Abstract

Based on the vector diffraction theory and the inverse Faraday effect, we numerically study the light-induced magnetization near the focus of a 4π high numerical aperture focusing configuration under the illumination of two counter- propagating radially polarized hollow Gaussian vortex beams. The simulated results demonstrate that, by selecting higher-order vortex beam modes (e.g. n=4with n – the beam order) and proper truncation parameter (e.g. β=1.75 with β– the ratio of the pupil radius to the incident beam waist), spherical and sub-wavelength longitudinal magnetization can be generated in the vicinity of focus. Such special magnetization feature is attributed to not only the interaction between optical vortices and the radially polarized beams, but also the completely destructive interference of azimuthal components and the constructive interference of the longitudinal component of the two counter-propagating radially polarized vortex beams. This spherical and sub-wavelength longitudinal magnetization distribution may be of interest for applications in all-optical magnetic recording and confocal and magnetic resonance microscopy.

© 2015 Optical Society of America

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References

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  1. M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
    [Crossref]
  2. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
    [Crossref] [PubMed]
  3. A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
    [Crossref] [PubMed]
  4. S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
    [Crossref]
  5. P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
    [Crossref]
  6. M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
    [Crossref] [PubMed]
  7. Y. J. Zhang, Y. Okuno, and X. Xu, “All-optical magnetic superresolution with binary pupil filters,” J. Opt. Soc. Am. B 26(7), 1379–1383 (2009).
    [Crossref]
  8. V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
    [Crossref]
  9. L. P. Pitaevskii, “Electric forces in a transparent dispersive medium,” Sov. Phys. JETP-USSR 12, 1008–1013 (1961).
  10. J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
    [Crossref]
  11. A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
    [Crossref]
  12. L. E. Helseth, “Strongly focused electromagnetic waves in E×E* media,” Opt. Commun. 281(23), 5671–5673 (2008).
    [Crossref]
  13. L. E. Helseth, “Focusing of evanescent vector waves,” Opt. Commun. 283(1), 29–33 (2010).
    [Crossref]
  14. 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]
  15. 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]
  16. L. E. Helseth, “Light-induced magnetic vortices,” Opt. Lett. 36(6), 987–989 (2011).
    [Crossref] [PubMed]
  17. N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4π focusing of radially polarized light,” Opt. Lett. 29(17), 1968–1970 (2004).
    [Crossref] [PubMed]
  18. W. Chen and Q. Zhan, “Creating a spherical focal spot with spatially modulated radial polarization in 4Pi microscopy,” Opt. Lett. 34(16), 2444–2446 (2009).
    [Crossref] [PubMed]
  19. S. Yan, B. Yao, W. Zhao, and M. Lei, “Generation of multiple spherical spots with a radially polarized beam in a 4π focusing system,” J. Opt. Soc. Am. A 27(9), 2033–2037 (2010).
    [Crossref]
  20. S. Yan, B. Yao, and R. Rupp, “Shifting the spherical focus of a 4Pi focusing system,” Opt. Express 19(2), 673–678 (2011).
    [Crossref] [PubMed]
  21. G. Y. Chen, F. Song, and H. T. 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]
  22. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).
    [Crossref] [PubMed]
  23. Y. Cai and L. Zhang, “Propagation of a hollow Gaussian beam through a paraxial misaligned optical system,” Opt. Commun. 265(2), 607–615 (2006).
    [Crossref]
  24. Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
    [Crossref]
  25. Z. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16(24), 19926–19933 (2008).
    [Crossref] [PubMed]
  26. Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
    [Crossref]
  27. C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
    [Crossref]
  28. 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]
  29. K. Huang, P. Shi, X. L. Kang, X. B. 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).
    [Crossref] [PubMed]
  30. Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
    [Crossref]
  31. Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
    [Crossref] [PubMed]
  32. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [Crossref] [PubMed]
  33. 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]
  34. Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
    [Crossref]
  35. G. H. Yuan, S. B. Wei, and X. C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
    [Crossref] [PubMed]
  36. Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
    [Crossref]
  37. Q. Li, X. Zhao, B. Zhang, Y. Zheng, L. Zhou, L. Wang, Y. Wu, and Z. Fang, “Nanofocusing of longitudinally polarized light using absorbance modulation,” Appl. Phys. Lett. 104(6), 061103 (2014).
    [Crossref]
  38. Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
    [Crossref]

