Abstract

In this paper, the use of a total absorption attenuated total reflection (ATR) method to measure complex refractive indices and thicknesses of thin foils is discussed. Our studies show that in a prism metal-foil coupling system, the gap thickness between the prism and the metal-foil modifies the state of the coupled surface plasmons on the metal-foil interface, and yields total absorption at three different incident angles, under optimum conditions, respectively. The dependence of the conditions for total absorption on the complex refractive index and on the foil thickness is discussed. By preparing three prism coupling systems with different refractive indices, and by measuring the incident angle at minimum reflectance in each system, complex refractive indices and foil thicknesses of thin gold-foils have been measured.

© 1980 Optical Society of America

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References

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  1. A. Otto, “Excitation of non-radiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
    [Crossref]
  2. R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Phys. 237, 98–106 (1970).
    [Crossref]
  3. A. S. Barker, “Optical measurements of surface plasmons in gold,” Phys. Rev. B 8, 5418–5426 (1973).
    [Crossref]
  4. G. J. Kovas and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
    [Crossref]
  5. R. Kretzman, “Über optische Konstanten dicker Metallschichten in Sichtbaren und nahen Ultrarote,” Ann. Phys. 37, 303–325 (1940).
    [Crossref]
  6. N. M. Bashara and D. W. Peterson, “Ellipsometer study of anomalous absorption in very thin dielectric films on evaporated metals,” J. Opt. Soc. Am. 56, 1320–1331 (1966).
    [Crossref]
  7. V. Shah and T. Tamir, “Brewster phenomena in lossy structures,” Opt. Commun. 23, 113–117 (1977).
    [Crossref]
  8. H. Kitajima and K. Hano, “Anomalies of electromagnetic waves in multilayered structures containing anisotropy,” J. Opt. Soc. Am. 68, 1963–1701 (1978).
    [Crossref]
  9. A. B. Buckman and C. Kuo, “Coupled surface plasmons in structures with thin metallic layers,” J. Opt.Soc. Am. 69, 343–347 (1979).
    [Crossref]
  10. A. R. Melnyk and M. J. Harrison, “Theory of optical excitations of plasmons in metals,” Phys. Rev. B 2, 835–850 (1970).
    [Crossref]
  11. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [Crossref]
  12. P. K. Tien and R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
    [Crossref]
  13. R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N. Hamm, “Optical constants of vacuum-evaporated silver films,” J. Opt. Soc. Am. 54, 1434–1437 (1964).
    [Crossref]
  14. D. K. Burge and H. E. Bennet, “Effect of a thin surface film on the ellipsometric determination of optical constants,” J. Opt. Soc. Am. 54, 1428–1433 (1964).
    [Crossref]
  15. L. G. Schulz, “The experimental study of the optical properties of metal and the relation of the results to the Drude free electron theory,” Adv. Phys. 6, 102–144 (1957).
    [Crossref]
  16. K. Furuya and Y. Suematsu, “Mode dependent radiation losses of dielectric waveguides with external-higher-index layers,” Trans. IECE Jpn. 57-C, 411–418 (1974).
  17. E. G. Loewen and M. Neviere, “Dielectric coated gratings: a curious property,” Appl. Opt. 16, 3009–3011 (1977).
    [Crossref] [PubMed]
  18. H. Kitajima, K. Hieda, and Y. Suematsu, Topical Conference on Basic Optical Properties of Materials, NBSSP 574, 234–237 (1980).
  19. J. Koyama and H. Nishihara, Light Wave Electronics (Korona, Japan, 1978, p. 324.
  20. G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 12th edition (Longmans, London, 1959), p. 82.
  21. H. Kitajima, K. Hieda, and Y. Suematsu, “Optimum conditions in the attenuated total reflection technique,” Appl. Opt. (to be published).
  22. H. Kitajima, K. Hieda, and Y. Suematsu, “Measurement of ultra thin films deposited on metal substrates using ATR,” Appl. Opt. (to be published).

