Abstract

We propose an improved method for attenuated-total-reflection experiments in the Otto configuration. This new technique overcomes the difficulties that arise from the nonuniformity of the air coupling gap. Thus attenuated-total-reflection measurements, under ideal adapted conditions, can be made for a wide range of wavelengths. The determination of optical constants by a three-parameter least-square fit of the experimental data to Fresnel’s theory always yields ambiguous results. We found that the ambiguity is caused by the loss of the phase angle in the reflectometry. Measurements for many air gap thicknesses in normal or extreme attenuated-total-reflection techniques, overcome this difficulty.

© 1992 Optical Society of America

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References

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  1. E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  2. H. E. de Bruijn, R. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
    [CrossRef]
  3. H. Kitajima, K. Hieda, “Use of a total absorption ATR method to measure complex refractive indices of metal-foils,” J. Opt. Soc. Am. 70, 1507–1512 (1980).
    [CrossRef]
  4. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
    [CrossRef]
  5. P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).
  6. G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminum,” Thin Solid Films 123, 9–17 (1985).
    [CrossRef]
  7. W. M. Robertson, E. Fullerton, “Reexamination of the surface-plasma-wave technique for determining the dielectric constants and thickness of metal films,” J. Opt. Soc. Am. B 6, 1584–1590 (1989).
    [CrossRef]
  8. F. Yang, G. W. Bradberry, J. R. Sambles, “Infrared surface plasmon-polaritons on Ni, Pd, and Pt,” J. Mod. Opt. 36, 1405–1410 (1989).
    [CrossRef]
  9. F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).
  10. M. Owner-Petersen, Bo-Shen Zhu, E. Dalsgaard, “Extreme attenuation of optical internal reflection used for determination of optical properties of metals,” J. Opt. Soc. Am. A 4, 1741–1747 (1987).
    [CrossRef]
  11. L. G. Schulz, “The optical constants of silver, gold, copper, and aluminium. I. The absorption coefficient k,” J. Opt. Soc. Am. 44, 357–362 (1954); L. G. Schulz, F. R. Tangherlini, “Optical constants of silver, gold, copper, and aluminium. II. The index of refraction n,” J. Opt. Soc. Am. 44, 362–368 (1954).
    [CrossRef]
  12. M. N. Tillin, J. R. Sambles, “A surface plasmon-polariton study of the dielectric constants of reactive metals: aluminium,” Thin Solid Films 167, 73–83 (1988).
    [CrossRef]
  13. A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
    [CrossRef]
  14. F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminium,” Phys. Rev. B 24, 892–903 (1981).
    [CrossRef]

1990 (2)

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

H. E. de Bruijn, R. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
[CrossRef]

1989 (2)

1988 (1)

M. N. Tillin, J. R. Sambles, “A surface plasmon-polariton study of the dielectric constants of reactive metals: aluminium,” Thin Solid Films 167, 73–83 (1988).
[CrossRef]

1987 (1)

1985 (1)

G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminum,” Thin Solid Films 123, 9–17 (1985).
[CrossRef]

1983 (1)

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

1981 (1)

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminium,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

1980 (1)

1971 (2)

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

1968 (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

1954 (1)

Bradberry, G. W.

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

F. Yang, G. W. Bradberry, J. R. Sambles, “Infrared surface plasmon-polaritons on Ni, Pd, and Pt,” J. Mod. Opt. 36, 1405–1410 (1989).
[CrossRef]

Corset, J.

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Dalsgaard, E.

de Bruijn, H. E.

Dubarry-Barbe, J. P.

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Dumas, P.

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Fullerton, E.

Greve, J.

Hieda, K.

Jarvis, D. J.

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

Kitajima, H.

Kooyman, R. H.

Kretschmann, E.

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Levy, Y.

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Mathewson, A. G.

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Myers, H. P.

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Owner-Petersen, M.

Pastore, G. F.

G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminum,” Thin Solid Films 123, 9–17 (1985).
[CrossRef]

Riviere, D.

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Robertson, W. M.

Sambles, J. R.

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

F. Yang, G. W. Bradberry, J. R. Sambles, “Infrared surface plasmon-polaritons on Ni, Pd, and Pt,” J. Mod. Opt. 36, 1405–1410 (1989).
[CrossRef]

M. N. Tillin, J. R. Sambles, “A surface plasmon-polariton study of the dielectric constants of reactive metals: aluminium,” Thin Solid Films 167, 73–83 (1988).
[CrossRef]

Schulz, L. G.

Segall, B.

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminium,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

Szmulowicz, F.

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminium,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

Tillin, M. N.

M. N. Tillin, J. R. Sambles, “A surface plasmon-polariton study of the dielectric constants of reactive metals: aluminium,” Thin Solid Films 167, 73–83 (1988).
[CrossRef]

Yang, F.