2014 (6)

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

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]

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

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

2013 (4)

Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
[Crossref]

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

G. Y. Chen, F. Song, and H. T. 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]

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]

2012 (4)

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (4)

L. E. Helseth, “Focusing of evanescent vector waves,” Opt. Commun. 283(1), 29–33 (2010).
[Crossref]

S. Yan, B. Yao, W. Zhao, and M. Lei, “Generation of multiple spherical spots with a radially polarized beam in a 4π focusing system,” J. Opt. Soc. Am. A 27(9), 2033–2037 (2010).
[Crossref]

Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
[Crossref]

K. Huang, P. Shi, X. L. Kang, X. B. 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).
[Crossref] [PubMed]

2009 (2)

2008 (3)

L. E. Helseth, “Strongly focused electromagnetic waves in E×E* media,” Opt. Commun. 281(23), 5671–5673 (2008).
[Crossref]

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]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16(24), 19926–19933 (2008).
[Crossref] [PubMed]

2007 (2)

A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
[Crossref]

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

2006 (1)

Y. Cai and L. Zhang, “Propagation of a hollow Gaussian beam through a paraxial misaligned optical system,” Opt. Commun. 265(2), 607–615 (2006).
[Crossref]

2004 (1)

2003 (2)

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).
[Crossref] [PubMed]

2002 (2)

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

2000 (1)

1965 (1)

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
[Crossref]

1961 (1)

L. P. Pitaevskii, “Electric forces in a transparent dispersive medium,” Sov. Phys. JETP-USSR 12, 1008–1013 (1961).

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]

Ackerman, E. J.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Albrecht, M.

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

Anbarasan, P. M.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Atutov, S. N.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Bestm, M. E.

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

Biancalana, V.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Bokor, N.

Brown, T. G.

Burchianti, A.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Cai, Y.

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Y. Cai and L. Zhang, “Propagation of a hollow Gaussian beam through a paraxial misaligned optical system,” Opt. Commun. 265(2), 607–615 (2006).
[Crossref]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).
[Crossref] [PubMed]

Calabrese, R.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Chen, G. Y.

Chen, W.

Chen, Z.

Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
[Crossref]

Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
[Crossref] [PubMed]

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]

Dai, J.

Davidson, N.

De Greve, K.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Dovzhenko, Y.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Fang, Z.

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

Gan, F.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Grinolds, M. S.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Gu, M.

Guidi, V.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Hansteen, F.

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

Helseth, L. E.

L. E. Helseth, “Light-induced magnetic vortices,” Opt. Lett. 36(6), 987–989 (2011).
[Crossref] [PubMed]

L. E. Helseth, “Focusing of evanescent vector waves,” Opt. Commun. 283(1), 29–33 (2010).
[Crossref]

L. E. Helseth, “Strongly focused electromagnetic waves in E×E* media,” Opt. Commun. 281(23), 5671–5673 (2008).
[Crossref]

Holtom, G. R.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Hong, S.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Hopkins, D. F.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Hu, W.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Huang, K.

Itoh, A.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

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

Jaroszewicz, Z.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Jiang, Y.

Kang, X. L.

Khorsand, A. R.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

Kimel, A. V.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

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

A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
[Crossref]

Kirilyuk, A.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
[Crossref]

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

Lei, M.

Li, Q.

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

Li, X.

Li, Y. P.

Li, Z.

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Liao, J.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Lin, Q.

Liu, S.

Liu, Z.

Lu, X.

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).
[Crossref] [PubMed]

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]

Ma, H.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Mai, B.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Majors, P. D.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Maletinsky, P.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Malmstrom, L. D.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
[Crossref]

Marinelli, C.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Mariotti, E.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Minard, K. R.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Moi, L.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Moser, A.