1979 (1)

A. B. Buckman and C. Kuo, “Coupled surface plasmons in structures with thin metallic layers,” J. Opt.Soc. Am. 69, 343–347 (1979).
[Crossref]

1978 (1)

H. Kitajima and K. Hano, “Anomalies of electromagnetic waves in multilayered structures containing anisotropy,” J. Opt. Soc. Am. 68, 1963–1701 (1978).
[Crossref]

1977 (3)

V. Shah and T. Tamir, “Brewster phenomena in lossy structures,” Opt. Commun. 23, 113–117 (1977).
[Crossref]

E. G. Loewen and M. Neviere, “Dielectric coated gratings: a curious property,” Appl. Opt. 16, 3009–3011 (1977).
[Crossref] [PubMed]

G. J. Kovas and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[Crossref]

1974 (1)

K. Furuya and Y. Suematsu, “Mode dependent radiation losses of dielectric waveguides with external-higher-index layers,” Trans. IECE Jpn. 57-C, 411–418 (1974).

1973 (1)

A. S. Barker, “Optical measurements of surface plasmons in gold,” Phys. Rev. B 8, 5418–5426 (1973).
[Crossref]

1970 (3)

P. K. Tien and R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
[Crossref]

R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Phys. 237, 98–106 (1970).
[Crossref]

A. R. Melnyk and M. J. Harrison, “Theory of optical excitations of plasmons in metals,” Phys. Rev. B 2, 835–850 (1970).
[Crossref]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

1968 (1)

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

1966 (1)

1964 (2)

1957 (1)

L. G. Schulz, “The experimental study of the optical properties of metal and the relation of the results to the Drude free electron theory,” Adv. Phys. 6, 102–144 (1957).
[Crossref]

1940 (1)

R. Kretzman, “Über optische Konstanten dicker Metallschichten in Sichtbaren und nahen Ultrarote,” Ann. Phys. 37, 303–325 (1940).
[Crossref]

Arakawa, E. T.

Barker, A. S.

A. S. Barker, “Optical measurements of surface plasmons in gold,” Phys. Rev. B 8, 5418–5426 (1973).
[Crossref]

Bashara, N. M.

Bennet, H. E.

Bruns, R.

R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Phys. 237, 98–106 (1970).
[Crossref]

Buckman, A. B.

A. B. Buckman and C. Kuo, “Coupled surface plasmons in structures with thin metallic layers,” J. Opt.Soc. Am. 69, 343–347 (1979).
[Crossref]

Burge, D. K.

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Furuya, K.

K. Furuya and Y. Suematsu, “Mode dependent radiation losses of dielectric waveguides with external-higher-index layers,” Trans. IECE Jpn. 57-C, 411–418 (1974).

Hamm, R. N.

Hano, K.

H. Kitajima and K. Hano, “Anomalies of electromagnetic waves in multilayered structures containing anisotropy,” J. Opt. Soc. Am. 68, 1963–1701 (1978).
[Crossref]

Harrison, M. J.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitations of plasmons in metals,” Phys. Rev. B 2, 835–850 (1970).
[Crossref]

Hieda, K.

H. Kitajima, K. Hieda, and Y. Suematsu, “Optimum conditions in the attenuated total reflection technique,” Appl. Opt. (to be published).

H. Kitajima, K. Hieda, and Y. Suematsu, “Measurement of ultra thin films deposited on metal substrates using ATR,” Appl. Opt. (to be published).

H. Kitajima, K. Hieda, and Y. Suematsu, Topical Conference on Basic Optical Properties of Materials, NBSSP 574, 234–237 (1980).

Huebner, R. H.

Kaye, G. W. C.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 12th edition (Longmans, London, 1959), p. 82.

Kitajima, H.

H. Kitajima and K. Hano, “Anomalies of electromagnetic waves in multilayered structures containing anisotropy,” J. Opt. Soc. Am. 68, 1963–1701 (1978).
[Crossref]

H. Kitajima, K. Hieda, and Y. Suematsu, Topical Conference on Basic Optical Properties of Materials, NBSSP 574, 234–237 (1980).

H. Kitajima, K. Hieda, and Y. Suematsu, “Optimum conditions in the attenuated total reflection technique,” Appl. Opt. (to be published).

H. Kitajima, K. Hieda, and Y. Suematsu, “Measurement of ultra thin films deposited on metal substrates using ATR,” Appl. Opt. (to be published).

