Abstract

The redistribution of the energy flow of tightly focused ellipticity-variant vector optical fields is presented. We theoretically design and experimentally generate this kind of ellipticity-variant vector optical field, and further explore the redistribution of the energy flow in the focal plane by designing different phase masks, including fanlike phase masks and vortex phase masks, on them. The flexibly controlled transverse energy flow rings of the tightly focused ellipticity-variant vector optical fields with and without phase masks can be used to transport multiple absorptive particles along certain paths, which may be widely applied in optical trapping and manipulation.

© 2017 Chinese Laser Press

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References

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2015 (3)

2014 (1)

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel–Gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

2013 (2)

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, C. Y. Zenkova, and N. V. Gorodynska, “Circular motion of particles by the help of the spin part of the internal energy flow,” Proc. SPIE 8882, 88820A (2013).
[Crossref]

Y. Pan, Y. N. Li, S. M. Li, Z. C. Ren, Y. Si, C. Tu, and H. T. Wang, “Vector optical fields with bipolar symmetry of linear polarization,” Opt. Lett. 38, 3700–3703 (2013).
[Crossref]

2012 (3)

2011 (6)

2010 (5)

X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35, 3928–3930 (2010).
[Crossref]

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

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[Crossref]

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref]

2009 (5)

2007 (2)

2005 (1)

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[Crossref]

2004 (1)

2003 (2)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).
[Crossref]

2002 (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, 1576–1578 (2002).
[Crossref]

2000 (1)

1996 (1)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref]

1990 (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. London A 253, 358–379 (1959).
[Crossref]

Aiello, A.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Alonso, M. A.

Andersen, U. L.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Angelsky, O. V.

Banzer, P.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref]

Beckley, A. M.

Bekshaev, A.

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

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Bekshaev, A. Y.

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, C. Y. Zenkova, and N. V. Gorodynska, “Circular motion of particles by the help of the spin part of the internal energy flow,” Proc. SPIE 8882, 88820A (2013).
[Crossref]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012).
[Crossref]

Berry, M. V.

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

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

Bliokh, K.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

Brown, T. G.

Cai, Y.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel–Gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

Chen, H.

Chen, J.

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

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

Chen, Z.

Cheng, W.

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, 1576–1578 (2002).
[Crossref]

Ciattoni, A.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[Crossref]

Crosignani, B.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[Crossref]

Cui, K.

D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
[Crossref]

Di Porto, P.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[Crossref]

Ding, B.

Ding, J.

Ding, J. P.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).
[Crossref]

Elser, D.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref]

Euser, T. G.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Feng, X.

D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
[Crossref]

Ford, D. H.

Förtsch, M.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref]

Gabriel, C.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Gan, X.

Gorodynska, N. V.

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, C. Y. Zenkova, and N. V. Gorodynska, “Circular motion of particles by the help of the spin part of the internal energy flow,” Proc. SPIE 8882, 88820A (2013).
[Crossref]

Gorsky, M. P.

Gu, 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, 1576–1578 (2002).
[Crossref]

Guo, C. S.

Han, W.

Hanson, S. G.

Hao, J.

Hao, X.

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

Heckenberg, N. R.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref]

Huang, Y.

D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
[Crossref]

Huang, Z.

Jiao, X.

Joly, N. Y.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Kimura, W. D.

Kong, L. J.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Kozawa, Y.

Kuang, C. F.

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref]

Lerman, G. M.

Leuchs, G.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).
[Crossref]

Levy, U.

Li, P.

Li, S. M.

Y. Pan, Y. N. Li, S. M. Li, Z. C. Ren, Y. Si, C. Tu, and H. T. Wang, “Vector optical fields with bipolar symmetry of linear polarization,” Opt. Lett. 38, 3700–3703 (2013).
[Crossref]

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Li, Y.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Li, Y. N.

Liu, F.

D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
[Crossref]

Liu, S.

Liu, X.

Lou, K.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Lu, F.

Maksimyak, A. P.

Maksimyak, P. P.

Marquardt, C.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

Ni, W. J.

Novotny, L.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

Pan, Y.

Peng, T.

Qian, B.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).
[Crossref]

Ren, Z. C.

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. London A 253, 358–379 (1959).
[Crossref]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref]

Russell, P. St. J.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
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Tian, Y.

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Tidwell, S. C.

Tu, C.

Y. Pan, Y. N. Li, S. M. Li, Z. C. Ren, Y. Si, C. Tu, and H. T. Wang, “Vector optical fields with bipolar symmetry of linear polarization,” Opt. Lett. 38, 3700–3703 (2013).
[Crossref]

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Vasnetsov, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

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G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel–Gauss beam,” Phys. Rev. A 89, 043807 (2014).
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Wang, Q.

