Abstract

A versatile method for determination of the optical constants is described that can be applied to a variety of coating materials. It is based on the use of an optical thin film synthesis program to adjust the constants of dispersion equations until a good fit is obtained between measured and calculated spectral transmittance and/or reflectance curves. The sensitivity of the determination can be increased by a suitable combination of measurement quantities. Because more than the minimum amount of data can be used, sensitivity to measurement errors and the chances of obtaining multiple solutions can both be reduced. To illustrate the method optical constants are determined of MgF2, ZnS, MgO, Inconel, and Si films in the visible part of the spectrum and of ITO films in the 0.4–12.0-μm range.

© 1983 Optical Society of America

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References

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  1. F. Abeles, Prog. Opt. 2, 251 (1963).
  2. O. S. Heavens, Phys. Thin Films 2, 193 (1964).
  3. P. Rouard, P. Bousquet, Prog. Opt. 4, 145 (1965).
    [CrossRef]
  4. L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
    [CrossRef]
  5. L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
    [CrossRef]
  6. L. Ward, A. Nag, J. Phys. D 3, 462 (1970).
    [CrossRef]
  7. R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
    [CrossRef]
  8. R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
    [CrossRef]
  9. H. Bohme, Optik 62, 27 (1982).
  10. L. Ward, J. Phys. D 15, 1361 (1982).
    [CrossRef]
  11. J. M. Bennett, M. J. Booty, Appl. Opt. 5, 41 (1966).
    [CrossRef] [PubMed]
  12. J. E. Nestell, R. W. Christy, Appl. Opt. 11, 643 (1972).
    [CrossRef] [PubMed]
  13. W. N. Hansen, J. Opt. Soc. Am. 63, 793 (1973).
    [CrossRef]
  14. W. E. Case, Appl. Opt. 22, 1832 (1983).
    [CrossRef] [PubMed]
  15. R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.
  16. S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
    [CrossRef]
  17. K. Kozima, W. Suëtaka, P. N. Schatz, J. Opt. Soc. Am. 56, 181 (1966).
    [CrossRef]
  18. P.-O. Nilsson, Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  19. E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).
  20. L. J. Alperovich, V. N. Pushkarev, Opt. Spectrosc. USSR 47, 516 (1979).
  21. H. W. Verleur, J. Opt. Soc. Am. 58, 1356 (1968).
    [CrossRef]
  22. C. J. Powell, J. Opt. Soc. Am. 59, 738 (1969).
    [CrossRef]
  23. J. Rivory, Opt. Commun. 1, 334 (1970).
    [CrossRef]
  24. H. M. Liddell, J. Phys. D 7, 1588 (1974).
    [CrossRef]
  25. D. Smith, P. W. Baumeister, Appl. Opt. 18, 111 (1979).
    [CrossRef] [PubMed]
  26. E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
    [CrossRef]
  27. I. Ohlidal, K. Navratil, Thin Solid Films 67, 245 (1980).
    [CrossRef]
  28. J. A. Dobrowolski, Appl. Opt. 20, 74 (1981).
    [CrossRef] [PubMed]
  29. P. A. Temple, Appl. Phys. Lett. 34, 677 (1979).
    [CrossRef]
  30. J. N. Hodgson, Optical Absorption and Dispersion in Solids (Chapman & Hall, London, 1970).
  31. Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Vol. 3: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974).
  32. H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).
  33. R. Vierne, Opt. Acta 19, 209 (1972).
    [CrossRef]
  34. W. V. Goodell, J. K. Coulter, R. B. Johnson, J. Opt. Soc. Am. 63, 185 (1973).
    [CrossRef]
  35. This film was prepared and measured by J. Webb, Division of Chemistry, National Research Council of Canada;see J. Webb, J. Appl. Phys. 53, 9043 (1982).
    [CrossRef]
  36. T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).
  37. A. Rosencwaig, T. W. Hindley, Appl. Opt. 20, 606 (1981).
    [CrossRef] [PubMed]

1983 (1)

1982 (2)

H. Bohme, Optik 62, 27 (1982).

L. Ward, J. Phys. D 15, 1361 (1982).
[CrossRef]

1981 (2)

1980 (1)

I. Ohlidal, K. Navratil, Thin Solid Films 67, 245 (1980).
[CrossRef]

1979 (3)

P. A. Temple, Appl. Phys. Lett. 34, 677 (1979).
[CrossRef]

L. J. Alperovich, V. N. Pushkarev, Opt. Spectrosc. USSR 47, 516 (1979).

D. Smith, P. W. Baumeister, Appl. Opt. 18, 111 (1979).
[CrossRef] [PubMed]

1978 (1)

T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).

1976 (1)

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

1974 (1)

H. M. Liddell, J. Phys. D 7, 1588 (1974).
[CrossRef]

1973 (2)

1972 (2)

1971 (1)

R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
[CrossRef]

1970 (4)

L. Ward, A. Nag, J. Phys. D 3, 462 (1970).
[CrossRef]

R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
[CrossRef]

E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).

