Abstract

We report the first observation of the Goos-Hänchen shift of a light beam incident on a bare metal surface. This phenomenon is particularly interesting because the Goos-Hänchen shift for p polarized light in metals is negative and much bigger than the positive shift for s polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a p polarized beam of light.

© 2007 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
    [Crossref]
  2. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
    [Crossref]
  3. K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen effect: A simple example of time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
    [Crossref]
  4. R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56, 1092–1094 (1988).
    [Crossref]
  5. F. Bretenaker, A. L. Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
    [Crossref] [PubMed]
  6. H. Gilles, S. Girard, and J. Hamel, “Simple technique for measuring the Goos-Hänchen effect with polarization modulation and a position-sensitive detector,” Opt. Lett. 27, 1421–1423 (2002).
    [Crossref]
  7. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
    [Crossref]
  8. R. H. Renard, “Total reflection: A new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am. 54, 1190–1197 (1964).
    [Crossref]
  9. H. K. V. Lotsch, “Reflection and refraction of a beam of light at a plane interface,” J. Opt. Soc. Am. 58, 551–561 (1968).
    [Crossref]
  10. D. J. Rhodes and C. K. Carniglia, “Measurement of the Goos-Hänchen shift at grazing incidence using Lloyd’s mirror,” J. Opt. Soc. Am. 67, 679–683 (1977).
    [Crossref]
  11. T. Tamir and H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 71, 1397–1413 (1971).
    [Crossref]
  12. B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
    [Crossref]
  13. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14, 3024 (2006).
    [Crossref] [PubMed]
  14. L. G. Wang and S. Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 221102 (2005).
    [Crossref]
  15. X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
    [Crossref]
  16. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, A. L. Floch, and L. Dutriaux, “Measurement of positive and negative Goos-Hänchen effects for metallic gratings near Wood anomalies,” Opt. Lett. 26, 666–668 (2001).
    [Crossref]
  17. H. Wolter, “Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimum-strahlkennzeichnung,” Z. Naturforsch. 5a, 143–153 (1950).
  18. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik32, 116–137, 189–204, 299–319, 553–569 (1970).
  19. W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A. 25, 2099–2101 (1982).
    [Crossref]
  20. P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
    [Crossref]
  21. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27, 680–682 (2002).
    [Crossref]
  22. Note that the expressions for the phase in ref. [19] contain a misprint.
  23. E. D. Palik, Handbook of optical constants of solids (Academic Press, London, 1985), 1st ed.
  24. LASEROPTIK, Gneisenaustr. 14, D-30826 Garbsen, Germany.
  25. T. Tamir, “Nonspecular phenomena in beam fields reflected by multilayered media,” J. Opt. Soc. Am. A 3, 558–565 (1986).
    [Crossref]
  26. W. Nasalski, “Modified reflectance and geometrical deformations of gaussian beams reflected at a dielectric interface,” J. Opt. Soc. Am. A 6, 1447–1454 (1989).
    [Crossref]

2007 (1)

P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

2006 (1)

2005 (1)

L. G. Wang and S. Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 221102 (2005).
[Crossref]

2004 (1)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

2002 (2)

2001 (1)

2000 (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

1992 (1)

F. Bretenaker, A. L. Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[Crossref] [PubMed]

1989 (1)

1988 (1)

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56, 1092–1094 (1988).
[Crossref]

1986 (1)

1982 (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A. 25, 2099–2101 (1982).
[Crossref]

1978 (1)

B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
[Crossref]

1977 (1)

1972 (1)

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen effect: A simple example of time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

1971 (1)

T. Tamir and H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 71, 1397–1413 (1971).
[Crossref]

1968 (1)

1964 (1)

1950 (1)

H. Wolter, “Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimum-strahlkennzeichnung,” Z. Naturforsch. 5a, 143–153 (1950).

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[Crossref]

Anicin, B. A.

B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
[Crossref]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Bertoni, H. L.

T. Tamir and H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 71, 1397–1413 (1971).
[Crossref]

Bonnet, C.

Bretenaker, F.

Carniglia, C. K.

Chan, S. W.

Chauvat, D.

Chen, C.W.

P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Chiang, H. P.

P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Chiu, K. W.

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen effect: A simple example of time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

Dutriaux, L.

Emile, O.

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Fazlic, R.

B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
[Crossref]

Floch, A. L.

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A. 25, 2099–2101 (1982).
[Crossref]

Gilles, H.

Girard, S.

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[Crossref]

Gragg, R. F.

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56, 1092–1094 (1988).
[Crossref]

Hamel, J.

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[Crossref]

He, J.

He, S.

Hesselink, L.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Kopric, M

B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
[Crossref]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

Lai, H. M.

H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27, 680–682 (2002).
[Crossref]

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

Leung, P. T.

P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

Lotsch, H. K. V.

