Abstract

It is well known from quantum mechanics that weak measurements offer a means of amplifying and detecting very small phenomena. We present here the experimental observation of the Goos–Hänchen shift via a weak measurement approach.

© 2013 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  2. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]
  3. F. I. Fedorov, Dokl. Akad. 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. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef]
  6. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef]
  7. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  8. H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).
    [CrossRef]
  9. D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
    [CrossRef]
  10. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
    [CrossRef]
  11. M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
    [CrossRef]
  12. W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
    [CrossRef]
  13. 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]
  14. M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
    [CrossRef]
  15. I. Duck, P. Stevenson, and E. Sudarshan, Phys. Rev. D 40, 2112 (1989).
    [CrossRef]
  16. Y. Aharonov, D. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
    [CrossRef]
  17. Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
    [CrossRef]
  18. J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
    [CrossRef]
  19. N. Ritchie, J. Story, and R. Hulet, Phys. Rev. Lett. 66, 1107 (1991).
    [CrossRef]
  20. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef]
  21. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 1st ed. (Academic, 1990).
  22. Y. Qin, Y. Li, X. Feng, Y.-F. Xiao, H. Yang, and Q. Gong, Opt. Express 19, 9636 (2011).
    [CrossRef]
  23. 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]
  24. M. R. Dennis and J. B. Goette, New J. Phys. 14, 073013 (2012).
    [CrossRef]
  25. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
    [CrossRef]
  26. X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108(2006).
    [CrossRef]

2012 (5)

M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
[CrossRef]

W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[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. R. Dennis and J. B. Goette, New J. Phys. 14, 073013 (2012).
[CrossRef]

2011 (1)

2010 (2)

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]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[CrossRef]

2009 (2)

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

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

2008 (2)

2007 (2)

2006 (3)

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

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

H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).
[CrossRef]

2004 (2)

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

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]

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. SSSR 105, 465 (1955).

1947 (1)

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

’t Hooft, G. W.

Aharonov, Y.

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

Aiello, A.

W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[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]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[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]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[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.

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

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

Eliel, E. R.

Fedorov, F. I.

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

Felbacq, D.

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

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]

Goette, J. B.

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

Gong, Q.

Goos, F.

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

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, New J. Phys. 14, 073016 (2012).
[CrossRef]

Hänchen, H.

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

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.

Hentschel, M.

H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).
[CrossRef]

Hermosa, N.

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[CrossRef]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[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]

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]

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]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 1st ed. (Academic, 1990).

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]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 1st ed. (Academic, 1990).

Li, Y.

Loffler, W.

W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

Merano, M.

M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
[CrossRef]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[CrossRef]

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

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[CrossRef]

Mistura, G.

M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
[CrossRef]

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]

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]

Qin, Y.

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 1st ed. (Academic, 1990).

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]

Schomerus, H.

H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).
[CrossRef]

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]

Smaâli, R.

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[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]

Sudarshan, E.

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

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

Umbriaco, G.

M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
[CrossRef]

Vaidman, L.

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

van Exter, M. P.

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.

W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (2012).
[CrossRef]

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[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]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[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).
[CrossRef]

Appl. Phys. Lett. (1)

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

Dokl. Akad. Nauk. SSSR (1)

F. I. Fedorov, Dokl. Akad. 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]

Nature (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef]

New J. Phys. (2)

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

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

Opt. Express (2)

Opt. Lett (1)

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett 35, 3562 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

M. Merano, G. Umbriaco, and G. Mistura, Phys. Rev. A 86, 033842 (2012).
[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)

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

H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).
[CrossRef]

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

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

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

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

W. Loffler, A. Aiello, and J. P. Woerdman, Phys. Rev. Lett. 109, 213901 (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]

Science (1)

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

Other (1)

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 1st ed. (Academic, 1990).

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Figures (3)

Fig. 1.
Fig. 1.

Setup for the weak measurement of the GH shift. The polarizer P1 is followed by an analyzer composed of quarter-wave plate (QWP), half-wave plate (HWP), and polarizer (P2). L1 and L2 are the lenses of the beam expander.

Fig. 2.
Fig. 2.

Left: beam profile for (ϵ=102rad). Right: beam profile for perfect crossing (ϵ=0rad).

Fig. 3.
Fig. 3.

Experimental data (squares) are compared with the theoretical predictions for the GH shift in TIR.

Equations (7)

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

|cos(α)exp[(x)2w2]sin(α)exp[(x)2w2]|,
|cos(α)eiδ2exp[(xDp)2w2]sin(α)eiδ2exp[(xDs)2w2]|,
|eiδ200eiδ2|.
|cos(α)exp[(xDp)2w2]sin(α)exp[(xDs)2w2]|,
f(x)=cos(β)cos(α)exp[(xDp)2w2]+sin(β)sin(α)exp[(xDs)2w2].
f(x)=cos(α+β)ϕ(xa;ϵ,w0,ΔGH),
ϕ(x)=12[(1+ϵ)exp[(x12ΔGH)2w2](1ϵ)exp[(x+12ΔGH)2w2]].

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