Abstract

The tight focusing properties of optical fields combining a spiral phase and cylindrically symmetric state of polarization are presented. First, we theoretically analyze the mathematical characterization, Stokes parameters, and Poincaré sphere representations of arbitrary cylindrical vector (CV) vortex beams. Then, based on the vector diffraction theory, we derive and build an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input CV vortex beams. The calculations reveal that a generalized CV vortex beam can generate a sharper focal spot than that of a radially polarized (RP) plane beam in the focal plane. Besides, the focal size decrease accompanies its elongation along the optical axis. Hence, it seems that there is a trade-off between the transverse and axial resolutions. In addition, under the precondition that the absolute values between polarization order and topological charge are equal, a higher-order CV vortex can also achieve a smaller focal size than an RP plane beam. Further, the intensity for the sidelobe admits a significant suppression. To give a deep understanding of the peculiar focusing properties, the magnetic field and Poynting vector distributions are also demonstrated in detail. These properties may be helpful in applications such as optical trapping and manipulation of particles and superresolution microscopy imaging.

© 2018 Optical Society of America

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References

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2017 (4)

2015 (4)

2014 (4)

2013 (6)

2012 (2)

2011 (8)

2010 (2)

2009 (5)

2008 (1)

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

2007 (5)

2006 (1)

2005 (1)

2004 (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

2003 (1)

2002 (1)

2000 (2)

1999 (1)

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

1995 (1)

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[Crossref]

Aiello, A.

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

April, A.

Arlt, J.

Bai, J.

Barton, P. A.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Bernet, S.

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

Bokor, N.

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279, 229–234 (2007).
[Crossref]

Born, M.

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

Boshier, M. G.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Brown, T. G.

Bu, J.

Cao, G. W.

Chen, C.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Chen, S.

Chen, W.

Chen, Z.

Cheng, H.

Cheng, W.

Chong, C. T.

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

Davidson, N.

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279, 229–234 (2007).
[Crossref]

Dehez, H.

Ding, B.

Ding, J.

Dorpe, P. V.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Dou, X.

Du, L.

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

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, 2891 (2013).
[Crossref]

Eberl, K.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

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, 2891 (2013).
[Crossref]

Fortin, P. L.

P. L. Fortin and M. Piché, “Direct-field electron acceleration with ultrafast radially polarized laser beams: scaling laws and optimization,” J. Phys. B 43, 025401 (2009).
[Crossref]

Fron, E.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Fürhapter, S.

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

Gabriel, C.

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

Gao, X.

Gao, X.-Z.

Geng, T.

Gerhardts, R. R.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

Golub, I.

Gu, M.

Guo, C.-S.

Guo, H.

Han, T.

Han, W.

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, 1766–1769 (2011).
[Crossref]

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Hinds, E. A.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Hofkens, J.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Holleczek, A.

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

Hu, Q.

Huang, K.

Hughes, I. G.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Hutchison, J. A.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Jesacher, A.

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

Jia, B.

Jiang, M.

Kang, X.-L.

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Kenens, B.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Khonina, S. N.

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, 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, 1766–1769 (2011).
[Crossref]

Leger, J. R.

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, 2891 (2013).
[Crossref]

Leuchs, G.

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

Li, J.

Li, K.

Li, P.

Li, Y.

Li, Y. P.

Li, Y.-N.

Li, Y.-P.

Li, Z.

Lin, H.

Lin, J.

Ling, X.

Liu, C.-K.

Liu, D.

J. Shu, Z. Chen, J. Pu, J. Zhu, and D. Liu, “Tight focusing of partially coherent and radially polarized vortex beams,” Opt. Commun. 295, 5–10 (2013).
[Crossref]

Liu, S.

Liu, W.

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, 1766–1769 (2011).
[Crossref]

Liu, Y.

Liu, Z.

Lu, G.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Lukyanchuk, B.

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

Luo, H.

Man, Z.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

Marquardt, C.

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

Maurer, C.

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

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Min, C.

