Abstract

We put forward a double-slit interference device based on two metal subwavelength slit arrays to measure the orbital angular momentum (OAM) and the polarization of beams simultaneously. The subwavelength slit serves as a localized spatial polarizer, and each slit array can be regarded as a wide diffraction-slit. When an OAM beam is normally incident upon the two slit arrays, the interference fringes twist, and the displacement depends on the topological charge of OAM beams. We present a detailed theoretical analysis of this measurement model. This model does not need additional reference light and is a linear model.

© 2014 Optical Society of America

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  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
    [CrossRef]
  3. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
    [CrossRef]
  4. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef]
  5. J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef]
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef]
  8. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
    [CrossRef]
  9. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
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  22. Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).
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    [CrossRef]
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    [CrossRef]

2014 (2)

2013 (3)

2012 (4)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

A. Belmonte and J. P. Torres, Opt. Lett. 37, 2940 (2012).
[CrossRef]

2011 (3)

2010 (2)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

2009 (2)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

G. Berkhout and M. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2006 (2)

Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef]

H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
[CrossRef]

2005 (1)

2003 (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

1996 (1)

J. W. Goodman and S. C. Gustafson, Opt. Eng. 35, 1513 (1996).
[CrossRef]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Ahmed, N.

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Alencar, M. A. R. C.

Alfano, R. R.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
[CrossRef]

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M.

G. Berkhout and M. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Belmonte, A.

Berkhout, G.

G. Berkhout and M. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Bernet, S.

Birnbaum, K.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Bozovich, A.

Chávez-Cerda, S.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Chen, J.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Curtis, J. E.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Dolinar, S.

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Dong, J.

Erkmen, B. I.

Evans, S.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Ferreira, Q. S.

Fonseca, E.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Fonseca, E. J. S.

Fürhapter, S.

Ghai, D. P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman and S. C. Gustafson, Opt. Eng. 35, 1513 (1996).
[CrossRef]

Grier, D. G.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Gu, B.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Gustafson, S. C.

J. W. Goodman and S. C. Gustafson, Opt. Eng. 35, 1513 (1996).
[CrossRef]

Hickmann, J.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Hickmann, J. M.

Huang, D.

Huang, H.

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Jesacher, A.

Jesus-Silva, A. J.

Kang, M.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Li, S.

Li, Y.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Mesquita, P. H. F.

Milione, G.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nolan, D. A.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, M. J. Padgett, and M. W. Beijersbergen, Opt. Lett. 36, 1863 (2011).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Qiu, M.

Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Ritsch-Marte, M.

Ruan, Z.

Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef]

Senthilkumaran, P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Shi, L.

Silva, J. G.

Sirohi, R. S.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Soares, W.

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Sztul, H. I.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J. P.

A. Belmonte and J. P. Torres, Opt. Lett. 37, 2940 (2012).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Vuong, L. T.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Wang, H.-T.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

Wang, J.

Z. Zhao, J. Wang, S. Li, and A. E. Willner, Opt. Lett. 38, 932 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Willner, A. E.

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yan, Y.

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Zhang, X.

Zhao, Z.

Zhou, H.

J. Opt. A (1)

G. Berkhout and M. Beijersbergen, J. Opt. A 11, 094021 (2009).
[CrossRef]

Nat. Photonics (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Eng. (1)

J. W. Goodman and S. C. Gustafson, Opt. Eng. 35, 1513 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, Opt. Lasers Eng. 47, 123 (2009).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. A (2)

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, Phys. Rev. A 85, 035801 (2012).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (5)

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Hickmann, E. Fonseca, W. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic structure of the double-slit interference device. Inset, structure of the slit array. (b) Normalized transmission and (c) polarization extinction ratio dependence on wavelength.

Fig. 2.
Fig. 2.

(a) RSD of amplitude and (b) SD of phase dependence on wavelength. (c) Output amplitude and phase of the single ordinary air slit at 2180.2 nm. (d) Output amplitude and phase of the subwavelength slit array at 2180.2 nm. Insets: zoom in phase distributions.

Fig. 3.
Fig. 3.

(a) Phase on two diffraction slits when TC equals 1. (b) Phase difference between the two diffraction slits along the y direction.

Fig. 4.
Fig. 4.

Interference patterns from different OAM beams incident on two slits, calculated from Fresnel diffraction.

Fig. 5.
Fig. 5.

Revision for the half amount of twist at different measuring lines. D: absolute error.

Fig. 6.
Fig. 6.

Interference patterns for TC = 20 , calculated from Fresnel diffraction.

Equations (6)

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

E x ( r , θ ) = A ( r ) exp ( i l θ ) exp ( i m r 2 ) ,
δ ϕ ( y ) = ϕ 2 ( y ) ϕ 1 ( y ) = l π 2 l arctan 2 y a ,
I ( x , y ) cos 2 ( π a x λ d + δ ϕ ( y ) 2 ) .
Δ x = λ d / a .
x = λ d l a π arctan 2 y a .
x ( 0 ) = a 2 π / ( 2 λ l d ) .

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