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

Nie, Y.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Nie, Z.

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Okuno, Y.

Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
[Crossref]

Y. J. Zhang, Y. Okuno, and X. Xu, “All-optical magnetic superresolution with binary pupil filters,” J. Opt. Soc. Am. B 26(7), 1379–1383 (2009).
[Crossref]

Parkinson, C. I.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Pershan, P. S.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
[Crossref]

Pillai, T. V. S.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Pitaevskii, L. P.

L. P. Pitaevskii, “Electric forces in a transparent dispersive medium,” Sov. Phys. JETP-USSR 12, 1008–1013 (1961).

Pu, J.

Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
[Crossref]

Qi, J.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Rajesh, K. B.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Rasing, T.

A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
[Crossref]

Rasing, Th.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

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

Ravi, V.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Rettner, C. T.

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

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]

Rudavets, A. G.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Rupp, R.

Savoini, M.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

Scansani, E.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

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, G.

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[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.

Song, F.

Song, Y.

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

Stanciu, C. D.

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

Sun, X.

Suresh, P.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Terris, B. D.

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

Thiel, L.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Tomassetti, L.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Tsukamoto, A.

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

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

van der Ziel, J. P.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
[Crossref]

Veronesi, S.

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Walsworth, R. L.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Wang, F.

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Wang, H.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

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, L.

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

Wang, S.

Wang, Y.

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

Warner, M.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Weber, T. J.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Wei, C.

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Wei, J.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Wei, S. B.

Wind, R. A.

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Wu, G.

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Wu, Y.

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

Xu, X.

Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
[Crossref]

Y. J. Zhang, Y. Okuno, and X. Xu, “All-optical magnetic superresolution with binary pupil filters,” J. Opt. Soc. Am. B 26(7), 1379–1383 (2009).
[Crossref]

Yacoby, A.

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[Crossref] [PubMed]

Yan, S.

Yang, J.

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Yao, B.

Youngworth, K. S.

Yuan, G. H.

Yuan, X. C.

Zha, Y.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Zhan, Q.

Zhang, B.

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

Zhang, L.

Y. Cai and L. Zhang, “Propagation of a hollow Gaussian beam through a paraxial misaligned optical system,” Opt. Commun. 265(2), 607–615 (2006).
[Crossref]

Zhang, X.

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Zhang, X. B.

Zhang, Y.

Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
[Crossref]

Zhang, Y. J.

Zhao, D.

Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
[Crossref]

Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
[Crossref] [PubMed]

Zhao, W.

Zhao, X.

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

Appl. Phys. B (1)

C. Wei, X. Lu, G. Wu, F. Wang, and Y. Cai, “A new method for generating a hollow Gaussian beam,” Appl. Phys. B 115(1), 55–60 (2014).
[Crossref]

Appl. Phys. Lett. (2)

M. Albrecht, C. T. Rettner, A. Moser, M. E. Bestm, and B. D. Terris, “Recording performance of high-density patterned perpendicular magnetic media,” Appl. Phys. Lett. 81(15), 2875–2877 (2002).
[Crossref]

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

J. Opt. (2)

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, “Generation of sub-wavelength longitudinal magnetic probe using high numerical aperture lens axicon and binary phase plate,” J. Opt. 14(5), 055704 (2012).
[Crossref]

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

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

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

Laser and Photon. Rev. (1)

A. V. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials,” Laser and Photon. Rev. 1(3), 275–287 (2007).
[Crossref]

Nat. Nanotechnol. (1)

M. S. Grinolds, M. Warner, K. De Greve, Y. Dovzhenko, L. Thiel, R. L. Walsworth, S. Hong, P. Maletinsky, and A. Yacoby, “Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins,” Nat. Nanotechnol. 9(4), 279–284 (2014).
[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]

Opt. Commun. (4)