Wang, T. T.

Wang, X. L.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

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

X. L. Wang, J. P. 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, 3549–3551 (2007).
[Crossref]

Wei, S. B.

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[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. London A 253, 358–379 (1959).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wu, G.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel–Gauss beam,” Phys. Rev. A 89, 043807 (2014).
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Yuan, G. H.

Yuan, X. C.

Zeng, T.

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O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, C. Y. Zenkova, and N. V. Gorodynska, “Circular motion of particles by the help of the spin part of the internal energy flow,” Proc. SPIE 8882, 88820A (2013).
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O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012).
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Zhan, Q.

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D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
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C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
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Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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J. Mod. Opt. (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917–1926 (2003).
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J. Opt. (2)

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

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

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

Opt. Express (9)

Y. Zhang and B. Ding, “Magnetic field distribution of a highly focused radially-polarized light beam,” Opt. Express 17, 22235–22239 (2009).
[Crossref]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004).
[Crossref]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref]

P. Li, S. Liu, G. Xie, T. Peng, and J. Zhao, “Modulation mechanism of multi-azimuthal masks on the redistributions of focused azimuthally polarized beams,” Opt. Express 23, 7131–7139 (2015).
[Crossref]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[Crossref]

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

O. V. Angelsky, M. P. Gorsky, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Yu. Zenkova, “Investigation of optical currents in coherent and partially coherent vector fields,” Opt. Express 19, 660–672 (2011).
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Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23, 17701–17710 (2015).
[Crossref]

Opt. Lett. (9)

H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36, 3179–3181 (2011).
[Crossref]

Y. Pan, Y. N. Li, S. M. Li, Z. C. Ren, Y. Si, C. Tu, and H. T. Wang, “Vector optical fields with bipolar symmetry of linear polarization,” Opt. Lett. 38, 3700–3703 (2013).
[Crossref]

W. Han, W. Cheng, and Q. Zhan, “Flattop focusing with full Poincaré beams under low numerical aperture illumination,” Opt. Lett. 36, 1605–1607 (2011).
[Crossref]

G. M. Lerman and U. Levy, “Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization,” Opt. Lett. 32, 2194–2196 (2007).
[Crossref]

X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35, 3928–3930 (2010).
[Crossref]

X. Jiao, S. Liu, Q. Wang, X. Gan, P. Li, and J. Zhao, “Redistributing energy flow and polarization of a focused azimuthally polarized beam with rotationally symmetric sector-shaped obstacles,” Opt. Lett. 37, 1041–1043 (2012).
[Crossref]

X. L. Wang, J. P. 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, 3549–3551 (2007).
[Crossref]

S. Sato and Y. Kozawa, “Radially polarized annular beam generated through a second-harmonic-generation process,” Opt. Lett. 34, 3166–3168 (2009).
[Crossref]

F. Lu, W. Zheng, and Z. Huang, “Coherent anti-Stokes Raman scattering microscopy using tightly focused radially polarized light,” Opt. Lett. 34, 1870–1872 (2009).
[Crossref]

Phys. Rev. A (2)

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel–Gauss beam,” Phys. Rev. A 89, 043807 (2014).
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[Crossref]

Phys. Rev. Lett. (5)

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94, 073902 (2005).
[Crossref]

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[Crossref]

Proc. R. Soc. London 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. London A 253, 358–379 (1959).
[Crossref]

Proc. SPIE (1)

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, C. Y. Zenkova, and N. V. Gorodynska, “Circular motion of particles by the help of the spin part of the internal energy flow,” Proc. SPIE 8882, 88820A (2013).
[Crossref]

Sci. Rep. (2)

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

D. Zhang, X. Feng, K. Cui, F. Liu, and Y. Huang, “Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters,” Sci. Rep. 5, 11982 (2015).
[Crossref]

Other (2)

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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Figures (9)

