Abstract

The program for the synthesis of nonabsorbing thin film systems by the method of gradual evolution [ J. A. Dobrowolski, Appl. Opt. 4, 937 ( 1965)] has been extended to include new features and to handle absorbing materials. In the analysis mode the new program calculates the spectral transmittance, reflectance, and absorptance of any absorbing multilayer system for any angle of incidence or plane of polarization. The CIE chromaticity coordinates of the coating can also be calculated. Information on the stability of the system is obtained from an automatically repeated analysis with randomly perturbed values of the construction parameters. As in the original program the synthesis mode does not presuppose a starting design; a layer system consisting of real absorbing or nonabsorbing coating materials may be gradually evolved. The evolution and refinement are governed by the value of a merit function defined specially for each problem. In the new program it is possible to control the sensitivity of the system performance to changes in the construction parameters. The monitoring information mode yields data useful for the construction of a multilayer. The construction parameter determination mode deduces the actual parameters from the measured performance of the system. The operation of the program is illustrated by examples.

© 1981 Optical Society of America

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References

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  1. J. A. Dobrowolski, Appl. Opt. 4, 937 (1965).
    [CrossRef]
  2. R. J. Scheuerman, J. H. Beardsley, Final Technical Report for Phase I—Unsupported Thin Film Beam Splitter, NAS5-10292, (Perkin-Elmer Corp., Norwalk, 1968).
  3. J. J. Walls, in Proceedings of the Fourteenth Conference of the Society of Vacuum Coaters (1971), p. 75.
  4. M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).
  5. P. H. Berning, Phys. Thin Films 1, 69 (1963).
  6. H. A. Macleod, Thin Film Filters (Elsevier, New York, 1969).
  7. Z. Knittl, Optics of Thin Films (Wiley, London, 1976).
  8. J. R. Partington, An Advanced Treatise on Physical Chemistry, Vol. 4, (Longmans, London, 1953), p. 522.
  9. Ref. 8, p. 526.
  10. L. Bergmann, C. Schaefer, Lehrbuch der Experimental-physik, Vol. 3 (Walter de Gruyter, Berlin, 1974), p. 249.
  11. J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.
  12. A. Bloom, Appl. Opt. 20, 66 (1981).
    [CrossRef] [PubMed]
  13. H. Zycha, Appl. Opt. 12, 979 (1973).
    [CrossRef] [PubMed]
  14. C. Holm, Appl. Opt. 18, 1978 (1979).
    [CrossRef] [PubMed]
  15. Sh. A. Furman, E. G. Stolov, Opt. Spectrosc. 41, 380 (1976).
  16. A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).
  17. O. S. Heavens, H. M. Liddell, Opt. Acta 15, 129 (1968).
  18. K. V. S. R. Apparao, Indian J. Pure Appl. Phys. 15, 270 (1977).
  19. C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980).
    [CrossRef]
  20. J. A. Dobrowolski, Appl. Opt. 9, 1396 (1970).
    [CrossRef] [PubMed]
  21. J. A. Dobrowolski, Appl. Opt. 12, 1885 (1973).
    [CrossRef] [PubMed]
  22. J. A. Dobrowolski, D. Lowe, Appl. Opt. 17, 3039 (1978).
    [CrossRef] [PubMed]
  23. J. A. Dobrowolski, A. J. Waldorf, J. Opt. Soc. Am. 60, 725 (1970).
  24. E. Pelletier, P. Giacomo, Le Vide 27, 157, 1 (1972).
  25. W. V. Goodell, J. K. Coulter, P. B. Johnson, J. Opt. Soc. Amer. 63, 185 (1973).
    [CrossRef]
  26. J. T. Cox, G. Hass, W. R. Hunter, Appl. Opt. 14, 1247 (1975).
    [CrossRef] [PubMed]
  27. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

1981

1980

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980).
[CrossRef]

1979

C. Holm, Appl. Opt. 18, 1978 (1979).
[CrossRef] [PubMed]

J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.

1978

1977

K. V. S. R. Apparao, Indian J. Pure Appl. Phys. 15, 270 (1977).

1976

Sh. A. Furman, E. G. Stolov, Opt. Spectrosc. 41, 380 (1976).

1975

M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).

J. T. Cox, G. Hass, W. R. Hunter, Appl. Opt. 14, 1247 (1975).
[CrossRef] [PubMed]

1973

1972

E. Pelletier, P. Giacomo, Le Vide 27, 157, 1 (1972).

1970

J. A. Dobrowolski, A. J. Waldorf, J. Opt. Soc. Am. 60, 725 (1970).

J. A. Dobrowolski, Appl. Opt. 9, 1396 (1970).
[CrossRef] [PubMed]

1968

O. S. Heavens, H. M. Liddell, Opt. Acta 15, 129 (1968).

1965

1963

P. H. Berning, Phys. Thin Films 1, 69 (1963).

1962

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).

