Abstract

We investigate experimentally the dependence of the Goos-Hänchen shift on the surface properties of an air-metal interface. The shift depends on the microscopic roughness of the metal surface but it is insensitive to the large-scale variations associated with surface non-flatness. Both an effective medium model of roughness and the Rayleigh-Rice theory of scattering are used to interpret the observed phenomenon.

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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(7-8), 333–346 (1947).
    [CrossRef]
  2. M. Merano, A. Aiello, G. W. 't Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15(24), 15928–15934 (2007).
    [CrossRef] [PubMed]
  3. LASEROPTIK, Gneisenaustr. 14, D-30826 Garbsen, Germany.
  4. J. C. Stover, Optical Scattering Measurements and Analysis (SPIE, Washington, 1995), 2nd ed pp 43.
  5. G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
    [CrossRef]
  6. W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A 25(4), 2099–2101 (1982).
    [CrossRef]
  7. E. D. Palik, Handbook of optical constants of solids (Academic Press, London, 1985), 1st ed.
  8. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
    [CrossRef]
  9. R. Schiffer, “Reflectivity of a slightly rough surface,” Appl. Opt. 26(4), 704–712 (1987).
    [CrossRef] [PubMed]
  10. D. Franta and I. Ohlidal, “Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4-6), 459–467 (2005).
    [CrossRef]
  11. D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
    [CrossRef]
  12. D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
    [CrossRef]
  13. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988), 1st ed.
  14. F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
    [CrossRef]

2007 (1)

2005 (1)

D. Franta and I. Ohlidal, “Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4-6), 459–467 (2005).
[CrossRef]

1987 (1)

1982 (2)

G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
[CrossRef]

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A 25(4), 2099–2101 (1982).
[CrossRef]

1980 (1)

D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
[CrossRef]

1979 (1)

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[CrossRef]

1977 (1)

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Aiello, A.

Ames, G. H.

G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
[CrossRef]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
[CrossRef]

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[CrossRef]

Bacon, D. D.

D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
[CrossRef]

Braundmeier, A. J.

G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
[CrossRef]

Celli, V.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

Eliel, E. R.

Franta, D.

D. Franta and I. Ohlidal, “Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4-6), 459–467 (2005).
[CrossRef]

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A 25(4), 2099–2101 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Hall, D. G.

G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Hill, N. R.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[CrossRef]

Kinsbron, E.

D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
[CrossRef]

Marvin, A.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

Merano, M.

Ohlidal, I.

D. Franta and I. Ohlidal, “Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4-6), 459–467 (2005).
[CrossRef]

Schiffer, R.

't Hooft, G. W.

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[CrossRef]

Toigo, F.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

van Exter, M. P.

Wild, W. J.

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A 25(4), 2099–2101 (1982).
[CrossRef]

Woerdman, J. P.

Ann. Phys. (2)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1-2), 87–102 (1948).
[CrossRef]

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[CrossRef]

Appl. Opt. (1)

Opt. Commun. (2)

D. Franta and I. Ohlidal, “Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4-6), 459–467 (2005).
[CrossRef]

G. H. Ames, D. G. Hall, and A. J. Braundmeier., “Surface roughness measurements of CaF2 thin-films,” Opt. Commun. 43(4), 247–250 (1982).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shift from absorbing media,” Phys. Rev. A 25(4), 2099–2101 (1982).
[CrossRef]

Phys. Rev. B (3)

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[CrossRef]

D. E. Aspnes, E. Kinsbron, and D. D. Bacon, “Optical properties of Au: sample effects,” Phys. Rev. B 21(8), 3290–3299 (1980).
[CrossRef]

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, “Optical properties of rough surfaces: General theory and the small roughness limit,” Phys. Rev. B 15(12), 5618–5626 (1977).
[CrossRef]

Other (4)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988), 1st ed.

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

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

J. C. Stover, Optical Scattering Measurements and Analysis (SPIE, Washington, 1995), 2nd ed pp 43.

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Figures (5)

Fig. 1
Fig. 1

Characterization of Au-coated mirrors. On the left we show the Twyman-Green interferogram measuring the flatness of mirror II. On the right we show an AFM image of mirror III.

Fig. 2
Fig. 2

Schematic drawing of the experimental set-up.

Fig. 3
Fig. 3

Goos-Hänchen shift for mirror I (optical-quality substrate). Experimental data are shown as solid dots and the corresponding theoretical curve, for an ideal flat surface, has been derived from [6,2]. The open dots show displacements orthogonal to the plane of incidence; the theoretical line in this case indicates zero displacement.

Fig. 4
Fig. 4

Goos-Hänchen shift for mirror II (window glass substrate). Experimental data are shown as solid dots and the corresponding theoretical curve is for an ideal flat surface.

Fig. 5
Fig. 5

Goos-Hänchen shift for mirror III (microscopically rough substrate). Experimental data are shown as solid dots. The theoretical black curve is for an ideal flat surface, the red curve is the prediction for the effective medium model, the blue curve refers to Rayleigh-Rice theory of scattering.

Tables (1)

Tables Icon

Table 1 Surface properties of the three mirror substrates investigated in this paper, the optical-quality substrate (I), the window glass substrate (II) and the rough substrate (III).

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