Y. Zhang, X. Dou, Y. Yang, C. Xie, J. Bu, C. Min, and X. Yuan, “Flexible generation of femtosecond cylindrical vector beams,” Chin. Opt. Lett. 15, 030007 (2017).
[Crossref]

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 2891 (2013).
[Crossref]

Mizuno, H.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Ni, W.-J.

Nickel, H.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

Noda, S.

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Padgett, M. J.

Pan, Y.

Peng, T.

Piché, M.

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20, 14891–14905 (2012).
[Crossref]

P. L. Fortin and M. Piché, “Direct-field electron acceleration with ultrafast radially polarized laser beams: scaling laws and optimization,” J. Phys. B 43, 025401 (2009).
[Crossref]

Ping, Y. S.

Porfirev, A. P.

Pu, J.

Qian, B.

Qiu, C.-W.

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]

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, 78 (2007).
[Crossref]

Rocha, S. A.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Roeffaers, M. B. J.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Rosenbusch, P.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Saba, C. V.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Sakai, K.

Sato, S.

Sauer, B. E.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[Crossref]

Seeger, M.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

Shen, J.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 2891 (2013).
[Crossref]

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, 2891 (2013).
[Crossref]

Sheppard, C.

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

Sheppard, C. J. R.

Shi, L.

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

Shi, P.

Shi, W.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

Shu, J.

J. Shu, Z. Chen, J. Pu, and Y. Liu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam through a dielectric interface,” J. Opt. Soc. Am. A 31, 1180–1185 (2014).
[Crossref]

J. Shu, Z. Chen, J. Pu, J. Zhu, and D. Liu, “Tight focusing of partially coherent and radially polarized vortex beams,” Opt. Commun. 295, 5–10 (2013).
[Crossref]

Skidanov, R. V.

Su, L.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Sui, G.

Sun, C.-C.

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Tan, J.

Teng, J.

Tian, B.

Tian, J.

Tu, C.-G.

Ujii, H.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Urbach, H. P.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

Wan, C.

Wang, H.

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

Wang, H.-T.

Wang, J.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 1766–1769 (2011).
[Crossref]

Wang, X.-L.

Wang, Y.

Wei, S. B.

Weiss, D.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

Wen, S.

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

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

Xie, B.

Xie, C.

Xu, J.

Yang, Y.

Ye, H.

Ye, P. D.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

Yew, E. Y. S.

Yin, K.

Youngworth, K. S.

Yu, P.

Yu, Y.

Yuan, G.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 2891 (2013).
[Crossref]

Yuan, G. H.

Yuan, H.

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Yuan, X.

Y. Zhang, X. Dou, Y. Yang, C. Xie, J. Bu, C. Min, and X. Yuan, “Flexible generation of femtosecond cylindrical vector beams,” Chin. Opt. Lett. 15, 030007 (2017).
[Crossref]

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

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 2891 (2013).
[Crossref]

Yuan, X.-C.

Zeng, T.

Zhan, Q.

Zhang, G.-L.

Zhang, X.

Zhang, X. B.

Zhang, Y.

Zhao, J.

Zhao, M.-D.

Zhao, Y.

Zhou, X.

Zhu, J.

J. Shu, Z. Chen, J. Pu, J. Zhu, and D. Liu, “Tight focusing of partially coherent and radially polarized vortex beams,” Opt. Commun. 295, 5–10 (2013).
[Crossref]

Zhu, S.