J. Rivory, Opt. Commun. 1, 334 (1970).
[CrossRef]

1969 (1)

1968 (2)

1967 (3)

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

1966 (2)

1965 (1)

P. Rouard, P. Bousquet, Prog. Opt. 4, 145 (1965).
[CrossRef]

1964 (1)

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

1963 (2)

F. Abeles, Prog. Opt. 2, 251 (1963).

S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[CrossRef]

Abeles, F.

F. Abeles, Prog. Opt. 2, 251 (1963).

Allen, T. H.

T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).

Alperovich, L. J.

L. J. Alperovich, V. N. Pushkarev, Opt. Spectrosc. USSR 47, 516 (1979).

Apfel, J. H.

T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).

Baumeister, P. W.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

Bennett, J. M.

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

J. M. Bennett, M. J. Booty, Appl. Opt. 5, 41 (1966).
[CrossRef] [PubMed]

Bergmann-Schaefer,

Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Vol. 3: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974).

Bohme, H.

H. Bohme, Optik 62, 27 (1982).

Booty, M. J.

Botten, L. C.

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.

Bousquet, P.

P. Rouard, P. Bousquet, Prog. Opt. 4, 145 (1965).
[CrossRef]

Carniglia, C. K.

T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).

Case, W. E.

Christy, R. W.

Coulter, J. K.

Dobrowolski, J. A.

Goodell, W. V.

Hansen, W. N.

Heavens, O. S.

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

Hindley, T. W.

Hodgson, J. N.

J. N. Hodgson, Optical Absorption and Dispersion in Solids (Chapman & Hall, London, 1970).

Johnson, R. B.

Julien, L. S.

R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
[CrossRef]

R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
[CrossRef]

Kozima, K.

Liddell, H. M.

H. M. Liddell, J. Phys. D 7, 1588 (1974).
[CrossRef]

Lupashko, E. A.

E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).

Maeda, S.

S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[CrossRef]

McKenzie, D. R.

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.

McPhedran, R. C.

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.

Miller, R. F.

R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
[CrossRef]

R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
[CrossRef]

Miloslavskii, V. K.

E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).

Nag, A.

L. Ward, A. Nag, J. Phys. D 3, 462 (1970).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

Navratil, K.

I. Ohlidal, K. Navratil, Thin Solid Films 67, 245 (1980).
[CrossRef]

Nestell, J. E.

Netterfield, R. P.

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.

Nilsson, P.-O.

Ohlidal, I.

I. Ohlidal, K. Navratil, Thin Solid Films 67, 245 (1980).
[CrossRef]

Pelletier, E.

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Powell, C. J.

Pushkarev, V. N.

L. J. Alperovich, V. N. Pushkarev, Opt. Spectrosc. USSR 47, 516 (1979).

Rivory, J.

J. Rivory, Opt. Commun. 1, 334 (1970).
[CrossRef]

Roche, P.

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Rosencwaig, A.

Rouard, P.

P. Rouard, P. Bousquet, Prog. Opt. 4, 145 (1965).
[CrossRef]

Schatz, P. N.

K. Kozima, W. Suëtaka, P. N. Schatz, J. Opt. Soc. Am. 56, 181 (1966).
[CrossRef]

S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[CrossRef]

Shklyarevskii, I. M.

E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).

Smith, D.

Suëtaka, W.

Taylor, A. J.

R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
[CrossRef]

R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
[CrossRef]

Temple, P. A.

P. A. Temple, Appl. Phys. Lett. 34, 677 (1979).
[CrossRef]

Thyagarajan, G.

S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[CrossRef]

Verleur, H. W.

Vidal, B.

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Vierne, R.

R. Vierne, Opt. Acta 19, 209 (1972).
[CrossRef]

Ward, L.

L. Ward, J. Phys. D 15, 1361 (1982).
[CrossRef]

L. Ward, A. Nag, J. Phys. D 3, 462 (1970).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

Webb, J.

This film was prepared and measured by J. Webb, Division of Chemistry, National Research Council of Canada;see J. Webb, J. Appl. Phys. 53, 9043 (1982).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

P. A. Temple, Appl. Phys. Lett. 34, 677 (1979).
[CrossRef]

Br. J. Appl. Phys. (2)

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 277 (1967).
[CrossRef]

L. Ward, A. Nag, Br. J. Appl. Phys. 18, 1629 (1967).
[CrossRef]

J. Chem. Phys. (1)

S. Maeda, G. Thyagarajan, P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Phys. D (5)

H. M. Liddell, J. Phys. D 7, 1588 (1974).
[CrossRef]

L. Ward, A. Nag, J. Phys. D 3, 462 (1970).
[CrossRef]

R. F. Miller, A. J. Taylor, L. S. Julien, J. Phys. D 3, 1957 (1970).
[CrossRef]

R. F. Miller, L. S. Julien, A. J. Taylor, J. Phys. D 4, 1100 (1971).
[CrossRef]

L. Ward, J. Phys. D 15, 1361 (1982).
[CrossRef]

Natl. Bur. Stand. U.S. Spec. Publ. (1)

