Abstract

Weak measurements have recently allowed for the observation of the spin-Hall effect of light in reflection or transmission, which is a spin-dependent light beam shift orthogonal to the plane of incidence. We report here the observation of the Imbert–Fedorov (IF) shift via a weak value amplification scheme. The IF effect does not depend on the spin of the incident photon only, but it has richer polarization dependence. We prove that weak measurements allow for a complete experimental characterization of the polarization properties of this tiny optical effect.

© 2014 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
  2. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]
  3. F. I. Fedorov, Dokl. Akad. Nauk. Nauk SSSR 105, 465 (1955).
  4. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
    [CrossRef]
  5. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef]
  6. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef]
  7. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  8. Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
    [CrossRef]
  9. Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
    [CrossRef]
  10. Y. Qin, Y. Li, X. Feng, Y.-F. Xiao, H. Yang, and Q. Gong, Opt. Express 19, 9636 (2011).
    [CrossRef]
  11. G. Jayaswal, G. Mistura, and M. Merano, Opt. Lett. 38, 1232 (2013).
    [CrossRef]
  12. J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
    [CrossRef]
  13. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef]
  14. M. R. Dennis and J. B. Götte, New J. Phys. 14, 073013 (2012).
    [CrossRef]
  15. F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
    [CrossRef]
  16. J. B. Götte and M. R. Dennis, Opt. Lett. 38, 2295 (2013).
    [CrossRef]
  17. Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
    [CrossRef]
  18. Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
    [CrossRef]
  19. I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
    [CrossRef]
  20. N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
    [CrossRef]
  21. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
    [CrossRef]
  22. G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
    [CrossRef]
  23. O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).
  24. G. Strübi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
    [CrossRef]
  25. X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
    [CrossRef]
  26. V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
    [CrossRef]

2013 (4)

G. Strübi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
[CrossRef]

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

G. Jayaswal, G. Mistura, and M. Merano, Opt. Lett. 38, 1232 (2013).
[CrossRef]

J. B. Götte and M. R. Dennis, Opt. Lett. 38, 2295 (2013).
[CrossRef]

2012 (4)

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

M. R. Dennis and J. B. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
[CrossRef]

2011 (1)

2010 (1)

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

2009 (3)

Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

2008 (2)

2006 (2)

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

2004 (1)

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

1991 (1)

N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef]

1990 (1)

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef]

1989 (1)

I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

1988 (1)

Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

1972 (1)

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

1955 (1)

F. I. Fedorov, Dokl. Akad. Nauk. Nauk SSSR 105, 465 (1955).

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).

Aharonov, Y.

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef]

Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Aiello, A.

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Albert, D.

Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Bliokh, K. Y.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Boyd, R. W.

O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).

Bruder, C.

G. Strübi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
[CrossRef]

Dalgliesh, R. M.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

de Haan, V.-O.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Dennis, M. R.

J. B. Götte and M. R. Dennis, Opt. Lett. 38, 2295 (2013).
[CrossRef]

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

M. R. Dennis and J. B. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

Dixon, P. B.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

Duck, I.

I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Ebbesen, T. W.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Fedorov, F. I.

F. I. Fedorov, Dokl. Akad. Nauk. Nauk SSSR 105, 465 (1955).

Feng, X.

Genet, C.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Gong, Q.

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).

Gorodetski, Y.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Götte, J. B.

J. B. Götte and M. R. Dennis, Opt. Lett. 38, 2295 (2013).
[CrossRef]

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

M. R. Dennis and J. B. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).

Hasman, E.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

He, H.

Hermosa, N.

G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
[CrossRef]

Hesselink, L.

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Howell, J. C.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

Hulet, R.

N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef]

Imbert, C.

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Jayaswal, G.

Jordan, A. N.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

Kleiner, V.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Kraan, W. H.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Langridge, S.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Li, Y.

Magaña-Loaiza, O. S.

O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).

Merano, M.

