Abstract

We show experimentally that the angular Goos–Hänchen (GH) effect can be easily observed, also without employing its resonant enhancement at Brewster incidence. An s-polarized beam was used to decouple the polarization from the propagation dynamics of the beam. We found that, in this case, the angular GH effect can be strongly enhanced by increasing the angular aperture of the Gaussian beam. Our experiments suggest a route toward observing the angular GH effect for true scalar waves, such as acoustic waves and quantum matter waves.

© 2010 Optical Society of America

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  1. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  2. F. Bretenaker, A. L. Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  3. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
    [CrossRef]
  4. 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] [PubMed]
  5. D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
    [CrossRef]
  6. J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
    [CrossRef]
  7. Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962(1974).
  8. C. C. Chan and T. Tamir, Opt. Lett. 10, 378 (1985).
    [CrossRef] [PubMed]
  9. M. A. Porras, Opt. Commun. 131, 13 (1996).
    [CrossRef]
  10. W. Nasalski, J. Opt. Soc. Am. A 13, 172 (1996).
    [CrossRef]
  11. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef] [PubMed]
  12. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef] [PubMed]
  13. V. G. Fedoseyev, Opt. Commun. 282, 1247 (2009).
    [CrossRef]
  14. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef] [PubMed]
  15. Acoustic waves are not scalar waves in general. For example, acoustic waves in solid-state physics can be nonscalar.
  16. A. Schoch, Acustica 2, 18 (1952).
  17. H. L. Bertoni and T. Tamir, Appl. Phys. 2, 157 (1973).
    [CrossRef]
  18. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, A. L. Floch, and L. Dutriaux, Opt. Lett. 26, 666 (2001).
    [CrossRef]
  19. A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
    [CrossRef]
  20. S. C. Miller, Jr., and N. Ashby, Phys. Rev. Lett. 29, 740(1972).
    [CrossRef]
  21. J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
    [CrossRef]
  22. V. O. de Haan, J. Plomp, T. M. Rekveldt, W. H. Kraan, and A. A. van Well, Phys. Rev. Lett. 104, 010401 (2010).
    [CrossRef] [PubMed]
  23. M. Maaza and B. Pardo, Opt. Commun. 142, 84(1997).
    [CrossRef]
  24. The difference between a neutron and a photon from a spin (polarization) point of view is as follows. A neutron is a massive particle whose spin ½ is not coupled to the propagation direction of the neutron beam; contrarily, a photon is a zero-mass particle whose paraxial spin ½ is either parallel or antiparallel with the propagation direction of the photon beam.
  25. Y. Fainman and J. Shamir, Appl. Opt. 23, 3188 (1984).
    [CrossRef] [PubMed]
  26. A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
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2010 (1)

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

2009 (3)

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef] [PubMed]

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

V. G. Fedoseyev, Opt. Commun. 282, 1247 (2009).
[CrossRef]

2008 (3)

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

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

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

2007 (1)

2006 (2)

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

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

2005 (1)

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

2001 (1)

1997 (1)

M. Maaza and B. Pardo, Opt. Commun. 142, 84(1997).
[CrossRef]

1996 (2)

1992 (1)

F. Bretenaker, A. L. Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

1974 (1)

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962(1974).

1973 (2)

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

H. L. Bertoni and T. Tamir, Appl. Phys. 2, 157 (1973).
[CrossRef]

1972 (1)

S. C. Miller, Jr., and N. Ashby, Phys. Rev. Lett. 29, 740(1972).
[CrossRef]

1952 (1)

A. Schoch, Acustica 2, 18 (1952).

1947 (1)

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

Aiello, A.

Antar, Y. M.

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962(1974).

Ashby, N.

S. C. Miller, Jr., and N. Ashby, Phys. Rev. Lett. 29, 740(1972).
[CrossRef]

Bertoni, H. L.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

H. L. Bertoni and T. Tamir, Appl. Phys. 2, 157 (1973).
[CrossRef]

Bliokh, K. Y.

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

Bliokh, Y. P.

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

Boerner, W. M.

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962(1974).

Bonnet, C.

Breazeale, M. A.

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

Bretenaker, F.

Chan, C. C.

Chauvat, D.

de Haan, V. O.

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

Declercq, N. F.

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

Duan, Z.

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Dutriaux, L.

Eliel, E. R.

Emile, O.

Fainman, Y.

Fedoseyev, V. G.

V. G. Fedoseyev, Opt. Commun. 282, 1247 (2009).
[CrossRef]

Felsen, L. B.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Floch, A. L.