Kovas, G. J.

G. J. Kovas and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[Crossref]

Koyama, J.

J. Koyama and H. Nishihara, Light Wave Electronics (Korona, Japan, 1978, p. 324.

Kretzman, R.

R. Kretzman, “Über optische Konstanten dicker Metallschichten in Sichtbaren und nahen Ultrarote,” Ann. Phys. 37, 303–325 (1940).
[Crossref]

Kuo, C.

A. B. Buckman and C. Kuo, “Coupled surface plasmons in structures with thin metallic layers,” J. Opt.Soc. Am. 69, 343–347 (1979).
[Crossref]

Laby, T. H.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 12th edition (Longmans, London, 1959), p. 82.

Loewen, E. G.

MacRae, R. A.

Melnyk, A. R.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitations of plasmons in metals,” Phys. Rev. B 2, 835–850 (1970).
[Crossref]

Neviere, M.

Nishihara, H.

J. Koyama and H. Nishihara, Light Wave Electronics (Korona, Japan, 1978, p. 324.

Otto, A.

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

Peterson, D. W.

Raether, H.

R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Phys. 237, 98–106 (1970).
[Crossref]

Schulz, L. G.

L. G. Schulz, “The experimental study of the optical properties of metal and the relation of the results to the Drude free electron theory,” Adv. Phys. 6, 102–144 (1957).
[Crossref]

Scott, G. D.

G. J. Kovas and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[Crossref]

Shah, V.

V. Shah and T. Tamir, “Brewster phenomena in lossy structures,” Opt. Commun. 23, 113–117 (1977).
[Crossref]

Suematsu, Y.

K. Furuya and Y. Suematsu, “Mode dependent radiation losses of dielectric waveguides with external-higher-index layers,” Trans. IECE Jpn. 57-C, 411–418 (1974).

H. Kitajima, K. Hieda, and Y. Suematsu, Topical Conference on Basic Optical Properties of Materials, NBSSP 574, 234–237 (1980).

H. Kitajima, K. Hieda, and Y. Suematsu, “Measurement of ultra thin films deposited on metal substrates using ATR,” Appl. Opt. (to be published).

H. Kitajima, K. Hieda, and Y. Suematsu, “Optimum conditions in the attenuated total reflection technique,” Appl. Opt. (to be published).

Tamir, T.

V. Shah and T. Tamir, “Brewster phenomena in lossy structures,” Opt. Commun. 23, 113–117 (1977).
[Crossref]

Tien, P. K.

Ulrich, R.

Adv. Phys. (1)

L. G. Schulz, “The experimental study of the optical properties of metal and the relation of the results to the Drude free electron theory,” Adv. Phys. 6, 102–144 (1957).
[Crossref]

Ann. Phys. (1)

R. Kretzman, “Über optische Konstanten dicker Metallschichten in Sichtbaren und nahen Ultrarote,” Ann. Phys. 37, 303–325 (1940).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (5)

J. Opt.Soc. Am. (1)

A. B. Buckman and C. Kuo, “Coupled surface plasmons in structures with thin metallic layers,” J. Opt.Soc. Am. 69, 343–347 (1979).
[Crossref]

Opt. Commun. (1)

V. Shah and T. Tamir, “Brewster phenomena in lossy structures,” Opt. Commun. 23, 113–117 (1977).
[Crossref]

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Phys. Rev. B (3)

A. R. Melnyk and M. J. Harrison, “Theory of optical excitations of plasmons in metals,” Phys. Rev. B 2, 835–850 (1970).
[Crossref]

A. S. Barker, “Optical measurements of surface plasmons in gold,” Phys. Rev. B 8, 5418–5426 (1973).
[Crossref]

G. J. Kovas and G. D. Scott, “Optical excitation of surface plasma waves in layered media,” Phys. Rev. B 16, 1297–1311 (1977).
[Crossref]

Trans. IECE Jpn. (1)

K. Furuya and Y. Suematsu, “Mode dependent radiation losses of dielectric waveguides with external-higher-index layers,” Trans. IECE Jpn. 57-C, 411–418 (1974).