Apparao, K. V. S. R.

K. V. S. R. Apparao, Indian J. Pure Appl. Phys. 15, 270 (1977).

Beardsley, J. H.

R. J. Scheuerman, J. H. Beardsley, Final Technical Report for Phase I—Unsupported Thin Film Beam Splitter, NAS5-10292, (Perkin-Elmer Corp., Norwalk, 1968).

Bergmann, L.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental-physik, Vol. 3 (Walter de Gruyter, Berlin, 1974), p. 249.

Berning, P. H.

P. H. Berning, Phys. Thin Films 1, 69 (1963).

Bloom, A.

Chinnery, D. N. W.

M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).

Coulter, J. K.

W. V. Goodell, J. K. Coulter, P. B. Johnson, J. Opt. Soc. Amer. 63, 185 (1973).
[CrossRef]

Cox, J. T.

Dobrowolski, J. A.

Ermolaev, A. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).

Furman, Sh. A.

Sh. A. Furman, E. G. Stolov, Opt. Spectrosc. 41, 380 (1976).

Giacomo, P.

E. Pelletier, P. Giacomo, Le Vide 27, 157, 1 (1972).

Goodell, W. V.

W. V. Goodell, J. K. Coulter, P. B. Johnson, J. Opt. Soc. Amer. 63, 185 (1973).
[CrossRef]

Granqvist, C. G.

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980).
[CrossRef]

Hass, G.

Heavens, O. S.

O. S. Heavens, H. M. Liddell, Opt. Acta 15, 129 (1968).

Hjortsberg, A.

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980).
[CrossRef]

Holm, C.

Hunter, W. R.

Jiang, B-C.

J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.

Johnson, P. B.

W. V. Goodell, J. K. Coulter, P. B. Johnson, J. Opt. Soc. Amer. 63, 185 (1973).
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976).

Liddell, H. M.

O. S. Heavens, H. M. Liddell, Opt. Acta 15, 129 (1968).

Lowe, D.

Macleod, H. A.

H. A. Macleod, Thin Film Filters (Elsevier, New York, 1969).

McDowell, M. W.

M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).

Minkov, I. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).

Partington, J. R.

J. R. Partington, An Advanced Treatise on Physical Chemistry, Vol. 4, (Longmans, London, 1953), p. 522.

Pelletier, E.

E. Pelletier, P. Giacomo, Le Vide 27, 157, 1 (1972).

Schaefer, C.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental-physik, Vol. 3 (Walter de Gruyter, Berlin, 1974), p. 249.

Scheuerman, R. J.

R. J. Scheuerman, J. H. Beardsley, Final Technical Report for Phase I—Unsupported Thin Film Beam Splitter, NAS5-10292, (Perkin-Elmer Corp., Norwalk, 1968).

Stolov, E. G.

Sh. A. Furman, E. G. Stolov, Opt. Spectrosc. 41, 380 (1976).

Tang, J.-F.

J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.

Theron, E.

M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).

Vlasov, A. G.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).

Waldorf, A. J.

J. A. Dobrowolski, A. J. Waldorf, J. Opt. Soc. Am. 60, 725 (1970).

Walls, J. J.

J. J. Walls, in Proceedings of the Fourteenth Conference of the Society of Vacuum Coaters (1971), p. 75.

Zheng, Q.

J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.

Zycha, H.

Appl. Opt.

Appl. Phys. Lett.

C. G. Granqvist, A. Hjortsberg, Appl. Phys. Lett. 36, 139 (1980).
[CrossRef]

Indian J. Pure Appl. Phys.

K. V. S. R. Apparao, Indian J. Pure Appl. Phys. 15, 270 (1977).

J. Opt. Soc. Am.

J. A. Dobrowolski, A. J. Waldorf, J. Opt. Soc. Am. 60, 725 (1970).

J. Opt. Soc. Amer.

W. V. Goodell, J. K. Coulter, P. B. Johnson, J. Opt. Soc. Amer. 63, 185 (1973).
[CrossRef]

J. Zhejiany Univ.

J.-F. Tang, B-C. Jiang, Q. Zheng, J. Zhejiany Univ. 3, 13 (1979). An English translation of this paper is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario, Canada, KIA S6.

Le Vide

E. Pelletier, P. Giacomo, Le Vide 27, 157, 1 (1972).

Opt. Acta

O. S. Heavens, H. M. Liddell, Opt. Acta 15, 129 (1968).

Opt. Spectrosc.

Sh. A. Furman, E. G. Stolov, Opt. Spectrosc. 41, 380 (1976).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spectrosc. 13, 142 (1962).

