Abstract

Considering an azimuthally polarized vortex beam with a Gaussian annulus as an incoming light, light induced magnetization fields for both a single high NA lens and a pair of high NA lenses are investigated theoretically. We deduce analytical formulas for the parameters of a magnetization needle and a magnetization chain when the angular width of the incident beam is far less than its central angular position. Through these analytical formulas, the properties of the magnetization needle and the magnetization chain are very clear and distinct. Compared with parameter optimizing to produce an ultralong magnetization needle with lateral sub-wavelength scale and a super-long spherical magnetization chain with three-dimensional super resolution, the analytical method is direct and has a theoretical guideline. The validity of these formulas is proved, compared to numerical solutions. The present work regarding these super-resolution magnetization patterns is of great value in high density all-optical magnetic recording, atomic trapping as well as confocal and magnetic resonance microscopy.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]

2017 (4)

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam,” Appl. Opt. 56(7), 1940–1946 (2017).
[Crossref] [PubMed]

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

P. Singh, A. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Opt. Lasers Eng. 91, 187–195 (2017).
[Crossref]

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017).
[Crossref]

2016 (4)

2015 (7)

2014 (3)

S. Wang, X. Li, J. Zhou, and M. Gu, “Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics,” Opt. Lett. 39(17), 5022–5025 (2014).
[Crossref] [PubMed]

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

2013 (3)

2012 (2)

2011 (1)

2010 (2)

2009 (1)

2008 (2)

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

G. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[Crossref] [PubMed]

2007 (3)

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

T. Grosjean, D. Courjon, and C. Bainier, “Smallest lithographic marks generated by optical focusing systems,” Opt. Lett. 32(8), 976–978 (2007).
[Crossref] [PubMed]

2004 (1)

2003 (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]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

1965 (1)

J. van der Ziel, P. Pershan, and L. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190–193 (1965).
[Crossref]

1959 (1)

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

Anbarasan, P.

April, A.

Bainier, C.

Barton, P.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Boshier, M.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Brown, T.

Cai, Y.

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Cao, Y.

Chen, G.

Chen, J.

Chen, Z.

Courjon, D.

Dehez, H.

Ding, W.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Dovzhenko, Y.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Du, L.

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Fang, Z.

Fu, L.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Gong, L.

Greve, K.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Grinolds, M.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Grosjean, T.

Gu, B.

Gu, M

Gu, M.

Hansteen, F.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Hinds, E.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

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, 9977 (2015).
[Crossref] [PubMed]

Hong, S.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Hu, K.

Huang, K.

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, 9977 (2015).
[Crossref] [PubMed]

K. Huang, P. Shi, X. Kang, X. Zhang, Y. Li, L. Wang, Y. Wang, and Z. Fang, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
[Crossref]

Hughes, I.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Itoh, A.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Jaroszewicz, Z.

Jia, B.

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

H. Lin, B. Jia, and M. Gu, “Dynamic generation of Debye diffraction-limited multifocal arrays for direct laser printing nanofabrication,” Opt. Lett. 36(3), 406–408 (2011).
[Crossref] [PubMed]

Jiang, Y.

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, 9977 (2015).
[Crossref] [PubMed]

Kang, X.

Kimel, A.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Kirilyuk, A.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Lerman, G.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Levy, U.

Li, D.

Li, M.

Li, Q.

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Li, X.

Li, Y.

Li, Z.

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Liang, Y.

Lin, H.

Liu, X.

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, and C. Sheppard, “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, 9977 (2015).
[Crossref] [PubMed]

Ma, W.

Maletinsky, P.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Malmstrom, L.

J. van der Ziel, P. Pershan, and L. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190–193 (1965).
[Crossref]

Man, Z.

Min, C.

Nie, Z.

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam,” Appl. Opt. 56(7), 1940–1946 (2017).
[Crossref] [PubMed]

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017).
[Crossref]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Spherical and sub-wavelength longitudinal magnetization generated by 4π tightly focusing radially polarized vortex beams,” Opt. Express 23(2), 690–701 (2015).
[Crossref] [PubMed]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Achievement and steering of light-induced sub-wavelength longitudinal magnetization chain,” Opt. Express 23(16), 21296–21305 (2015).
[Crossref] [PubMed]

Okuno, Y.

Pershan, P.

J. van der Ziel, P. Pershan, and L. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190–193 (1965).
[Crossref]

Piché, M.

