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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  1. F. Goos and H. Hanchen, "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-Hanchen 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-H¨anchen 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-Hanchen 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-H¨anchen effect," Phys. Rev. E 62, 7330-7339 (2000).
    [CrossRef]
  8. R. H. Renard, "Total reflection: A new evaluation of the Goos-Hanchen 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-Hanchen 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. Anicin, R. Fazlic, and M Kopric, "Theoretical evidence for negative Goos-Hanchen shifts" J. Phys. A 11, 1657-1662 (1978).
    [CrossRef]
  13. J. He, J. Yi, and S. He, "Giant negative Goos-Hanchen 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 lefthanded 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-Hanchen 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 Minimumstrahlkennzeichnung," Z. Naturforsch. 5a, 143-153 (1950).
  18. H. K. V. Lotsch, "Beam displacement at total reflection: the Goos-Hanchen effect," Optik 32, 116-137, 189-204, 299-319, 553-569 (1970).
  19. W. J. Wild and C. L. Giles, " Goos-Hanchen 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-Hanchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
    [CrossRef]
  21. H. M. Lai, and S. W. Chan, "Large and negative Goos-Hanchen 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

P. T. Leung, C. W. Chen, and H. P. Chiang, "Large negative Goos-Hanchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

2006

2005

L. G. Wang and S. Y. Zhu, "Large negative lateral shifts from the Kretschmann-Raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

2004

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

2001

2000

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-H¨anchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[CrossRef]

1992

F. Bretenaker, A. L. Floch, and L. Dutriaux, "Direct measurement of the optical Goos-H¨anchen effect in lasers," Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

1989

1988

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

1982

W. J. Wild and C. L. Giles, " Goos-Hanchen shift from absorbing media," Phys. Rev. A. 25, 2099-2101 (1982).
[CrossRef]

1978

B. A. Anicin, R. Fazlic, and M Kopric, "Theoretical evidence for negative Goos-Hanchen shifts" J. Phys. A 11, 1657-1662 (1978).
[CrossRef]

1977

1972

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

1971

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

1964

1950

H. Wolter, "Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimumstrahlkennzeichnung," Z. Naturforsch. 5a, 143-153 (1950).

1948

K. Artmann, "Berechnung der Seitenversetzung des totalreflektierten Strahles," Ann. Phys. 437, 87-102 (1948).
[CrossRef]

1947

F. Goos and H. Hanchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 436, 333-346 (1947).
[CrossRef]

Am. J. Phys.

K. W. Chiu and J. J. Quinn, "On the Goos-Hanchen 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.

F. Goos and H. Hanchen, "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.

L. G. Wang and S. Y. Zhu, "Large negative lateral shifts from the Kretschmann-Raether configuration with lefthanded 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.

J. Opt. Soc. Am. A

J. Phys. A

B. A. Anicin, R. Fazlic, and M Kopric, "Theoretical evidence for negative Goos-Hanchen shifts" J. Phys. A 11, 1657-1662 (1978).
[CrossRef]

Opt. Commun.

P. T. Leung, C. W. Chen, and H. P. Chiang, "Large negative Goos-Hanchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A.

W. J. Wild and C. L. Giles, " Goos-Hanchen shift from absorbing media," Phys. Rev. A. 25, 2099-2101 (1982).
[CrossRef]

Phys. Rev. E

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-H¨anchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[CrossRef]

Phys. Rev. Lett.

F. Bretenaker, A. L. Floch, and L. Dutriaux, "Direct measurement of the optical Goos-H¨anchen effect in lasers," Phys. Rev. Lett. 68, 931-933 (1992).
[CrossRef] [PubMed]

Z. Naturforsch.

H. Wolter, "Untersuchungen zur Strahlversetzung bei Totalreflexion des Lichtes mit der Methode der Minimumstrahlkennzeichnung," Z. Naturforsch. 5a, 143-153 (1950).

Other

H. K. V. Lotsch, "Beam displacement at total reflection: the Goos-Hanchen effect," Optik 32, 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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