Optik

M. W. McDowell, D. N. W. Chinnery, E. Theron, Optik 44, 79 (1975).

Phys. Thin Films

P. H. Berning, Phys. Thin Films 1, 69 (1963).

Other

H. A. Macleod, Thin Film Filters (Elsevier, New York, 1969).

Z. Knittl, Optics of Thin Films (Wiley, London, 1976).

J. R. Partington, An Advanced Treatise on Physical Chemistry, Vol. 4, (Longmans, London, 1953), p. 522.

Ref. 8, p. 526.

L. Bergmann, C. Schaefer, Lehrbuch der Experimental-physik, Vol. 3 (Walter de Gruyter, Berlin, 1974), p. 249.

R. J. Scheuerman, J. H. Beardsley, Final Technical Report for Phase I—Unsupported Thin Film Beam Splitter, NAS5-10292, (Perkin-Elmer Corp., Norwalk, 1968).

J. J. Walls, in Proceedings of the Fourteenth Conference of the Society of Vacuum Coaters (1971), p. 75.

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

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Figures (8)

Fig. 1
Fig. 1

Refractive index and material vs thickness nets used in the search and gradual evolution methods of thin film synthesis.

Fig. 2
Fig. 2

Reflectance of a black absorber coating at different stages of its design.

Fig. 3
Fig. 3

Six-layer coating for radiative cooling.

Fig. 4
Fig. 4

A y ¯ λ tristimulus filter designed by the simultaneous refinement of two multilayers placed in series.

Fig. 5
Fig. 5

Change in spectral transmittance with thickness during the monitoring of the first layer of the black absorber coating.

Fig. 6
Fig. 6

Change in spectral transmittance with thickness during the monitoring of the second layer of the black absorber coating.

Fig. 7
Fig. 7

Fabrication information for the first and second layers of a black absorber coating.

Fig. 8
Fig. 8

Determination of the optical constants of a high-index material. The full curve represents the target (or measured) transmittance; the dashed and dotted lines correspond to the transmittance of the starting and the refined designs.

Tables (2)

Tables Icon

Table I Construction Parameters of Multilayers

Tables Icon

Table II Determination of Optical Constants

Equations (10)

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T R A Δ T Δ R R * A * Δ R * d T d λ d R d λ d A d λ d Δ T d λ d Δ R d λ d R * d λ d A * d λ d Δ R * d λ d T d θ d R d θ d A d θ d Δ T d θ d Δ R d θ d R * d θ d A * d θ d Δ R * d θ d 2 T d λ 2 d 2 R d λ 2 d 2 A d λ 2 d 2 Δ T d λ 2 d 2 Δ R d λ 2 d 2 R * d λ 2 d 2 A * d λ 2 d 2 Δ R * d λ 2 d 2 T d θ 2 d 2 R d θ 2 d 2 A d θ 2 d 2 Δ T d θ 2 d 2 Δ R d θ 2 d 2 R * d θ 2 d 2 A * d θ 2 d 2 Δ R * d θ 2 d 2 T d λ d θ d 2 R d λ d θ d 2 A d λ d θ d 2 Δ T d λ d θ d 2 Δ R d λ d θ d 2 R * d λ d θ d 2 A * d λ d θ d 2 Δ R * d λ d θ
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 ) = 1.0 + A 1.0 + ( B / λ ) 2 , k ( λ ) = C n ( λ ) · ( D · λ + E λ + 1 λ 3 ) ,
[ n ( λ ) - i k ( λ ) ] 2 = 1.0 - A λ 2 B ( 1 - i C λ ) .
M = M [ n s , k s , n m , ( n i , k i , t i ) , i = 1 , 2 , L ] .
M = [ 1 m i = 1 m ( Q i T - Q i δ Q i ) k ] 1 / k ,             k = 1 , 2 , 4 or 16 ,
M = { [ n 1 , s , k 1 , s , n 1 , m , ( n 1 , i , k 1 , i , t t , i ) , i = 1 , 2 , L 1 ] , [ n 2 , s , k 2 , s , n 2 , m , ( n 2 , i , k 2. i , t 2 , i ) , i = 1 , 2 , L 2 ] , [ n j , s , k j , s , n j , m , ( n j , i , k j , i , t j , i ) , i = 1 , 2 , L j ] } .
M = { 1 m 1 + m 2 + + m j [ i = 1 m 1 ( Q 1 , i T - Q 1 , i δ Q 1 , i ) k + i = 1 m 2 ( Q 2 , i T - Q 2 , i δ Q 2 , i ) k + ] } 1 / k .
M = [ 1 m i = 1 m ( Q i T - Q i δ Q i ) k ] 1 / k ,
M * = w o M + j = 1 l w j d M d X j ,

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