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

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, 2891 (2013).
[Crossref]

Zhuang, S.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (4)

J. Phys. B (1)

P. L. Fortin and M. Piché, “Direct-field electron acceleration with ultrafast radially polarized laser beams: scaling laws and optimization,” J. Phys. B 43, 025401 (2009).
[Crossref]

Nano Lett. (1)

Y. Zhang, J. Wang, J. Shen, Z. Man, W. Shi, C. Min, G. Yuan, S. Zhu, H. P. Urbach, and X. Yuan, “Plasmonic hybridization induced trapping and manipulation of a single Au nanowire on a metallic surface,” Nano Lett. 14, 6430–6436 (2014).
[Crossref]

Nat. Commun. (2)

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

L. Su, G. Lu, B. Kenens, S. A. Rocha, E. Fron, H. Yuan, C. Chen, P. V. Dorpe, M. B. J. Roeffaers, H. Mizuno, J. Hofkens, J. A. Hutchison, and H. Ujii, “Visualization of molecular fluorescence point spread functions via remote excitation switching fluorescence microscopy,” Nat. Commun. 6, 6287 (2015).
[Crossref]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of an needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 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, 78 (2007).
[Crossref]

Opt. Commun. (3)

J. Shu, Z. Chen, J. Pu, J. Zhu, and D. Liu, “Tight focusing of partially coherent and radially polarized vortex beams,” Opt. Commun. 295, 5–10 (2013).
[Crossref]

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, 1766–1769 (2011).
[Crossref]

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279, 229–234 (2007).
[Crossref]

Opt. Express (13)

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

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[Crossref]

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

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20, 14891–14905 (2012).
[Crossref]

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, 5363–5372 (2013).
[Crossref]

Y. Yu and Q. Zhan, “Optimization-free optical focal field engineering through reversing the radiation pattern from a uniform line source,” Opt. Express 23, 7527–7534 (2015).
[Crossref]

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

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

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, 4518–4525 (2010).
[Crossref]

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, 3698–3706 (2009).
[Crossref]

S. Liu, P. Li, T. Peng, and J. Zhao, “Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer,” Opt. Express 20, 21715–21721 (2012).
[Crossref]

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

Opt. Lett. (16)

W. Chen and Q. Zhan, “Creating a spherical focal spot with spatially modulated radial polarization in 4Pi microscopy,” Opt. Lett. 34, 2444–2446 (2009).
[Crossref]

H. Lin, B. Jia, and M. Gu, “Generation of an axially super-resolved quasi-spherical focal spot using an amplitude-modulated radially polarized beam,” Opt. Lett. 36, 2471–2473 (2011).
[Crossref]

B. Tian and J. Pu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam,” Opt. Lett. 36, 2014–2016 (2011).
[Crossref]

Q. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31, 867–869 (2006).
[Crossref]

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 beam,” Opt. Lett. 39, 630–633 (2014).
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S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39, 5274–5276 (2014).
[Crossref]

P. Yu, S. Chen, J. Li, H. Cheng, Z. Li, W. Liu, B. Xie, Z. Liu, and J. Tian, “Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces,” Opt. Lett. 40, 3229–3232 (2015).
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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, 888–890 (2011).
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E. Y. S. Yew and C. J. R. Sheppard, “Tight focusing of radially polarized Gaussian and Bessel-Gauss beams,” Opt. Lett. 32, 3417–3419 (2007).
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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, 99–101 (2003).
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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, 965–967 (2010).
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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, 1185–1187 (2011).
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G. H. Yuan, S. B. Wei, and X.-C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36, 3479–3481 (2011).
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J. Arlt and M. J. Padgett, “Generation of a beam with dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
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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, 848–850 (2005).
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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, 3549–3551 (2007).
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Photon. Res. (1)

Phys. Rev. Lett. (3)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. Eberl, and H. Nickel, “Electrons in a periodic magnetic field induced by a regular array of micromagnets,” Phys. Rev. Lett. 74, 3013–3016 (1995).
[Crossref]

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82, 468–471 (1999).
[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]

Other (2)

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Poincaré sphere representation for classical inseparable Bell-like states of the electromagnetic field,” arXiv:1007.2528 (2010).