G. Jayaswal, G. Mistura, and M. Merano, Opt. Lett. 38, 1232 (2013).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

Mirhosseini, M.

O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).

Mistura, G.

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Ornigotti, M.

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Plomp, J.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Puentes, G.

G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
[CrossRef]

Qin, Y.

Rekveldt, T. M.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Ritchie, N.

N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef]

Rodenburg, B.

O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).

Shitrit, N.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Starling, D. J.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

Stein, B.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

Stevenson, P.

I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Story, J.

N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef]

Strübi, G.

G. Strübi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
[CrossRef]

Sudarshan, E.

I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Töppel, F.

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Torres, J. P.

G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
[CrossRef]

Vaidman, L.

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef]

Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

van Well, A. A.

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Woerdman, J. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Xiao, Y.-F.

Yang, H.

Yin, X.

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Ann. Phys. (1)

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).

Appl. Phys. Lett. (1)

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Dokl. Akad. Nauk. Nauk SSSR (1)

F. I. Fedorov, Dokl. Akad. Nauk. Nauk SSSR 105, 465 (1955).

Nat. Photonics (1)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

New J. Phys. (3)

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

M. R. Dennis and J. B. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

Y. Aharonov and L. Vaidman, Phys. Rev. A 41, 11 (1990).
[CrossRef]

Phys. Rev. D (2)

I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Phys. Rev. Lett. (9)

N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

G. Puentes, N. Hermosa, and J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012).
[CrossRef]

V.-O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, A. A. van Well, R. M. Dalgliesh, and S. Langridge, Phys. Rev. Lett. 104, 010401 (2010).
[CrossRef]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, Phys. Rev. Lett. 109, 013901 (2012).
[CrossRef]

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

G. Strübi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
[CrossRef]

Science (1)

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Other (1)

O. S. Magaña-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” arXiv:1312.2981 (2013).

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Figures (5)

Fig. 1.
Fig. 1.

Setup for the weak measurement of the Imbert–Fedorov shift. L1 and L2, lenses with focal length 20 and 30 cm, respectively; P1 and P2, Glan–Thompson polarizers; QWP, quarter-wave plate; HWP, half-wave plate; and QD, quadrant detector. P1 preselects the polarization state and the polarization analyzer composed of QWP, HWP, and P2 postselects the final polarization state.

Fig. 2.
Fig. 2.

Beam profile of the light beam transmitted through the polarization analyzer. (a) Beam profile for when the weak measurements settings is still Gaussian. (b) Beam profile for minimum analyzer transmission.

Fig. 3.
Fig. 3.

Spatial IF beam shift for a 45° linearly polarized incident Gaussian beam. Shown is the observed polarization-differential shift (dots), where the solid line represents the theoretical prediction. The y axis on the right represents the amplified data with an amplification factor of 445.

Fig. 4.
Fig. 4.

Spatial IF beam shift for a ± circularly polarized incident Gaussian beam. Shown is the observed polarization-differential shift (dots). The solid line represents the theoretical prediction. The y axis on the right represents the amplified data with an amplification factor of 445.

Fig. 5.
Fig. 5.

Experimental study of the weak value amplification scheme as a function of ϵ. A faithful amplification of the optical beam shift is observed as long as the amplified signal scales linearly with 1/ϵ.

Equations (8)

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

IF=(1+cos(δ))cot(θ)σ2sin(δ)cot(θ)σ1,
σ2=[0ii0]σ1=[0110].
ψ|IF|pψ|p=cot(θ)ϵ(sin(δ)+i(1+cos(δ))),
ϕ|IF|pϕ|p=cot(θ)ϵ(1+cos(δ)isin(δ)),
yψ=λ2πcot(θ)ϵ(sin(δ)+zz0(1+cos(δ)),
yϕ=λ2πcot(θ)ϵ((1+cos(δ)zz0sin(δ)),
Q1=[i001]H=[1±ϵ±ϵ1],
Q2=[i±(i1)ϵ±(i1)ϵ1],

Metrics