Abstract

Redistributing the transverse energy flow in the focal plane of a tightly focused radially polarized optical field is described. We develop from theory a generalized analytical model for calculating the distributions of the electromagnetic field and the Poynting vector for a tightly focused radially polarized laser beam superposed with an optical vortex. We further explore the redistribution of the energy flow by designing phase masks, including traditional and annular vortex phase masks. Flexible control of the transverse energy flow rings is obtained with these phase masks. They provide a simple solution to transport absorptive particles along certain paths and therefore might be help in optical tweezer manipulations.

© 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 (4)

2016 (1)

L. Wei and H. P. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).
[Crossref]

2015 (4)

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).
[Crossref] [PubMed]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (4)

2012 (5)

2011 (7)

2010 (4)

2009 (3)

2008 (2)

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

T. G. Jabbour and S. M. Kuebler, “Vectorial beam shaping,” Opt. Express 16(10), 7203–7213 (2008).
[Crossref] [PubMed]

2007 (4)

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
[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]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

2005 (1)

2004 (1)

2003 (2)

C.-C. Sun and C.-K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28(2), 99–101 (2003).
[Crossref] [PubMed]

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

2002 (1)

2000 (2)

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(2), 1593–1596 (1996).
[Crossref] [PubMed]

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]

Angelsky, O. V.

April, A.

Arlt, J.

Arnold, C.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Bai, J.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Bo, F.

Brown, T.

Cai, Y.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Chen, H.

Chen, Z.

Cheng, W.

Chong, C. T.

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

D’Ambrosio, V.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Dehez, H.

Ding, J.

Dong, Y.

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] [PubMed]

Du, L.

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).
[Crossref] [PubMed]

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 (2013).
[Crossref] [PubMed]

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(2), 1593–1596 (1996).
[Crossref] [PubMed]

Fang, H.

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 (2013).
[Crossref] [PubMed]

Feng, B.

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(2), 1593–1596 (1996).
[Crossref] [PubMed]

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Gan, X.

Gao, X.-Z.

Gong, L.

Gorsky, M. P.

Gu, B.

Gu, M.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3(1), 998 (2012).
[Crossref] [PubMed]

Guo, C.-S.

Guo, H.

Gupta, D. N.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Han, T.

Han, W.

Hanson, S. G.

Hao, J.

Hao, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

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(2), 1593–1596 (1996).
[Crossref] [PubMed]

Hong, M.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Hu, Q.

Huang, K.

Huang, L.

Huang, Z.

Jabbour, T. G.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Jiang, M.

Jiao, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Jiao, X.

Kang, X. L.

Kant, N.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Kim, D. E.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Kitamura, K.

Kozawa, Y.

Ku, Y.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

Kuang, C.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

Kuebler, S. M.

Lan, T. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3(1), 998 (2012).
[Crossref] [PubMed]

Laurat, J.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Leger, J.

Lei, T.

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 (2013).
[Crossref] [PubMed]

Leuchs, G.

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

Li, J.

Li, P.

Li, X.

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).
[Crossref] [PubMed]

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3(1), 998 (2012).
[Crossref] [PubMed]

Li, Y.

Li, Y. P.

Li, Y.-N.

Li, Z. Y.

Lin, J.

Ling, L.

Liu, C.-K.

Liu, S.

Liu, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

Lu, F.

Lukyanchuk, B.

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

Luo, X.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Maksimyak, A. P.

Maksimyak, P. P.

Marrucci, L.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Min, C.

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 (2013).
[Crossref] [PubMed]

Ni, W.-J.

Noda, S.

Padgett, M. J.

Pan, Y.

Parigi, V.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Peng, T.

Piché, M.

Ping, Y. S.

Pu, J.

Qian, B.

Qin, F.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Qiu, C.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Qiu, C.-W.

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] [PubMed]

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

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[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(2), 1593–1596 (1996).
[Crossref] [PubMed]

Sakai, K.

Sato, S.

Sciarrino, F.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

Shen, J.

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 (2013).
[Crossref] [PubMed]

Shen, Z.