Pu, J.

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, 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, 9977 (2015).
[Crossref] [PubMed]

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Rajesh, K.

Rasing, T.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Richards, B.

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

Rosenbusch, P.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Saba, C.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Sauer, B.

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Sheppard, C.

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

Shi, P.

Singh, H.

H. Singh, A. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Singh, K.

P. Singh, A. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Opt. Lasers Eng. 91, 187–195 (2017).
[Crossref]

H. Singh, A. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Singh, P.

P. Singh, A. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Opt. Lasers Eng. 91, 187–195 (2017).
[Crossref]

Song, F.

Song, Y.

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017).
[Crossref]

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam,” Appl. Opt. 56(7), 1940–1946 (2017).
[Crossref] [PubMed]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Achievement and steering of light-induced sub-wavelength longitudinal magnetization chain,” Opt. Express 23(16), 21296–21305 (2015).
[Crossref] [PubMed]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Spherical and sub-wavelength longitudinal magnetization generated by 4π tightly focusing radially polarized vortex beams,” Opt. Express 23(2), 690–701 (2015).
[Crossref] [PubMed]

Stanciu, C.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

Thiel, L.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Tian, N.

Tian, Y.

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

Tsukamoto, A.

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

van der Ziel, J.

J. van der Ziel, P. Pershan, and L. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190–193 (1965).
[Crossref]

Vashisth, S.

H. Singh, A. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Walsworth, R.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Wang, H.

G. Chen, F. Song, and H. Wang, “Sharper focal spot generated by 4π tight focusing of higher-order Laguerre-Gaussian radially polarized beam,” Opt. Lett. 38(19), 3937–3940 (2013).
[Crossref] [PubMed]

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

Wang, J.

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Wang, L.

Wang, S.

Wang, W.

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

Wang, X.

Wang, Y.

Warner, M.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[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, 9977 (2015).
[Crossref] [PubMed]

Xu, X.

Yacoby, A.

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Yadav, A.

P. Singh, A. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Opt. Lasers Eng. 91, 187–195 (2017).
[Crossref]

H. Singh, A. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Yan, S.

Yan, W.

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam,” Appl. Opt. 56(7), 1940–1946 (2017).
[Crossref] [PubMed]

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017).
[Crossref]

Yao, B.

Youngworth, K.

Yu, Y.

Y. Yu and Q. Zhan, “Generation of uniform three-dimensional optical chain with controllable characteristics,” J. Opt. 17(10), 105606 (2015).
[Crossref]

Yuan, X.

Zhai, A.

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

Zhan, Q.

Y. Yu and Q. Zhan, “Generation of uniform three-dimensional optical chain with controllable characteristics,” J. Opt. 17(10), 105606 (2015).
[Crossref]

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

Zhang, B.

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Zhang, D.

Zhang, P.

Zhang, X.

Zhang, Y.

Zhao, H.

Zhao, X.

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Zheng, Y.

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Zhou, J.

Zhou, L.

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Zhu, L.

Zhu, S.

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Z. Man, C. Min, L. Du, Y. Zhang, S. Zhu, and X. Yuan, “Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes,” Opt. Express 24(2), 874–882 (2016).
[Crossref] [PubMed]

Zhu, Z.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

S. Zhu, J. Wang, X. Liu, Y. Cai, and Z. Li, “Generation of arbitrary radially polarized array beams by manipulating correlation structure,” Appl. Phys. Lett. 109(16), 161904 (2016).
[Crossref]

Q. Li, X. Zhao, B. Zhang, Y. Zheng, and L. Zhou, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
[Crossref]

Chin. Opt. Lett. (1)

J. Opt. (2)

Y. Yu and Q. Zhan, “Generation of uniform three-dimensional optical chain with controllable characteristics,” J. Opt. 17(10), 105606 (2015).
[Crossref]

W. Yan, Z. Nie, X. Zhang, Y. Wang, and Y. Song, “Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter,” J. Opt. 19(8), 085401 (2017).
[Crossref]

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

Light Sci. Appl. (1)

Z. Nie, H. Lin, X. Liu, A. Zhai, Y. Tian, W. Wang, D. Li, W. Ding, X. Zhang, Y. Song, and B. Jia, “Three-dimensional super-resolution longitudinal magnetization spot arrays,” Light Sci. Appl. 6, e17045 (2017).

