zhan, “Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields,” Appl. Opt. 54(27), 8123–8129 (2015).
[Crossref] [PubMed]

Y. Pan, B. Gu, D. Xu, Q. Zhan, and Y. Cui, “Varying focal fields with asymmetric-sector-shaped vector beams,” J. Opt. 17(1), 015603 (2015).
[Crossref]

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
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X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
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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), 253602 (2010).
[Crossref] [PubMed]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[Crossref] [PubMed]

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Guo, H.

Hao, J.

H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Alignment or spinning of laser trapped microscopic waveplates,” Nature 394(6691), 348–350 (1998).
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C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
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Huang, K.

Huang, L.

Huttunen, M. J.

Jaroszewicz, Z.

Jeffries, G. D.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
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Jones, P. H.

M. Rashid, O. M. Marago, 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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Kontio, J. M.

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A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “Asymmetric Laguerre-Gaussian beams,” Phys. Rev. A 93(6), 063858 (2016).
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A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “Asymmetric Laguerre-Gaussian beams,” Phys. Rev. A 93(6), 063858 (2016).
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V. G. Shvedov, C. Hnatovsky, N. Shostka, and W. Krolikowski, “Generation of vector bottle beams with a uniaxial crystal,” J. Opt. Soc. Am. B 30(1), 1–6 (2013).
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C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
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Lalithambigai, K.

Lei, M.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
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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).
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Leuchs, G.

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

Li, K.

Li, M.

Li, P.

Li, Y.

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[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), 253602 (2010).
[Crossref] [PubMed]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
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Li, Y. P.

Li, Z. Y.

Lian, M.

Liang, Y.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
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M. Li, S. Yan, B. Yao, Y. Liang, and P. Zhang, “Spinning and orbiting motion of particles in vortex beams with circular or radial polarizations,” Opt. Express 24(18), 20604–20612 (2016).
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Liu, S.

Lou, K.

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
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H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
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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).
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Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
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Marago, O. M.

M. Rashid, O. M. Marago, 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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Marqués, M. I.

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Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
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V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
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Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
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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).
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M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
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A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
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Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Alignment or spinning of laser trapped microscopic waveplates,” Nature 394(6691), 348–350 (1998).
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K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
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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).
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M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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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] [PubMed]

Pan, Y.

Y. Pan, B. Gu, D. Xu, Q. Zhan, and Y. Cui, “Varying focal fields with asymmetric-sector-shaped vector beams,” J. Opt. 17(1), 015603 (2015).
[Crossref]

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
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Porfirev, A. P.

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “Asymmetric Laguerre-Gaussian beams,” Phys. Rev. A 93(6), 063858 (2016).
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Pu, J.

Qin, J.

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
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Rashid, M.

M. Rashid, O. M. Marago, 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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C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Alignment or spinning of laser trapped microscopic waveplates,” Nature 394(6691), 348–350 (1998).
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D. B. Ruffner and D. G. Grier, “Optical forces and torques in nonuniform beams of light,” Phys. Rev. Lett. 108(17), 173602 (2012).
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Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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Shapiro, D.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
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Shi, P.

Shostka, N.

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
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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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Wang, H.

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[Crossref]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

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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), 253602 (2010).
[Crossref] [PubMed]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[Crossref] [PubMed]

Wang, H.-T.

H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

Wang, J.

Wang, L. G.

Wang, Q.

Wang, X.

X. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, “Configurable three-dimensional optical cage generated from cylindrical vector beams,” Opt. Commun. 282(17), 3421–3425 (2009).
[Crossref]

Wang, X. L.

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), 253602 (2010).
[Crossref] [PubMed]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[Crossref] [PubMed]

Wang, X.-L.

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] [PubMed]

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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Xu, D.

D. Xu, B. Gu, G. Rui, Q. Zhan, and Y. Cui, “Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors,” Opt. Express 24(4), 4177–4186 (2016).
[Crossref] [PubMed]

B. Gu, D. Xu, G. Rui, M. Lian, Y. Cui, and Q. Zhan, “Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields,” Appl. Opt. 54(27), 8123–8129 (2015).
[Crossref] [PubMed]

Y. Pan, B. Gu, D. Xu, Q. Zhan, and Y. Cui, “Varying focal fields with asymmetric-sector-shaped vector beams,” J. Opt. 17(1), 015603 (2015).
[Crossref]

B. Gu, Y. Pan, G. Rui, D. Xu, Q. Zhan, and Y. Cui, “Polarization evolution characteristics of focused hybridly polarized vector fields,” Appl. Phys. B 117(3), 915–926 (2014).
[Crossref]

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H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
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Yang, Y.

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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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Youngworth, K.

