Abstract

Attenuated-total-reflection spectra obtained by the optical excitation of surface plasmon polaritons can be interpreted in terms of two different virtual modes. It is shown that the HWHM of absorptance as a function of the incidence angle can be described by the decay constant of one of the modes. The attenuated-total-reflection resonance angle, on the other hand, is determined by the phase of another virtual mode. An experimental verification of this virtual-mode treatment is carried out for thick aluminum films.

© 1992 Optical Society of America

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References

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  1. A. Otto, “Excitation of non-radiative surface plasmon waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
    [CrossRef]
  2. E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  3. G. Borstel, H. J. Falge, “Surface phonon-polaritons at semi-infinite crystals,” Phys. Status Solidi B 83, 11–45 (1977).
    [CrossRef]
  4. L. Wendler, R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143, 131–148 (1987).
    [CrossRef]
  5. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4374 (1972).
    [CrossRef]
  6. A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
    [CrossRef]
  7. M. Klopfleisch, M. Golz, “Improved experimental method for the determination of optical constants by excitation of surface plasmon polaritons,” Appl. Opt. 31, xxxx–xxxx (1992).
    [CrossRef]
  8. G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminium,” Thin Solid Films 123, 9–17 (1985).
    [CrossRef]
  9. P. Dumas, J. P. Dubarry-Barbe, D. Riviere, Y. Levy, J. Corset, “Growth of thin alumina film on aluminium at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

1992 (1)

M. Klopfleisch, M. Golz, “Improved experimental method for the determination of optical constants by excitation of surface plasmon polaritons,” Appl. Opt. 31, xxxx–xxxx (1992).
[CrossRef]

1987 (1)

L. Wendler, R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143, 131–148 (1987).
[CrossRef]

1985 (1)

G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminium,” 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 aluminium at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

1977 (1)

G. Borstel, H. J. Falge, “Surface phonon-polaritons at semi-infinite crystals,” Phys. Status Solidi B 83, 11–45 (1977).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4374 (1972).
[CrossRef]

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 non-radiative surface plasmon waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Borstel, G.

G. Borstel, H. J. Falge, “Surface phonon-polaritons at semi-infinite crystals,” Phys. Status Solidi B 83, 11–45 (1977).
[CrossRef]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4374 (1972).
[CrossRef]

Corset, J.

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

Dubarry-Barbe, J. P.

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

Falge, H. J.

G. Borstel, H. J. Falge, “Surface phonon-polaritons at semi-infinite crystals,” Phys. Status Solidi B 83, 11–45 (1977).
[CrossRef]

Golz, M.

M. Klopfleisch, M. Golz, “Improved experimental method for the determination of optical constants by excitation of surface plasmon polaritons,” Appl. Opt. 31, xxxx–xxxx (1992).
[CrossRef]

Haupt, R.

L. Wendler, R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143, 131–148 (1987).
[CrossRef]

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4374 (1972).
[CrossRef]

Klopfleisch, M.

M. Klopfleisch, M. Golz, “Improved experimental method for the determination of optical constants by excitation of surface plasmon polaritons,” Appl. Opt. 31, xxxx–xxxx (1992).
[CrossRef]

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 aluminium 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 non-radiative surface plasmon waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Pastore, G. F.

G. F. Pastore, “Transmission interference spectrometric determination of the thickness and refractive index of barrier films on aluminium,” 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 aluminium at room temperature: a kinetic and spectrometric study by surface plasmon excitation,” J. Phys. (Paris) C10, 205–208 (1983).

Wendler, L.

L. Wendler, R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143, 131–148 (1987).
[CrossRef]

Appl. Opt. (1)

M. Klopfleisch, M. Golz, “Improved experimental method for the determination of optical constants by excitation of surface plasmon polaritons,” Appl. Opt. 31, xxxx–xxxx (1992).
[CrossRef]

J. Phys. (Paris) (1)

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

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4374 (1972).
[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]

Phys. Status Solidi B (2)

G. Borstel, H. J. Falge, “Surface phonon-polaritons at semi-infinite crystals,” Phys. Status Solidi B 83, 11–45 (1977).
[CrossRef]

L. Wendler, R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143, 131–148 (1987).
[CrossRef]

Thin Solid Films (1)

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

Z. Phys. (2)

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

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

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the four-layer system.