Z. Phys. (2)

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

R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Phys. 237, 98–106 (1970).
[Crossref]

Other (5)

H. Kitajima, K. Hieda, and Y. Suematsu, Topical Conference on Basic Optical Properties of Materials, NBSSP 574, 234–237 (1980).

J. Koyama and H. Nishihara, Light Wave Electronics (Korona, Japan, 1978, p. 324.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 12th edition (Longmans, London, 1959), p. 82.

H. Kitajima, K. Hieda, and Y. Suematsu, “Optimum conditions in the attenuated total reflection technique,” Appl. Opt. (to be published).

H. Kitajima, K. Hieda, and Y. Suematsu, “Measurement of ultra thin films deposited on metal substrates using ATR,” Appl. Opt. (to be published).

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Figures (11)

FIG. 1
FIG. 1

Plane-wave model of prism coupling structure.

FIG. 2
FIG. 2

Prism coupling structure showing relation of θin to θ1.

FIG 3
FIG 3

Curves showing incident angle and gap thickness as functions of complex refractive index for the no-reflection condition. θin and dg0 versus n″, where n′ is varied from 0.1 to 0.35 in steps of 0.05 (n1 =1.784, n2 = 1.0, n ̂ = n n ).

FIG. 4
FIG. 4

Curves showing incident angle and metal thickness as functions of complex refractive index for the no-reflection condition. θin and dm0 vs n″, where n′ is varied from 0.1 to 0.35 in steps of 0.05 (n1 = 1.784, n 2 = n ̂ = n i n , n3 = 1.0)

FIG. 5
FIG. 5

Curves showing thicknesses of gold-foil and gap as functions of incident angle for the no-reflection condition. dm0 and dg0 vs θin (n1 = 1.784, n2 n4 = 1.0, n ̂ = 0.2 i 3.315).

FIG. 6
FIG. 6

Vector trajectories of reflection coefficient as a function of incident angle for various gap thicknesses, B1 vs θin. The parameters of the prism metal-foil coupling system are the same as that of Fig. 5.

FIG. 7
FIG. 7

Curves showing incident angle and gap thickness as functions of complex refractive index for the no-reflection condition. θin and dg0 vs n″, where n′ is varied from 0.1 to 0.35 in steps of 0.05. (a) The gap region is filled with distilled water (n1 = 1.784, n2 = 1.331, n ̂ = n in ); (b)the prism is rutile and the gap is filled with distilled water (n1 = 2.584, n2 = 1.331, n ̂ = n in ).

FIG. 8
FIG. 8

Curves showing incident angles and gap thickness as functions of complex refractive index for the nonreflection condition. θin and dg0 vs n″, where n′ is varied from 0.1 to 0.35 in steps of 0.05 (metal thickness dm = 500 Å, glass substrate n4 = 1.512, wavelength λ0 = 6328 Å). Approximate values of the complex refractive index are obtained graphically, by using the values of incident angles which are shown in the Table I. (a) n1 = 1.784 (SF-11), n2 = 1.0 (air); (b) n1 = 1.784 (SF-11), n2 = 1.331 (distilled water); and (c) n1 = 2.584 (Rutile), n2 =1.331 (distilled water).

FIG. 9
FIG. 9

Curves giving the complex refractive index to be determined. n′ vs n″ (gold-foil thickness dm = 1000 Å). The crossing point is n ̂ = 0.21 i 3.315. Curves labeled 1, 2, and 3 are calculated with the data of the prism coupling systems shown in the Table I, respectively, i.e., the numbers 1, 2, and 3 correspond to the numbers in Table I.

FIG. 10
FIG. 10

Curves giving the complex refractive index to be determined. n′ vs n″ (gold-foil thickness dm = 500 Å). The crossing point is n ̂ = 0.21 i 3.315. The numbers of the curves correspond to the numbers on Table I.

Fig. 11
Fig. 11

Absorption characteristics showing the gap thickness at the measurement spot, and the ambiguity in determining n′ from an absorption characteristic alone. |B1|2 vs θin; dots are experimental data. * The complex index of Au-foil of 500 Å thick is n ̂ = 0.225 i 3.312. However, the curve used the index n ̂ = 0.175 i 3.312 fits the small dotted curve except near the minimum reflectances. By varying the gap thickness properly, the differences between these curves become very small.