H. K. V. Lotsch, “Reflection and refraction of a beam of light at a plane interface,” J. Opt. Soc. Am. 58, 551–561 (1968).
[Crossref]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik32, 116–137, 189–204, 299–319, 553–569 (1970).

Nasalski, W.

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids (Academic Press, London, 1985), 1st ed.

Quinn, J. J.

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen effect: A simple example of time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

Renard, R. H.

Rhodes, D. J.

Tamir, T.

T. Tamir, “Nonspecular phenomena in beam fields reflected by multilayered media,” J. Opt. Soc. Am. A 3, 558–565 (1986).
[Crossref]

T. Tamir and H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 71, 1397–1413 (1971).
[Crossref]

Wang, L. G.

L. G. Wang and S. Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 221102 (2005).
[Crossref]

Wild, W. J.

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A. 25, 2099–2101 (1982).
[Crossref]

Wolter, H.

H. Wolter, “Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimum-strahlkennzeichnung,” Z. Naturforsch. 5a, 143–153 (1950).

Xu, B. Y.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

Yi, J.

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

Zhu, S. Y.

L. G. Wang and S. Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 221102 (2005).
[Crossref]

Am. J. Phys. (2)

K. W. Chiu and J. J. Quinn, “On the Goos-Hänchen effect: A simple example of time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56, 1092–1094 (1988).
[Crossref]

Ann. Phys. (2)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[Crossref]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Appl. Phys. Lett. (2)

L. G. Wang and S. Y. Zhu, “Large negative lateral shifts from the Kretschmann-Raether configuration with left-handed materials,” Appl. Phys. Lett. 87, 221102 (2005).
[Crossref]

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372 (2004).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

J. Phys. A (1)

B. A. Aničin, R. Fazlić, and M Koprić, “Theoretical evidence for negative Goos-Hänchen shifts” J. Phys. A 11, 1657–1662 (1978).
[Crossref]

Opt. Commun. (1)

P. T. Leung, C.W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A. (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A. 25, 2099–2101 (1982).
[Crossref]

Phys. Rev. E (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos-Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[Crossref]

Phys. Rev. Lett. (1)

F. Bretenaker, A. L. Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[Crossref] [PubMed]

Z. Naturforsch. (1)

H. Wolter, “Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimum-strahlkennzeichnung,” Z. Naturforsch. 5a, 143–153 (1950).

Other (4)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik32, 116–137, 189–204, 299–319, 553–569 (1970).

Note that the expressions for the phase in ref. [19] contain a misprint.

E. D. Palik, Handbook of optical constants of solids (Academic Press, London, 1985), 1st ed.

LASEROPTIK, Gneisenaustr. 14, D-30826 Garbsen, Germany.

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Figures (5)

Fig. 1.
Fig. 1.

Geometry indicating the GH shift, defined as D. A beam of light with a finite transverse extent is incident from vacuum (medium 1) on a metal surface (medium 2). If the beam is s polarized, the displacement of the reflected beam (dotted line) with respect to the geometrical reflection (continuous line) is positive. If the beam is p polarized, the displacement is negative.

Fig. 2.
Fig. 2.

Curves representing the theoretical GH shift (normalized to the wavelength of light) for reflection by an Au surface. We used the experimental optical constants of Au at 826 nm [23]. It is important to note that while Dp is negative, Ds is positive and that |Dp |≫|Ds |.

Fig. 3.
Fig. 3.

Schematic drawing of the experimental set up.

Fig. 4.
Fig. 4.

Calculated reflectivity of Au at a wavelenght of 826 nm, as a function of the angle of incidence. We verified experimentally that the difference in the reflectivity for the s and p polarized beams is maximal at 80°.

Fig. 5.
Fig. 5.

Measured Goos-Hänchen shifts, i.e. the difference between Dp and Ds as a function of the angle of incidence. Experimental data are shown as solid dots and the corresponding theoretical curve has been derived from Fig. 2. The open dots show displacements orthogonal to the plane of incidence; the theoretical line in this case indicates zero displacement.

Equations (4)

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D = λ 2 π d δ ( θ ) d θ
δ s ( θ ) = m ( ln [ n 1 cos ( θ ) ( n ̂ 2 2 n 1 2 sin 2 ( θ ) ) 1 2 n 1 cos ( θ ) + ( n ̂ 2 2 n 1 2 sin 2 ( θ ) ) 1 2 ] ) ,
δ p ( θ ) = m ( ln [ n ̂ 2 2 cos ( θ ) n 1 ( n ̂ 2 2 n 1 2 sin 2 ( θ ) ) 1 2 n ̂ 2 2 cos ( θ ) + n 1 ( n ̂ 2 2 n 1 2 sin 2 ( θ ) ) 1 2 ] ) ,
Δ χ C ρ s I = ( ρ p ρ s ) ρ s · d p + ( D p D s ) .

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