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

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Figures (7)

Fig. 1.
Fig. 1. Higher-order PS representations for (a) m=1 and (b) m=2, respectively. Equatorial points (2Θ=0) represent CV polarized beams (0, 0) and (0, π), which represent radial and azimuthal polarization models for m=1.
Fig. 2.
Fig. 2. Calculated electric intensity distributions of the radial, azimuthal, longitudinal, and the total fields in the focal and through-focus planes for the input fields with (l,c)=(0,0), (1, 0), (1, π/4), and (1, π/2) when m=1. The sizes for all of the first four columns of images are 2.6λ×2.6λ. The sizes for all of the last columns of images are 2.6λ×4λ. All intensity distributions are normalized to the maximum intensity of the total field in the focal plane for each input light mode.
Fig. 3.
Fig. 3. Calculated electric field intensity profiles (a) in the focal plane and (b) along the optical axis for the input fields with (l,c)=(0,0), (1, 0), (1, π/4), and (1, π/2) when m=1. The peak intensity for each mode is normalized to 1.
Fig. 4.
Fig. 4. Calculated electric intensity distributions of the radial, azimuthal, longitudinal, and the total fields in the focal and through-focus planes for the input fields with (m,l)=(2,2), (3, 3), and (4, 4) when c=0. The sizes for all of the first four columns of images are 2.6λ×2.6λ. The sizes for all of the last columns of images are 2.6λ×4λ. All intensity distributions are normalized to the maximum intensity of the total field in the focal plane for each input light mode.
Fig. 5.
Fig. 5. Calculated electric field intensity profiles (a) in the focal plane and (b) along the optical axis for the input fields with (m,l)=(2,2), (3, 3), and (4, 4) when c=0. The peak intensity for each mode is normalized to 1.
Fig. 6.
Fig. 6. Calculated magnetic intensity distributions of the transverse, longitudinal, and the total fields in the focal and through-focus planes for the input fields with (m,l)=(4,4) and (4, 0) when c=0. The sizes for all of the images in the focal plane are 4λ×4λ. The sizes for the images in the through-focus plane are 4λ×6λ. All intensity distributions are normalized to the maximum intensity of the total field in the focal plane for each input light mode.
Fig. 7.
Fig. 7. Calculated (a) transverse and (b) longitudinal components of the normalized Poynting vectors of the tightly focused higher-order CV vortex beam with m=l=4 when c=0. The direction of the transverse energy flow is shown by the black arrows. Both Poynting vectors are normalized to the maximum of the total Poynting vector in the focal plane.

Equations (17)

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

E=A0exp(ilϕ)|U,
|U=12exp[i(mϕ+c)]e^r+12exp[i(mϕ+c)]e^l,
[S1S2S3]=[U|σ1|UU|σ2|UU|σ3|U]=[cos2csin2c0],
sin2Θ=S3/S0,
tan2ϕ=S2/S1,
E(ρ,ϕ,z)=iC202π0αsinθcosθl(θ)exp(ilϕ)Me×exp{ik[ρsinθcos(ϕϕ)+zcosθ]}dϕdθ,
l(θ)=exp[β2(sinθsinα)2]J1(2βsinθsinα),
Me=Meρe^ρ+Meϕe^ϕ+Meze^z,
Meρ=sin[(m1)ϕ+c]sin(ϕϕ)+cos[(m1)ϕ+c]cosθcos(ϕϕ),
Meϕ=sin[(m1)ϕ+c]cos(ϕϕ)+cos[(m1)ϕ+c]cosθsin(ϕϕ),
Mez=cos[(m1)ϕ+c]sinθ.
H(ρ,ϕ,z)=iC202π0αsinθcosθl(θ)exp(ilϕ)Mm×exp{ik[ρsinθcos(ϕϕ)+zcosθ]}dϕdθ,
Mm=Mmρe^ρ+Mmϕe^ϕ+Mmze^z,
Mmρ=cos[(m1)ϕ+c]sin(ϕϕ)sin[(m1)ϕ+c]cosθcos(ϕϕ),
Mmϕ=cos[(m1)ϕ+c]cos(ϕϕ)sin[(m1)ϕ+c]cosθsin(ϕϕ),
Mmz=sin[(m1)ϕ+c]sinθ.
Pc8πRe(E×H*),

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