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

F. Yang, G. W. Bradberry, J. R. Sambles, “Infrared surface plasmon-polaritons on Ni, Pd, and Pt,” J. Mod. Opt. 36, 1405–1410 (1989).
[CrossRef]

Zhu, Bo-Shen

Appl. Opt. (1)

J. Mod. Opt. (2)

F. Yang, G. W. Bradberry, J. R. Sambles, “Infrared surface plasmon-polaritons on Ni, Pd, and Pt,” J. Mod. Opt. 36, 1405–1410 (1989).
[CrossRef]

F. Yang, G. W. Bradberry, D. J. Jarvis, J. R. Sambles, “Characterization of thin absorbing films using infrared surface plasmons,” J. Mod. Opt.37, 977–991 (1990).

J. Opt. Soc. Am. (2)

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

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

J. Phys. (Paris) (1)

P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminum at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Phys. Rev. B (1)

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminium,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

Phys. Scr. (1)

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Thin Solid Films (2)

M. N. Tillin, J. R. Sambles, “A surface plasmon-polariton study of the dielectric constants of reactive metals: aluminium,” Thin Solid Films 167, 73–83 (1988).
[CrossRef]

G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminum,” Thin Solid Films 123, 9–17 (1985).
[CrossRef]

Z. Phys. (2)

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the optical setup: L1, light source; D1 and D2, irises; L1, L2, and L3, lenses; M, monochromator; P, polarizing prism; CH, chopper; GT, goniometer table; PR, coupling prism; S1, diffraction slit; AS and S2, adjustable slits; M, mirror; PD, detector; AMPL, amplifier; VM, voltmeter; Rec, recorder.

Fig. 2
Fig. 2

Measured ATR curves as a function of the reduced wave vector kx = n1 sin θ1. n1 and θ1 are the refractive index of the prism and the incidence angle on the prism base, respectively. Filled circles; measurement without the diaphragm; crosses; measurement with the diaphragm. Wavelength, 1000 nm.

Fig. 3
Fig. 3

(a) Real part of the dielectric function of the aluminum film. Open and filled circles are from the first and the second three-parameter fits, respectively. Crosses are from the two-parameter fit. (b) Imaginary part of the dielectric function of the aluminum film and its thickness. Open and filled circles are from the first and the second three-parameter fits, respectively. Crosses are from the two-parameter fit.

Fig. 4
Fig. 4

(a) Fitted parameter ∊′ as a function of the fitted air gap thickness d2 for experimental angle scan ATR at the wavelength 633 nm. Filled and open circles mark the two different fits, and the numbers 1 to 22 characterize the measurements for separate coupling gaps. (b) Fitted parameter ∊″ corresponding to the conditions of Fig. 4(a).

Fig. 5
Fig. 5

Model of the four-layer system.

Fig. 6
Fig. 6

Influence of the inaccuracy of the minimum angle θopt on the fitted optical constants in the two-parameter fit compared with the two solutions from the three-parameter fit. Wavelength, 1000 nm; grd, degree.

Fig. 7
Fig. 7

Typical experimental angle scan of extreme ATR for different wavelengths: 1, 450 nm; 2, 500 nm; 3, 550 nm; 4, 610 nm; 5, 700 nm; 6, 780 nm.

Fig. 8
Fig. 8

Dielectric function of the aluminum film obtained from extreme ATR measurements.

Equations (10)

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r ^ 1234 = r ^ 12 + r ^ 234 exp ( 2 i k ^ z 2 ω c d 2 ) 1 + r ^ 12 r ^ 234 exp ( 2 i k ^ z 2 ω c d 2 ) .
k ^ z 2 = [ ^ 2 - ( n 1 sin θ 1 ) 2 ] 1 / 2 .
r ^ 12 = 1.
R = r ^ 1234 2 = 1 + ( C r ^ 234 ) 2 + 2 C r ^ 234 cos ( δ 12 - δ 234 ) 1 + ( C r ^ 234 ) 2 + 2 C r ^ 234 cos ( δ 12 + δ 234 ) .
C = 1 r ^ 234 .
d 2 = log ( 1 / r ^ 234 ) 2 ω / c [ ( n 1 sin θ min ) 2 - 1 ] 1 / 2 .
δ 12 - δ 234 = π ,
C 2 + 2 C r ^ 234 2 ( cos δ 112 cos δ 234 - R + 1 R - 1 sin δ 12 sin δ 234 ) + 1 r ^ 234 2 = 0.
d 2 = log ( A ± ( A 2 - 1 ) 1 / 2 - log r ^ 234 2 ω / c [ ( n 1 sin θ ) 2 - 1 ] 1 / 2 .
R E = 1 + cos ( δ 12 - δ 234 ) 1 + cos ( δ 12 + δ 234 ) .

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