T. H. Allen, J. H. Apfel, C. K. Carniglia, Natl. Bur. Stand. U.S. Spec. Publ. 541, 33 (1978).

Nouv. Rev. Opt. (1)

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Opt. Acta (1)

R. Vierne, Opt. Acta 19, 209 (1972).
[CrossRef]

Opt. Commun. (1)

J. Rivory, Opt. Commun. 1, 334 (1970).
[CrossRef]

Opt. Spectrosc. USSR (2)

E. A. Lupashko, V. K. Miloslavskii, I. M. Shklyarevskii, Opt. Spectrosc. USSR 29, 419 (1970).

L. J. Alperovich, V. N. Pushkarev, Opt. Spectrosc. USSR 47, 516 (1979).

Optik (1)

H. Bohme, Optik 62, 27 (1982).

Phys. Thin Films (2)

O. S. Heavens, Phys. Thin Films 2, 193 (1964).

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

Prog. Opt. (2)

P. Rouard, P. Bousquet, Prog. Opt. 4, 145 (1965).
[CrossRef]

F. Abeles, Prog. Opt. 2, 251 (1963).

Thin Solid Films (1)

I. Ohlidal, K. Navratil, Thin Solid Films 67, 245 (1980).
[CrossRef]

Other (4)

J. N. Hodgson, Optical Absorption and Dispersion in Solids (Chapman & Hall, London, 1970).

Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Vol. 3: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974).

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, Appl. Opt. submitted for publication.

This film was prepared and measured by J. Webb, Division of Chemistry, National Research Council of Canada;see J. Webb, J. Appl. Phys. 53, 9043 (1982).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Thin film terminology.

Fig. 2
Fig. 2

Spectral transmittances and reflectances of three ZnS films of different metric thicknesses (0.528,0.413,0.264 μm) deposited simultaneously onto quartz substrates.

Fig. 3
Fig. 3

Spectral transmittance and reflectance curves of two 3-layer ZnS/MgF2/ZnS systems. The metric thicknesses of the layers in order of deposition on the quartz substrate are 0.205,0.353,0.198 μm and 0.163,0.285,0.161 μm, respectively.

Fig. 4
Fig. 4

Spectral transmittance curves of a 7-layer MgO/MgF2 system measured at two angles of incidence.

Fig. 5
Fig. 5

Spectral transmittance curves of a 7-layer ZrO2/MgO system measured at two angles of incidence.

Fig. 6
Fig. 6

Spectral transmittance and reflectance curves of three Inconel films of different thickness measured at two angles of incidence.

Fig. 7
Fig. 7

Spectral transmittance and reflectance curves of a silicon film on a glass substrate.

Fig. 8
Fig. 8

Spectral transmittance and reflectance curves of two ITO films of different metric thicknesses measured at two angles of incidence and the resulting optical constants.

Tables (2)

Tables Icon

Table I Dispersion Equation Constants for Various Materials

Tables Icon

Table II Optical Constants for Various Materials

Equations (8)

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M = { 1 m i = 1 m ( C i E i ε i ) 2 } 1 / 2 ,
M = M [ n s , k s , n m , ( n i , k i , t i ) , i = 1 , 2 , , l ]
n i = n i ( A i , B i , C i , ) , k i = k i ( A i , B i , C i , ) .
M = { 1 m 1 + m 2 + m j [ i = 1 m 1 ( C 1 , i E 1 , i ε 1 , i ) 2 + i = 1 m 2 ( C 2 , i E 2 , i ε 2 , i ) 2 + ] } 1 / 2 .
n 2 ( λ ) = A + k 2 ( λ ) + i = 1 J B i λ 2 ( λ 2 C i 2 ) ( λ 2 C i 2 ) 2 + D i 2 λ 2 k ( λ ) = 1 2 n ( λ ) i = 1 J B i D i λ 3 ( λ 2 C i 2 ) 2 + D i 2 λ 2 ,
n 2 ( λ ) = A + k 2 ( λ ) + B λ 2 ( 1 + C 2 λ 2 ) , k ( λ ) = B C λ 3 2 n ( λ ) ( 1 + C 2 λ 2 ) ,
n 2 ( λ ) = A + k 2 ( λ ) + B λ 2 ( 1 + C 2 λ 2 ) + i = 1 J B i λ 2 ( λ 2 C i 2 ) ( λ 2 C i 2 ) 2 + D i 2 λ 2 , k ( λ ) = 1 2 n ( λ ) B C λ 3 ( 1 + C 2 λ 2 ) + i = 1 J B i D i λ 3 ( λ 2 C i 2 ) 2 + D i 2 λ 2 .
n 2 ( λ ) = 1.0 + A 1.0 + ( B / λ ) 2 , k ( λ ) = C n ( λ ) D λ + E λ + 1 λ 3 ,

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