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 (2013).
[Crossref] [PubMed]

Sheppard, C.

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

Shi, P.

Sui, G.

Suk, H.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Sun, C.-C.

Tan, J.

Teng, J.

Tian, B.

Tien, C. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3(1), 998 (2012).
[Crossref] [PubMed]

Tu, C.-G.

Urbach, H. P.

L. Wei and H. P. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).
[Crossref]

Wan, C.

Wang, F.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Wang, H.

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

Wang, H. T.

Wang, H.-T.

Wang, Q.

Wang, S.

Wang, T.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

Wang, X.

Wang, X.-L.

Wang, Y.

Wei, L.

L. Wei and H. P. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).
[Crossref]

Wei, S. B.

Weng, X.

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]

Wu, G.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Wu, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Xie, X.

Xu, J.

Yang, L.

Yang, Y.

Ye, H.

Yin, K.

Youngworth, K.

Yu, Y.

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).
[Crossref] [PubMed]

Yuan, G.

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 (2013).
[Crossref] [PubMed]

Yuan, G. H.

Yuan, X.

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).
[Crossref] [PubMed]

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 (2013).
[Crossref] [PubMed]

Yuan, X. C.

Yuan, X.-C.

Zeng, T.

Zenkova, C. Yu.

Zhan, Q.

Zhang, B. F.

Zhang, G.-L.

Zhang, X.

Zhang, Y.

Zhao, J.

Zhao, M.-D.

Zhao, Y.

Zheng, W.

Zhou, J.

Zhu, B.

Zhu, S.

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 (2013).
[Crossref] [PubMed]

Zhu, Z.

Zhuang, S.

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

J. Opt. (1)

L. Wei and H. P. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Commun. (3)

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3(1), 998 (2012).
[Crossref] [PubMed]

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6(1), 7706 (2015).
[Crossref] [PubMed]

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 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

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

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Opt. Commun. (1)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun. 284(7), 1766–1769 (2011).
[Crossref]

Opt. Express (16)

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).
[Crossref] [PubMed]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).
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H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
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K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express 18(5), 4518–4525 (2010).
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T. G. Jabbour and S. M. Kuebler, “Vectorial beam shaping,” Opt. Express 16(10), 7203–7213 (2008).
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Y. Zhang and J. Bai, “Improving the recording ability of a near-field optical storage system by higher-order radially polarized beams,” Opt. Express 17(5), 3698–3706 (2009).
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W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
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K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
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H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express 21(5), 5363–5372 (2013).
[Crossref] [PubMed]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[Crossref] [PubMed]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).
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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(2), 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(14), 17701–17710 (2015).
[Crossref] [PubMed]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).
[Crossref] [PubMed]

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
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S. Liu, P. Li, T. Peng, and J. Zhao, “Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer,” Opt. Express 20(19), 21715–21721 (2012).
[Crossref] [PubMed]

Opt. Lett. (15)

B. Tian and J. Pu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam,” Opt. Lett. 36(11), 2014–2016 (2011).
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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(6), 1041–1043 (2012).
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J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000).
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F. Lu, W. Zheng, and Z. Huang, “Coherent anti-Stokes Raman scattering microscopy using tightly focused radially polarized light,” Opt. Lett. 34(12), 1870–1872 (2009).
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C.-C. Sun and C.-K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28(2), 99–101 (2003).
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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]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
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G. H. Yuan, S. B. Wei, and X.-C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
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K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
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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(16), 3179–3181 (2011).
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H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C.-W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
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J. Lin, K. Yin, Y. Li, and J. Tan, “Achievement of longitudinally polarized focusing with long focal depth by amplitude modulation,” Opt. Lett. 36(7), 1185–1187 (2011).
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L. Huang, H. Guo, J. Li, L. Ling, B. Feng, and Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012).
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Y. Zhao, Q. Zhan, Y. Zhang, and Y. P. Li, “Creation of a three-dimensional optical chain for controllable particle delivery,” Opt. Lett. 30(8), 848–850 (2005).
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L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38(8), 1331–1333 (2013).
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Photon. Res. (1)

Phys. Lett. A (1)