Nat. Nanotechnol. (1)

M. Grinolds, M. Warner, K. Greve, Y. Dovzhenko, L. Thiel, R. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9, 279–284 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Opt. Commun (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun 179(1), 1–7 (2000).
[Crossref]

Opt. Commun. (1)

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

Opt. Express (9)

K. Rajesh, Z. Jaroszewicz, and P. Anbarasan, “Improvement of lens axicon’s performance for longitudinally polarized beam generation by adding a dedicated phase transmittance,” Opt. Express 18(26), 26799–26805 (2010).
[Crossref]

G. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[Crossref] [PubMed]

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

Z. Man, C. Min, L. Du, Y. Zhang, S. Zhu, and X. Yuan, “Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes,” Opt. Express 24(2), 874–882 (2016).
[Crossref] [PubMed]

M. Li, S. Yan, B. Yao, Y. Liang, and P. Zhang, “Spinning and orbiting motion of particles in vortex beams with circular or radial polarizations,” Opt. Express 24(18), 20604–20612 (2016).
[Crossref] [PubMed]

K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Achievement and steering of light-induced sub-wavelength longitudinal magnetization chain,” Opt. Express 23(16), 21296–21305 (2015).
[Crossref] [PubMed]

Z. Nie, W. Ding, D. Li, X. Zhang, Y. Wang, and Y. Song, “Spherical and sub-wavelength longitudinal magnetization generated by 4π tightly focusing radially polarized vortex beams,” Opt. Express 23(2), 690–701 (2015).
[Crossref] [PubMed]

Opt. Lasers Eng. (2)

P. Singh, A. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Opt. Lasers Eng. 91, 187–195 (2017).
[Crossref]

H. Singh, A. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Opt. Lett. (8)

S. Wang, X. Li, J. Zhou, and M. Gu, “Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics,” Opt. Lett. 39(17), 5022–5025 (2014).
[Crossref] [PubMed]

Y. Jiang, X. Li, and M. Gu, “Generation of sub-diffraction-limited pure longitudinal magnetization by the inverse Faraday effect by tightly focusing an azimuthally polarized vortex beam,” Opt. Lett. 38(16), 2957–2960 (2013).
[Crossref] [PubMed]

K. Hu, Z. Chen, and J. Pu, “Generation of super-length optical needle by focusing hybridly polarized vector beams through a dielectric interface,” Opt. Lett. 37(16), 3303–3305 (2012).
[Crossref]

G. Chen, F. Song, and H. Wang, “Sharper focal spot generated by 4π tight focusing of higher-order Laguerre-Gaussian radially polarized beam,” Opt. Lett. 38(19), 3937–3940 (2013).
[Crossref] [PubMed]

H. Lin, B. Jia, and M. Gu, “Dynamic generation of Debye diffraction-limited multifocal arrays for direct laser printing nanofabrication,” Opt. Lett. 36(3), 406–408 (2011).
[Crossref] [PubMed]

K. Huang, P. Shi, X. Kang, X. Zhang, Y. Li, L. Wang, Y. Wang, and Z. Fang, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
[Crossref]

M. Gu, H. Lin, and X. Li, “Parallel multiphoton microscopy with cylindrically polarized multifocal arrays,” Opt. Lett. 38(18), 3627–3630 (2013).
[Crossref] [PubMed]

T. Grosjean, D. Courjon, and C. Bainier, “Smallest lithographic marks generated by optical focusing systems,” Opt. Lett. 32(8), 976–978 (2007).
[Crossref] [PubMed]

Optica (1)

Phys. Rev. Lett. (4)

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

J. van der Ziel, P. Pershan, and L. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190–193 (1965).
[Crossref]

C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref] [PubMed]

C. Saba, P. Barton, M. Boshier, I. Hughes, P. Rosenbusch, B. Sauer, and E. Hinds, “Reconstruction of a cold atom cloud by magnetic focusing,” Phys. Rev. Lett. 82(3), 468 (1999).
[Crossref]

Proc. Roy. Soc. A (1)

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

Sci. Rep. (1)

