Abstract

In this Letter, based on the Richards and Wolf diffraction theory, an ultralong optical needle with pure transverse polarization is numerically generated by tightly focusing an azimuthally polarized beam through an annular vortex binary filter. Such an ultralong transversely polarized optical needle is generated through the π phase shift between adjacent rings of the binary filter. We show that such a pure transverse optical needle can induce pure longitudinal magnetization with a subwavelength lateral size (0.38λ) and an ultralong longitudinal depth (7.48λ) through the inverse Faraday effect. The corresponding needle aspect ratio of 20 is twice as large as that of the longitudinal magnetization needle generated by electron beam lithography.

© 2014 Optical Society of America

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2013

2012

2011

2010

2009

2008

G. M. Lerman and U. Levy, Opt. Express 16, 4567 (2008).
[CrossRef]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

2007

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, and Th. Rasing, Laser Photon. Rev. 1, 275 (2007).
[CrossRef]

2005

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

2003

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, Opt. Express 11, 2747 (2003).
[CrossRef]

2001

S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001).
[CrossRef]

1999

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

1996

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

1995

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

1994

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

1966

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

1965

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, Phys. Rev. Lett. 15, 190 (1965).
[CrossRef]

1963

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

1961

L. P. Pitaevskii, Sov. Phys. JETP-USSR 12, 1008 (1961).

1959

B. Richards and E. Wolf, Proc. Roy. Soc. London Ser. A 253, 358 (1959).

Andrews, M. R.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

April, A.

Balbashov, A. M.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

Barton, P. A.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

Boshier, M. G.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

Chen, W.

Chiba, D.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Chou, S. Y.

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

Dadoenkova, N. N.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Dehez, H.

Durfee, D. S.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

Eberl, K.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Fischer, P. B.

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

Gan, X.

Ganic, D.

Gerhardts, R. R.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Gu, M.

Y. Jiang, X. Li, and M. Gu, Opt. Lett. 38, 2957 (2013).
[CrossRef]

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, Opt. Express 11, 2747 (2003).
[CrossRef]

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Hao, X.

Hinds, E. A.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

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, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Jiang, Y.

Kang, X.

Ketterle, W.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

Kimel, A. V.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, and Th. Rasing, Laser Photon. Rev. 1, 275 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

Kirilyuk, A.

A. V. Kimel, A. Kirilyuk, and Th. Rasing, Laser Photon. Rev. 1, 275 (2007).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

Kitamura, K.

Krauss, P. R.

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

Kuang, C.

Kurn, D. M.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

Lan, T. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Lerman, G. M.

Levy, U.

Li, X.

Y. Jiang, X. Li, and M. Gu, Opt. Lett. 38, 2957 (2013).
[CrossRef]

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Li, Y.

Lin, J.

Liu, X.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Lyubchanskii, I. L.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Lyubchanskii, M. I.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Malmstrom, L. D.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, Phys. Rev. Lett. 15, 190 (1965).
[CrossRef]

Matsukura, F.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Mewes, M.-O.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

Nakatani, Y.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Nickel, H.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Nikitov, S. A.

S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001).
[CrossRef]

Nishimoto, M.

Nishitani, Y.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Noda, S.

Ohno, H.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Okuno, Y.

Pershan, P. S.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, Phys. Rev. Lett. 15, 190 (1965).
[CrossRef]

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

Piche, M.

Pisarev, R. V.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

Pitaevskii, L. P.

L. P. Pitaevskii, Sov. Phys. JETP-USSR 12, 1008 (1961).

Rasing, Th.

A. V. Kimel, A. Kirilyuk, and Th. Rasing, Laser Photon. Rev. 1, 275 (2007).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. Roy. Soc. London Ser. A 253, 358 (1959).

Rosenbusch, P.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (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, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

Sakai, K.

Sauer, B. E.

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

Sawicki, M.

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Seeger, M.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Shapovalov, E. A.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, P.