Y. Cai and L. Zhang, “Propagation of a hollow Gaussian beam through a paraxial misaligned optical system,” Opt. Commun. 265(2), 607–615 (2006).
[Crossref]

Z. Nie, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of super-resolution longitudinally polarized beam with ultra-long depth of focus using radially polarized hollow Gaussian beam,” Opt. Commun. 331, 87–93 (2014).
[Crossref]

L. E. Helseth, “Strongly focused electromagnetic waves in E×E* media,” Opt. Commun. 281(23), 5671–5673 (2008).
[Crossref]

L. E. Helseth, “Focusing of evanescent vector waves,” Opt. Commun. 283(1), 29–33 (2010).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

Y. Nie, X. Li, J. Qi, H. Ma, J. Liao, J. Yang, and W. Hu, “Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator,” Opt. Laser Technol. 44(2), 384–389 (2012).
[Crossref]

Opt. Lasers Eng. (1)

Z. Nie, Z. Li, G. Shi, X. Zhang, Y. Wang, and Y. Song, “Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam,” Opt. Lasers Eng. 59, 93–97 (2014).
[Crossref]

Opt. Lett. (10)

G. H. Yuan, S. B. Wei, and X. C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
[Crossref] [PubMed]

K. Huang, P. Shi, X. L. Kang, X. B. 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).
[Crossref] [PubMed]

Z. Chen and D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37(8), 1286–1288 (2012).
[Crossref] [PubMed]

G. Y. Chen, F. Song, and H. T. 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]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28(13), 1084–1086 (2003).
[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]

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]

L. E. Helseth, “Light-induced magnetic vortices,” Opt. Lett. 36(6), 987–989 (2011).
[Crossref] [PubMed]

N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4π focusing of radially polarized light,” Opt. Lett. 29(17), 1968–1970 (2004).
[Crossref] [PubMed]

W. Chen and Q. Zhan, “Creating a spherical focal spot with spatially modulated radial polarization in 4Pi microscopy,” Opt. Lett. 34(16), 2444–2446 (2009).
[Crossref] [PubMed]

Optik (Stuttg.) (1)

Y. Zhang, Y. Okuno, and X. Xu, “Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights,” Optik (Stuttg.) 121(22), 2062–2066 (2010).
[Crossref]

Phys. Lett. A (1)

Z. Chen, J. Pu, and D. Zhao, “Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams,” Phys. Lett. A 377(34-36), 2231–2234 (2013).
[Crossref]

Phys. Rev. A (1)

S. N. Atutov, R. Calabrese, V. Guidi, B. Mai, A. G. Rudavets, E. Scansani, L. Tomassetti, V. Biancalana, A. Burchianti, C. Marinelli, E. Mariotti, L. Moi, and S. Veronesi, “Fast and efficient loading of a Rb magneto-optical trap using light-induced atomic desorption,” Phys. Rev. A 67(5), 053401 (2003).
[Crossref]

Phys. Rev. Lett. (3)

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

A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, “Role of magnetic circular dichroism in all-optical magnetic recording,” Phys. Rev. Lett. 108(12), 127205 (2012).
[Crossref] [PubMed]

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15(5), 190–193 (1965).
[Crossref]

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]

Rev. Sci. Instrum. (1)

P. D. Majors, K. R. Minard, E. J. Ackerman, G. R. Holtom, D. F. Hopkins, C. I. Parkinson, T. J. Weber, and R. A. Wind, “A combined confocal and magnetic resonance microscope for biological studies,” Rev. Sci. Instrum. 73(12), 4329–4338 (2002).
[Crossref]

Sov. Phys. JETP-USSR (1)

L. P. Pitaevskii, “Electric forces in a transparent dispersive medium,” Sov. Phys. JETP-USSR 12, 1008–1013 (1961).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the 4π focusing configuration. A MO film locates at the confocal plane of the system, which is illuminated by two counter-propagating radially polarized HG vortex beams.