Tables (1)

Tables Icon

TABLE I Refractive indices of prism coupling system and measured values of incident angle at the minimum reflectance for gold-foils. Operating wavelength λ0 = 6328 Å.

Equations (27)

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n j = ɛ j / ɛ 0 ( j = 1 , 2 , 4 ) real ,
n 3 = n ̂ = n i n ( j = 3 ) complex
= | n ̂ | exp [ i ϕ m ] ,
H j = exp [ i β x ] [ A j exp ( i γ j z ) + B j exp ( i γ j z ) ] , j = 1 to 4 ,
β = k 0 n j sin θ j ;
γ j = k 0 n j cos θ j ; Re ( γ j ) 0 , Im ( γ j ) 0 ;
γ 3 = | γ 3 | exp ( i ϕ γ ) ,
ϕ γ = π 2 1 2 tan 1 ( 2 n n n 2 n 2 + ( n 1 sin θ 1 ) 2 ) .
B 1 = R 12 exp ( i ϕ 12 ) + B 2 / A 2 1 + exp ( i ϕ 12 ) R 12 B 2 / A 2 ,
B 2 A 2 = R 23 exp ( i ϕ 23 ) + R 34 exp ( i ϕ 34 ) exp ( i 2 γ 3 d m ) 1 + R 23 R 34 exp [ i ( ϕ 32 + ϕ 34 ) ] exp ( i 2 γ 3 d m ) × exp ( 2 α g ) ,
R j k exp ( i ϕ j k ) = γ j / ɛ j γ k / ɛ k γ j / ɛ j + γ k / ɛ k ,
α g = i γ 2 d g = 2 π d g λ 0 ( n 1 n 2 sin θ 1 ) 2 1 .
R 12 exp ( i ϕ 12 ) = B 2 / A 2 .
| B 2 / A 2 | = R 23 exp ( 2 α g ) = 1 ,
arg ( B 2 / A 2 ) = ϕ 23 = ϕ 12 ± π ,
R 23 = | i n 2 ( n 1 n 2 sin θ 1 ) 2 1 | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] i n 2 ( n 1 n 2 sin θ 1 ) 2 1 + | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] | ,
ϕ 23 = π + tan 1 ( 1 n 2 ( n 1 n 2 sin θ 1 ) 2 1 + | γ 3 | | n ̂ | 2 sin ( 2 ϕ m ϕ γ ) | γ 3 | | n ̂ | 2 cos ( 2 ϕ m ϕ γ ) ) + tan 1 ( 1 n 2 ( n 1 n 2 sin θ 1 ) 2 1 | γ 3 | | n ̂ | 2 sin ( 2 ϕ m ϕ γ ) | γ 3 | | n ̂ | 2 cos ( 2 ϕ m ϕ γ ) ) ,
d g λ 0 = log ( R 23 ) { 4 π n 2 ( n 1 / n 2 ) sin θ 1 ] 2 1 } .
1 n 1 ( sin θ 1 ) 2 1 | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] 1 n 1 ( sin θ 1 ) 2 1 + | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] + i n 4 ( n 1 n 4 sin θ 1 ) 2 1 | γ 3 | | n ̂ | 2 exp [ i ( 2 ϕ m ϕ γ ) ] i n 4 ( n 1 n 4 sin θ 1 ) 2 1 × exp ( 2 α m )
α m = | γ 3 | d m .
1 + R 23 R 34 cos ( ϕ 23 + ϕ 34 ) exp ( 2 α m ) 0 ,
| R 23 R 34 sin ( ϕ 23 + ϕ 34 ) exp ( 2 α m ) | < 1 ,
α m = | γ 3 | d m .
n ̂ = 0.21 ± 0.01 i ( 3.315 ± 0.01 )
n ̂ = 0.2024 i 3.3198 ( vacuum evaporated )
n ̂ = 0.2017 ± 0.014 i ( 3.33 ± 0.04 ) ( vacuum evaporated ) .
n ̂ = 0.225 ± 0.01 i ( 3.312 ± 0.01 ) , d m = 500 ± 50 Å