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[Crossref]

Phys. Rev. A (2)

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(2), 1593–1596 (1996).
[Crossref] [PubMed]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Phys. Rev. Lett. (1)

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

Proc. R. Soc. Lond. A Math. Phys. Sci. (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]

Sci. Rep. (2)

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).
[Crossref] [PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram for the focusing system. A Radially polarized beam is firstly passing through spiral phase plate for loading optical vortex with topological l and subsequently focused by a high NA objective.
Fig. 2
Fig. 2 Transverse (a) and longitudinal (b) components of the normalized Poynting vectors in the focal plane of the tightly focused RP beam without any phase modulations. Both images have dimensions 3λ × 3λ.
Fig. 3
Fig. 3 Normalized Poynting vectors in the focal plane of the tightly focused RP beam with traditional vortex phase modulations when l = 1, 3, and 5, respectively. The transverse and longitudinal components are shown in the first and second rows. The direction of the transverse energy flow is indicated by black arrows. All images have dimensions 4λ × 4λ.
Fig. 4
Fig. 4 Normalized electromagnetic field intensity distributions in the focal plane of a tightly focused RP laser beam with traditional vortex phase modulations when l = 1, 3, and 5, corresponding to the first, second, and third rows, respectively. The transverse, longitudinal, and total field intensity distributions are shown in the first, second, and third columns, respectively. The fourth column gives the normalized total magnetic field intensity distributions in the focal plane. All images have dimensions of 4λ × 4λ.
Fig. 5
Fig. 5 Normalized Poynting vectors in the focal plane of the tightly focused RP beam with annular vortex phase modulations when l = 3, 4, 5, and 6, respectively. The transverse and longitudinal components are presented in the first and second rows. The direction of the transverse energy flow is indicated by black arrows. All images have dimensions of 5λ × 5λ.
Fig. 6
Fig. 6 Normalized electromagnetic field intensity distributions in the focal plane of the tightly focused RP beam with annular vortex phase modulations when l = 3, 4, 5, and 6, respectively (first, second, third, and fourth rows, respectively). The transverse, longitudinal, and total field intensity distributions are shown in the first, second, and third columns, respectively. The fourth column gives the normalized total magnetic field intensity distributions in the focal plane. All images have dimensions 5λ × 5λ.

Equations (12)

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E i ( r,φ,z )= A 0 circ(r/ r 0 )( cosφ e ^ x +sinφ e ^ y ) = A 0 circ(r/ r 0 )[ cosφ( cosφ e ^ r sinφ e ^ φ )+sinφ( sinφ e ^ r +cosφ e ^ φ ) ]. = A 0 circ(r/ r 0 ) e ^ r
E o ( ρ S , ϕ S , z S )= ikf 2π 0 2π 0 α sinθ cosθ Kcirc( sinθ/sinα ) l 0 ( θ,φ ) M e dφdθ,
K=exp{ ik[ z S cosθ+ ρ S sinθcos( ϕ ϕ S ) ] } =exp{ ik[ z S cosθ ρ S sinθcos( φ ϕ S ) ] }.
l 0 (θ,φ)=exp[ β 2 ( sinθ sinα ) 2 +iΦ(θ,φ) ] J 1 ( 2β sinθ sinα ),
Φ(θ,φ)={ lφforθ[ θ 1 , θ 2 ] 0otherwise
{ r 1 =fsin θ 1 r 2 =fsin θ 2 ,
{ τ 1 = r 1 r 0 = fsin θ 1 fsinα = sin θ 1 sinα τ 2 = r 2 r 0 = fsin θ 2 fsinα = sin θ 2 sinα .
M e =[ M ex M ey M ez ]=[ cosθcosφ cosθsinφ sinθ ].
H o ( ρ S , ϕ S , z S )= ikf 2π 0 2π 0 α sinθ cosθ Kcirc( sinθ/sinα ) l 0 ( θ,φ ) M m dφdθ,
M m =k× M e ,
M m =[ M mx M my M mz ]=[ sinφ cosφ 0 ].
P c 8π Re( E× H ),

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