Fig. 2
Fig. 2

Normalized magnetization distributions in the focal region of a single high NA aplanatic objective illuminated with radially polarized HG vortex beams with different orders. The parameters are: n=0 for (a1)-(a4), n=1 for (b1)-(b4), n=4 for (c1)-(c4); β=0.5 and NA=0.95 . (a1)-(c1), (a2)-(c2) and (a3)-(c3) are the contour plots of total magnetization (M), longitudinal component ( M z ) and azimuthal component ( M φ ) on the r-z plane.

Fig. 3
Fig. 3

Normalized magnetization distributions on the focal plane of a single high NA aplanatic objective illuminated with radially polarized HG vortex beams for (a) n=0 , (b) n=1 , and (c) n=4 ; other parameters are: β=0.5 and NA=0.95 . The blue, red and black curves represent the longitudinal, azimuthal and total magnetization distributions, respectively.

Fig. 4
Fig. 4

Normalized magnetization distributions in the focal region of a 4π high NA aplanatic objective illuminated with radially polarized HG vortex beams with different orders. The parameters are: n=0 for (a1)-(a4), n=1 for (b1)-(b4), n=4 for (c1)-(c4); β=0.5 and NA=0.95 . (a1)-(c1), (a2)-(c2) and (a3)-(c3) are the contour plots of total magnetization (M), longitudinal component ( M z ) and azimuthal component ( M φ ) on the r-z plane.

Fig. 5
Fig. 5

Normalized magnetization distributions on the focal plane of a 4π high NA aplanatic objective illuminated with radially polarized HG vortex beams for (a) n=0 , (b) n=1 , and (c) n=4 ; other parameters are: β=0.5 and NA=0.95 . The blue, red and black curves represent the longitudinal, azimuthal and total magnetization distributions along r axis and magenta curve represents total magnetization distribution along z axis.

Fig. 6
Fig. 6

Polarization characteristic of the magnetization field (a) under single lens tight focusing and (b) under 4π tight focusing in the r-z cross section. The parameters are n=4 , β=0.5 .

Fig. 7
Fig. 7

Dependence of the FWHM (a) in the transverse direction and (b) in the axial direction on the traction parameter β with different beam orders.

Fig. 8
Fig. 8

(a) Distribution of calculated magnetization in r-z plane and (b) calculated magnetization profiles along r axis (black curve) and along z axis (red dashed curve) when n=4 and β=1.75 .

Equations (8)

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E( r,φ,z )=[ E r ( r,φ,z ) E ϕ ( r,φ,z ) E z ( r,φ,z ) ]= A 0 exp(jφ)[ j R 1 ( r,φ,z ) R 2 ( r,φ,z ) 2 R 3 ( r,φ,z ) ],
R 1 (r,φ,z)= 0 θmax cosθ sinθcosθl(θ) ×[ J 2 (krsinθ) J 0 (krsinθ)]exp(jkzcosθ)dθ,
R 2 (r,φ,z)= 0 θmax cosθ sinθcosθl(θ) ×[ J 2 (krsinθ)+ J 0 (krsinθ)]exp(jkzcosθ)dθ,
R 3 (r,φ,z)= 0 θmax cosθ sin 2 θl(θ) × J 1 (krsinθ)exp(jkzcosθ)dθ,
l(θ)= ( β 2 sin 2 θ N A 2 ) 2 exp ( β 2 sin 2 θ N A 2 ) 2 ,
E(r,φ,z)= E 1 (r,φ,z)+ E 2 (r,φ,z),
M( r,φ,z )=jγE× E * ,
M(r,φ,z)=[ M r M φ M z ]=[ 2Im[ ( R 2 (r,φ,z)+ R 2 (r,φ,z) )* ( R 3 (r,φ,z)+ R 3 (r,φ,z) ) * ] 2Re[ ( R 1 (r,φ,z)+ R 1 (r,φ,z) )* ( R 3 (r,φ,z)+ R 3 (r,φ,z) ) * ] Re[ ( R 1 (r,φ,z)+ R 1 (r,φ,z) )* ( R 3 (r,φ,z)+ R 2 (r,φ,z) ) * ] ].

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