Stanciu, C. D.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Tailhades, Ph.

S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001).
[CrossRef]

Takayama, N.

Tan, J.

Tien, C. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Tsai, C. S.

S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001).
[CrossRef]

Tsukamoto, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Usachev, P. A.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

van der Ziel, J. P.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, Phys. Rev. Lett. 15, 190 (1965).
[CrossRef]

van Druten, N. J.

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

von Klitzing, K.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Wang, J.

Wang, T.

Wei, M. S.

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

Weiss, D.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. Roy. Soc. London Ser. A 253, 358 (1959).

Xu, X.

Ye, P. D.

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

Yin, K.

Zhan, Q.

Zhang, X.

Zhang, Y. J.

J. Appl. Phys.

S. Y. Chou, M. S. Wei, P. R. Krauss, and P. B. Fischer, J. Appl. Phys. 76, 6673 (1994).
[CrossRef]

J. Magn. Magn. Mater.

S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, J. Magn. Magn. Mater. 236, 320 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, J. Phys. D 36, R277 (2003).
[CrossRef]

Laser Photon. Rev.

A. V. Kimel, A. Kirilyuk, and Th. Rasing, Laser Photon. Rev. 1, 275 (2007).
[CrossRef]

Nat. Commun.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Nat. Photonics

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Nature

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and Th. Rasing, Nature 435, 655 (2005).
[CrossRef]

D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, and H. Ohno, Nature 455, 515 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

Phys. Rev. Lett.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, Phys. Rev. Lett. 15, 190 (1965).
[CrossRef]

P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[CrossRef]

M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett. 77, 416 (1996).
[CrossRef]

C. V. Saba, P. A. Barton, M. G. Boshier, I. G. Hughes, P. Rosenbusch, B. E. Sauer, and E. A. Hinds, Phys. Rev. Lett. 82, 468 (1999).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Proc. Roy. Soc. London Ser. A

B. Richards and E. Wolf, Proc. Roy. Soc. London Ser. A 253, 358 (1959).

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Other

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic illustration of the setup to generate the pure longitudinal magnetization needle. By using filter 1 at the back aperture of the objective, magnetization with the same orientation as the propagating direction of the beam (red “bars”) can be induced. Magnetization with the opposite orientation (blue “bars”) can be induced by using filter 2.

Fig. 2.
Fig. 2.

Electric field distribution in the focal plane (m=1). (a) Phase distributions of Er and Eφ, (b) cross sections of the normalized amplitudes of Er and Eφ, and (c) electric energy density and polarization distributions. λ is the wavelength of the incident beam in vacuum.

Fig. 3.
Fig. 3.

(a) Normalized electric energy density distribution and (b) magnetization distribution, in the axial plane.

Fig. 4.
Fig. 4.

Magnetization distributions with different modulations on the incident beam. (a) Different vortex filters, (b) cross sections (along the x axis) of the normalized magnetization distributions in the focal plane, and (c) cross sections (along the z axis) of the normalized magnetization distributions. The lines with different colors and styles under the filters in (a) represent the corresponding lateral and longitudinal cross sections of the induced magnetization in (b) and (c).

Equations (10)

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Einc=E0Tϕeϕ=i2E0Tϕ(eiϕeLeiϕeR),
Tϕ={ei(mϕ+π)RarRpeimϕRp<rR0.
E(r,φ,z)=[ErEφEz]=Aimθaθ0Tφ[V1iV20]eikzcosθcosθsinθdθ,
V1=Jm1(krsinθ)+Jm+1(krsinθ),
V2=Jm1(krsinθ)Jm+1(krsinθ),
Tφ={ei(mφ+π)θaθθpeimφθp<θθ0.
M=iγE×E*,
M=2γ|A|2Re(I1·I2)ez,
I1=θaθ0TφV1eikzcosθcosθsinθdθ,
I2=θaθ0Tφ*V2eikzcosθcosθsinθdθ.

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