Goos, F.

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

Hänchen, H.

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

Hasse, R. D.

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

Hosten, O.

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

Huang, J.

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Kraan, W. H.

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

Kwiat, P.

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

Ling, H. Y.

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Maaza, M.

M. Maaza and B. Pardo, Opt. Commun. 142, 84(1997).
[CrossRef]

McPherson, M. S.

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

Merano, M.

Miller, S. C.

S. C. Miller, Jr., and N. Ashby, Phys. Rev. Lett. 29, 740(1972).
[CrossRef]

Müller, D.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

Nasalski, W.

Nimtz, G.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

Pardo, B.

M. Maaza and B. Pardo, Opt. Commun. 142, 84(1997).
[CrossRef]

Plomp, J.

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

Porras, M. A.

M. A. Porras, Opt. Commun. 131, 13 (1996).
[CrossRef]

Ra, J. W.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Rekveldt, T. M.

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

Schoch, A.

A. Schoch, Acustica 2, 18 (1952).

Shamir, J.

Stahlhofen, A. A.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

't Hooft, G. W.

Tamir, T.

C. C. Chan and T. Tamir, Opt. Lett. 10, 378 (1985).
[CrossRef] [PubMed]

H. L. Bertoni and T. Tamir, Appl. Phys. 2, 157 (1973).
[CrossRef]

Teklu, A.

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

Tharanga, D.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

van Exter, M. P.

van Well, A. A.

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

Woerdman, J. P.

Zhang, W.

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Acustica (1)

A. Schoch, Acustica 2, 18 (1952).

Ann. Phys. (1)

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

Appl. Opt. (1)

Appl. Phys. (1)

H. L. Bertoni and T. Tamir, Appl. Phys. 2, 157 (1973).
[CrossRef]

Can. J. Phys. (1)

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962(1974).

Europhys. Lett. (1)

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, Europhys. Lett. 73, 526 (2006).
[CrossRef]

J. Appl. Phys. (1)

A. Teklu, M. A. Breazeale, N. F. Declercq, R. D. Hasse, and M. S. McPherson, J. Appl. Phys. 97, 084904 (2005).
[CrossRef]

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

Nat. Photon. (1)

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

Opt. Commun. (3)

V. G. Fedoseyev, Opt. Commun. 282, 1247 (2009).
[CrossRef]

M. A. Porras, Opt. Commun. 131, 13 (1996).
[CrossRef]

M. Maaza and B. Pardo, Opt. Commun. 142, 84(1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

J. Huang, Z. Duan, H. Y. Ling, and W. Zhang, Phys. Rev. A 77, 063608 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

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

S. C. Miller, Jr., and N. Ashby, Phys. Rev. Lett. 29, 740(1972).
[CrossRef]

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

F. Bretenaker, A. L. Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Science (1)

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

SIAM J. Appl. Math. (1)

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Other (2)

Acoustic waves are not scalar waves in general. For example, acoustic waves in solid-state physics can be nonscalar.

The difference between a neutron and a photon from a spin (polarization) point of view is as follows. A neutron is a massive particle whose spin ½ is not coupled to the propagation direction of the neutron beam; contrarily, a photon is a zero-mass particle whose paraxial spin ½ is either parallel or antiparallel with the propagation direction of the photon beam.

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Figures (4)

Fig. 1
Fig. 1

A TEM 00 Gaussian beam hits an air–glass interface. The reflected beam suffers the angular Goos–Hänchen effect. The angular deviation of the axis of the reflected beam relative to the specular direction is labeled as Θ AGH .

Fig. 2
Fig. 2

Setup to measure nonspecular reflection over a wide range of incident angles and with different beam angular apertures θ 0 . Reflection takes place at the surface of a right-angle BK7 glass prism. We measure the angular shift for a light beam focused by a cylindrical lens. See the text for details of the experimental procedure.

Fig. 3
Fig. 3

The theoretical curve gives the angular shift versus the angle of incidence for an s-polarized light beam with a wavelength of 820 nm , focused to a spot size of 12 μm . Dots are experimental data.

Fig. 4
Fig. 4

The angular GH shift increases with the square of the beam’s angular aperture. The solid curve corresponds to the theoretical prediction from Eq. (1). The angular aperture was changed by using cylindrical lenses of different focal lengths.

Equations (1)

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Θ AGH ( θ ) = θ 0 2 sin θ n 2 sin 2 θ .

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