Fig. 2
Fig. 2

Calculated influence of the air gap thickness on (a) the angle at the minimum reflectance and (b) the values of Rmin. Aluminum, ^ 4 = −52 + i22.2; silver, ^ 4 = −19 + i0.5; refractive index n1 = 1.735; wavelength, 633 nm).

Fig. 3
Fig. 3

Experimental ATR curves for different air gap thicknesses.

Fig. 4
Fig. 4

Real part of the propagation constant as a function of the air gap thickness. Curve 1, calculated for type I virtual mode; curve 2, calculated for type II virtual mode; curve 3, kxmin from the calculated ATR; points C–T, kxmin from the experimental ATR curves.

Fig. 5
Fig. 5

Imaginary part of the propagation constant as a function of the air gap thickness. Curve 1, calculated for type I virtual mode; curve 2, calculated for type II virtual mode; points C–T, from the experimentally determined HWHM.

Equations (19)

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R p = r ^ 1234 2 = H r 2 H i 2 ,
r ^ 1234 = r ^ 12 + r ^ 234 exp - 2 α ^ 2 d 2 1 + r ^ 12 r ^ 234 exp - 2 α ^ 2 d 2 ,
r ^ 234 = r ^ 23 + r ^ 34 exp - 2 α ^ 3 d 3 1 + r ^ 23 r ^ 34 exp - 2 α ^ 3 d 3 ,
r ^ i j = ^ j α ^ i - ^ i α ^ j ^ j α ^ i + ^ i α ^ j ,
α ^ i = ω c ( ^ 1 sin 2 θ 1 - ^ i ) 1 / 2 .
k ^ x = ω c ( ^ 2 ^ 4 ) 1 / 2 ^ 2 + ^ 4
( ^ 2 α ^ 2 + ^ 1 α ^ 1 ) C + B ( ^ 2 α ^ 2 - ^ 1 α ^ 1 ) exp ( 2 α ^ 2 d 2 ω c ) = 0 ,
C = ( ^ 3 α ^ 3 + ^ 2 α ^ 2 ) ( ^ 4 α ^ 4 + ^ 3 α ^ 3 ) + ( ^ 3 α ^ 3 - ^ 2 α ^ 2 ) ( ^ 4 α ^ 4 - ^ 3 α ^ 3 ) exp ( 2 α ^ 3 d 3 ω c ) ,
B = ( ^ 3 α ^ 3 - ^ 2 α ^ 2 ) ( ^ 4 α ^ 4 + ^ 3 α ^ 3 ) + ( ^ 3 α ^ 3 + ^ 2 α ^ 2 ) ( ^ 4 α ^ 4 - ^ 3 α ^ 3 ) exp ( 2 α ^ 3 d 3 ω c ) ,
α ^ i = ( k ^ x 2 - ^ i ) 1 / 2 .
C ( ^ 2 α ^ 2 - ^ 1 α ^ 1 ) - B ( ^ 2 α ^ 2 + ^ 1 α ^ 1 ) exp ( 2 α ^ z d z ω c ) = 0.
r ^ = n 24 + z 24 ( r ^ 12 ) - 1 exp ( 2 α ^ 2 d 2 ω c ) n 24 + z 24 r ^ 12 exp ( 2 α ^ 2 d 2 ω c ) r ^ 12 ,
n 24 = ( ^ 4 α ^ 4 + ^ 2 α ^ 2 ) ,
z 24 = ( ^ 4 α ^ 4 - ^ 2 α ^ 2 ) .
r ^ 124 = k x - ( k x 0 + δ k x ) - i ( k x 0 - δ k x ) k x - ( k x 0 + δ k x ) - i ( k x 0 + δ k x ) r ^ 12 .
A = 4 k x 0 δ k x ( k x - k x 0 - δ k x ) 2 + ( k x 0 + δ k x ) 2 .
k x = k x 0 + δ k x .
Δ k x = k x 0 + δ k x = n 1 [ sin ( θ min + δ θ ) - sin θ min ] ,
k x 0 + δ k x n 1 δ θ cos θ min .

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