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, 9977 (2015).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Schematic illustration of a 4π tight focusing system. A MO film lies in the confocal plane of the configuration, which is illuminated by two counter-propagating azimuthally polarized vortex beams. AP1 and AP2 denote two counter-propagating azimuthally polarized beams, SPP1 and SPP2 signify two identical spiral phase plates, L1 and L2 respresent two high NA objective lenses.
Fig. 2
Fig. 2 FWHMs vs various central angles for the transverse optical needle, the longitudinal optical needle and the magnetization needle.
Fig. 3
Fig. 3 DOFs of the magnetization needles vs Δθ for θ0 = 45 degrees, 60 degrees, 75 degrees.
Fig. 4
Fig. 4 (a) and (b), the light needle with dual channels and the corresponding magnetization needle for m = 2. The rest parameters are chosen as θ0 = 75 degrees and Δθ = 0.01.
Fig. 5
Fig. 5 The distance between dual channels of magnetization needle vs θ0 for different m.
Fig. 6
Fig. 6 The differences based on the numerical and analytical results. In (a), the differences between the lateral FWHMs of magnetization needles with a single channel. In (b), the differences between the longitudinal DOFs of magnetization needles with a single channel.
Fig. 7
Fig. 7 Both the lateral FWHM and the axial FWHM of the central magnetization spot vs the central angle.
Fig. 8
Fig. 8 Displacement vs ϕ0 and θ0.
Fig. 9
Fig. 9 The differences based on the numerical solutions and analytical expressions. In (a), the differences between the lateral FWHMs of the central magnetization spots. In (b), the differences between the axial FWHMs of the central magnetization spots.

Equations (18)

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

E = [ E r E φ E z ] = A j m 0 θ max T ( φ ) [ V 1 j V 2 0 ] exp ( j k z cos θ ) E 0 ( θ ) cos θ sin θ d θ ,
V 1 = J m 1 ( k r sin θ ) + J m + 1 ( k r sin θ ) ,
V 2 = J m 1 ( k r sin θ ) J m + 1 ( k r sin θ ) ,
T ( φ ) = exp ( j m φ ) .
E r = A j m T ( φ ) V 1 exp ( z 2 / z 0 2 + j k z cos θ 0 ) cos θ 0 sin θ 0 ,
E φ = A j m + 1 T ( φ ) V 2 exp ( z 2 / z 0 2 + j k z cos θ 0 ) cos θ 0 sin θ 0 ,
I t = | E r | 2 + | E φ | 2 = 2 | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) + J m + 1 2 ( k r sin θ 0 ) ] .
M = j γ E × E * ,
M = j γ ( E r E φ * E φ E r * ) e z = 2 γ | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) J m + 1 2 ( k r sin θ 0 ) ] e z .
E ( r , φ , z ) = E 1 ( r , φ , z ) + exp ( j ϕ 0 ) E 2 ( r , φ , z ) ,
E r = 2 A j m T ( φ ) exp ( j ϕ 0 / 2 ) cos θ 0 sin θ 0 V 1 exp ( z 2 / z 0 2 ) cos ( k z cos θ 0 + ϕ 0 / 2 ) ,
E φ = 2 A j m + 1 T ( φ ) exp ( j ϕ 0 / 2 ) cos θ 0 sin θ 0 V 2 exp ( z 2 / z 0 2 ) cos ( k z cos θ 0 + ϕ 0 / 2 ) .
I t = 4 | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) + J m + 1 2 ( k r sin θ 0 ) ] cos 2 ( k z cos θ 0 + ϕ 0 / 2 ) .
M = 8 γ | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) J m + 1 2 ( k r sin θ 0 ) ] cos 2 ( k z cos θ 0 + ϕ 0 / 2 ) e z .
E r = 2 A j m + 1 T ( φ ) cos θ 0 sin θ 0 V 1 exp ( z 2 / z 0 2 ) sin ( k z cos θ 0 + ϕ 0 / 2 ) ,
E φ = 2 A j m + 2 T ( φ ) cos θ 0 sin θ 0 V 2 exp ( z 2 / z 0 2 ) sin ( k z cos θ 0 + ϕ 0 / 2 ) .
I t = 4 | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) + J m + 1 2 ( k r sin θ 0 ) ] sin 2 ( k z cos θ 0 + ϕ 0 / 2 ) .
M = 8 γ | A | 2 cos θ 0 sin 2 θ 0 exp ( 2 z 2 / z 0 2 ) [ J m 1 2 ( k r sin θ 0 ) J m + 1 2 ( k r sin θ 0 ) ] sin 2 ( k z cos θ 0 + ϕ 0 / 2 ) e z .

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