Yu, X.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

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H. Chen, Z. Yu, J. Hao, Z. Chen, J. Xu, J. Ding, and H.-T. Wang, “Separation of spin angular momentum in space-variant linearly polarized beam,” Appl. Phys. B 114(3), 355–359 (2014).
[Crossref]

Yuan, X.

Z. Man, L. Du, Y. Zhang, C. Min, S. Fu, and X. Yuan, “Focal and optical trapping behaviors of radially polarized vortex beam with broken axial symmetry,” AIP Adv. 7(6), 065109 (2017).
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Zhan, Q.

Zhang, P.

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Figures (6)

Fig. 1
Fig. 1 (a) Experimentally measured Stokes parameters of the generated PE-AV vector field. (b) Experimentally measured and (c) theoretically predicted SoP distributions.
Fig. 2
Fig. 2 Normalized intensity patterns of the focused PE-AV vector field in the transverse plane for z = 0 (top row) and in the longitudinal plane for x = 0 (bottom row), by taking λ = 532 nm, NA = 1.26, n1 = 1.33, and β = 1. (a) and (d) also show the polarization projections (white: LH polarization; black: RH polarization) on the x-y and z-y planes, respectively.
Fig. 3
Fig. 3 Normalized transverse (top row) and longitudinal LMs (bottom row) of the tightly focused PE-AV vector field in the x-y plane. The magnitudes and directions of the transverse LMs are illustrated by the colorbar and arrows in (a)-(c), respectively. The parameters for calculations are λ = 532 nm, NA = 1.26, n1 = 1.33, β = 1, and z = 0.
Fig. 4
Fig. 4 Normalized transverse (top row) and longitudinal AMs (bottom row) of the tightly focused PE-AV vector field in the x-y plane. The magnitudes and directions of the transverse AMs are illustrated by the colorbar and arrows in (a)-(c), respectively. The parameters for calculations are the same as those in Fig. 3.
Fig. 5
Fig. 5 Transverse (top row) and longitudinal (bottom row) force distributions produced by the tightly focused EP-AV vector field in the x-y plane (z = 0) and x-z plane (y = 0), respectively. The parameters for calculations are P = 100 mW, λ = 532 nm, NA = 1.26, β = 1, n1 = 1.33, n2 = 1.60, and a = 30 nm.
Fig. 6
Fig. 6 Transverse spin torque T trans spin (a) and longitudinal orbital torque T z orb (b) exerted on a Rayleigh particle induced by the tightly focused PE-AV vector field in the x-y plane (z = 0). The parameters for calculations are the same as those in Fig. 5.

Equations (17)

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E (ρ,ϕ)= E 0 exp( ρ 2 ω 2 )[ cos( ϕ 2 2π ) e x +sin( ϕ 2 2π ) e y ].
A x (θ,ϕ)= E 0 exp( β 2 sin 2 θ sin 2 α )cos( ϕ 2 2π ),
A y (θ,ϕ)= E 0 exp( β 2 sin 2 θ sin 2 α )sin( ϕ 2 2π ),
E x (r,φ,z)= ikf 2π 0 Θ 0 2π sinθ cosθ e ik(zcosθ+rsinθcos(ϕφ)) ×[ A x (θ,ϕ)( cos 2 ϕcosθ+ sin 2 ϕ) + A y (θ,ϕ)cosϕsinϕ(cosθ1)]dθdϕ,
E y (r,φ,z)= ikf 2π 0 Θ 0 2π sinθ cosθ e ik(zcosθ+rsinθcos(ϕφ)) ×[ A x (θ,ϕ)cosϕsinϕ(cosθ1) + A y (θ,ϕ)( cos 2 ϕ+ sin 2 ϕcosθ)]dθdϕ,
E z (r,φ,z)= ikf 2π 0 Θ 0 2π sinθ cosθ e ik(zcosθ+rsinθcos(ϕφ)) ×[ A x (θ,ϕ)cosϕsinθ+ A y (θ,ϕ)sinϕsinθ]dθdϕ.
P = ε 0 2 ω ¯ Im[ E * ×(× E )],
P spin = ε 0 4 ω ¯ ×Im[ E * × E ],
P orb = ε 0 2 ω ¯ Im[ E * () E ].
J = r × P ,
J spin = ε 0 2 ω ¯ Im[( E * × E ],
J orb = ε 0 2 ω ¯ r ×Im[ E * () E ].
F grad = 1 4 Re(α)| E | 2 ,
F radi = ω ¯ ε 0 Im(α) P orb ,
α= α 0 1i α 0 k 3 /(6π ε 0 ) , α 0 =4π ε 0 a 3 n 2 2 / n 1 2 1 n 2 2 / n 1 2 +2 .
T spin = 1 2 |α | 2 Re[ 1 α 0 * E × E * ].
T orb = r × F .

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