Fig. 1.
Fig. 1. (a) Schematic of the PS in the spherical coordinate system represented by the traditional latitude and longitude circles, (b) the sine-form varying ellipticity ϵ A in a range of [ 1 , 1 ] along δ , and (c) the sine-form varying ellipticity ϵ B in a range of [0, 1] along δ .
Fig. 2.
Fig. 2. Schematic of the experimental setup for generating the desired EV-VOFs. L1 and L2, a pair of lenses; λ / 2 , half-wave plates; SF, spatial filter; G, Ronchi phase grating; PC, computer.
Fig. 3.
Fig. 3. Generated EV-VOFs when ( m , n ) = ( 1 , 0 ) , (2, 0), (0, 1), and (1, 1). The first row gives the total intensity patterns and corresponding schematics of the SoPs, and the second and third rows show the simulated and measured x -component intensity patterns, respectively, for the EV-VOFs with the sine-form varying ellipticity in a range of [ 1 , 1 ] .
Fig. 4.
Fig. 4. Generated EV-VOFs when ( m , n ) = ( 1 , 0 ) , (2, 0), (0, 1), and (1, 1). The first row gives the total intensity patterns and corresponding schematics of the SoPs, and the second and third rows show the simulated and measured x -component intensity patterns, respectively, for the EV-VOFs with the sine-form varying ellipticity in a range of [0, 1].
Fig. 5.
Fig. 5. Intensity distributions and the Poynting vectors in the focal plane of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [ 1 , 1 ] when ( m , n ) = ( 2 , 0 ) , (4, 0), and (6, 0) (left, middle, and right columns, respectively). The intensity patterns of the tightly focused fields are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4 λ × 4 λ .
Fig. 6.
Fig. 6. Schematic structures of the phase masks and the Poynting vectors of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when ( m , n ) = ( 1 , 0 ) . The cases of twofold, fourfold, and sixfold fanlike phase masks are shown in the first, second, and third columns, respectively. The schematics of fanlike phase masks are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images in the second and third rows have dimensions of 4 λ × 4 λ .
Fig. 7.
Fig. 7. Transverse components of the Poynting vectors of the tightly focused EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when ( m , n ) = ( 1 , 0 ) . The cases of twofold, fourfold, and sixfold fanlike phase masks are shown in the first, second, and third rows, respectively. The rotation angles of the phase masks in columns 1–4 are 0, π / 4 , π / 2 , and 3 π / 4 , respectively. The insets show the corresponding fanlike phase masks used. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4 λ × 4 λ .
Fig. 8.
Fig. 8. Intensity distributions and the Poynting vectors of the tightly focused vortex EV-VOFs with the sine-form varying ellipticity in a range of [0, 1] when ( m , l ) = ( 3,1 ) , (4, 2), (5, 2), and (6, 3) (columns 1–4, respectively). The intensity patterns of the tightly focused fields are shown in the first row, and the transverse and longitudinal components of the normalized Poynting vectors in the focal plane are shown in the second and third rows, respectively. The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4 λ × 4 λ .
Fig. 9.
Fig. 9. Transverse components of the normalized Poynting vectors of the tightly focused vortex EV-VOFs with the sine-form varying ellipticity in a range of [ 1 , 1 ] when ( m , l ) = ( 1 , 5 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 4 , 5 ) , ( 5 , 5 ) , and (6, 5). The direction of the transverse energy flow is shown by the black arrows. All images have dimensions of 4 λ × 4 λ .

Equations (11)

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S ^ ( 2 ϕ , 2 α ) = [ sin ( α + π / 4 ) exp ( j ϕ ) e ^ r cos ( α + π / 4 ) exp ( j ϕ ) e ^ l ] = [ cos α ( cos ϕ e ^ x + sin ϕ e ^ y ) j sin α ( sin ϕ e ^ x + cos ϕ e ^ y ) ] ,
ϵ = sin ( 2 α ) ,
ϵ A = sin [ δ ( ϕ , r ) π / 2 ] ,
ϵ B = | sin [ δ ( ϕ , r ) / 2 ] | ,
E = cos α e ^ x + j sin α e ^ y = cos [ sin 1 ϵ ( x , y ) 2 ] e ^ x + j sin [ sin 1 ϵ ( x , y ) 2 ] e ^ y .
E = 0 θ m 0 2 π P ( θ ) M e K ( ϕ , θ ) sin θ d ϕ d θ ,
M e = [ ( E ρ cos θ cos ϕ E ϕ sin ϕ ) e ^ x ( E ρ cos θ sin ϕ + E ϕ cos ϕ ) e ^ y E ρ sin θ e ^ z ] ,
K ( ϕ , θ ) = e j k [ z cos θ + r sin θ cos ( φ ϕ ) ] ,
H = 0 θ m 0 2 π P ( θ ) M m K ( ϕ , θ ) sin θ d ϕ d θ ,
M m = [ ( E ρ sin ϕ E ϕ cos θ cos ϕ ) e ^ x ( E ρ cos ϕ E ϕ cos θ sin ϕ ) e ^ y E ϕ sin θ e ^ z ] .
P Re [ E * × H ] Im [ ( E * · ) E ] + 1 2 × Im ( E * × E ) ,

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