Abstract

An iterative Monte Carlo thickness-varying strategy is presented and used to optimize normal-incidence thin-film multilayer designs and demonstrated for a variety of circumstances. The technique does not get trapped in local minima and, in principle, can home in on the best global design.

© 1986 Optical Society of America

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References

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  1. A. L. Bloom, Appl. Opt. 20, 67 (1981).
    [CrossRef]
  2. J. A. Dobrowolski, Appl. Opt. 4, 937 (1965).
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  5. P. Baumeister, R. Moore, K. Walsh, J. Opt. Soc. Am. 67, 1039 (1977).
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  7. J. A. Dobrowolski, Appl. Opt. 20, 74 (1981).
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  8. C. Holm, Appl. Opt. 18, 1978 (1979).
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  9. H. Zycha, Appl. Opt. 12, 979 (1973).
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  10. E. G. Stolov, Sov. J. Opt. Technol. 43, 352 (1976).
  11. Z. Les, J. Kuros, Thin Solid Films 46, 117 (1977).
    [CrossRef]
  12. J. F. Tang, Q. Zheng, J. Opt. Soc. Am. 72, 1522 (1982).
    [CrossRef]
  13. H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Hilger, Bristol, UK, 1981).
  14. B. Aspvall, R. E. Stone, J. Algorithms 1, 1 (1980).
    [CrossRef]
  15. P. R. Adby, M. A. H. Dempster, Introduction to Optimization Methods (Chapman and Hall, London, 1974).
  16. L. C. W. Dixon, G. P. Szegö, eds., Towards Global Optimization (North-Holland, New York, 1975).
  17. M. Chang, U. J. Gibson, Appl. Opt. 20, 74 (1981).
    [CrossRef]
  18. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
    [CrossRef]
  19. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  20. I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

1984 (1)

I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

1982 (1)

1981 (3)

1980 (1)

B. Aspvall, R. E. Stone, J. Algorithms 1, 1 (1980).
[CrossRef]

1979 (1)

1978 (1)

1977 (3)

P. Baumeister, R. Moore, K. Walsh, J. Opt. Soc. Am. 67, 1039 (1977).
[CrossRef]

A. L. Bloom, D. Fischer, J. Opt. Soc. Am. 67, 1429 (1977).

Z. Les, J. Kuros, Thin Solid Films 46, 117 (1977).
[CrossRef]

1976 (1)

E. G. Stolov, Sov. J. Opt. Technol. 43, 352 (1976).

1973 (2)

1965 (1)

1953 (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Adby, P. R.

P. R. Adby, M. A. H. Dempster, Introduction to Optimization Methods (Chapman and Hall, London, 1974).

Aspvall, B.

B. Aspvall, R. E. Stone, J. Algorithms 1, 1 (1980).
[CrossRef]

Baumeister, P.

Bloom, A. L.

A. L. Bloom, Appl. Opt. 20, 67 (1981).
[CrossRef]

A. L. Bloom, D. Fischer, J. Opt. Soc. Am. 67, 1429 (1977).

Bohachevsky, I. O.

I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

Borgogno, J. P.

Chang, M.

Cornwell, L. W.

Dempster, M. A. H.

P. R. Adby, M. A. H. Dempster, Introduction to Optimization Methods (Chapman and Hall, London, 1974).

Dobrowolski, J. A.

Fischer, D.

A. L. Bloom, D. Fischer, J. Opt. Soc. Am. 67, 1429 (1977).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Gibson, U. J.

Holm, C.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Kuros, J.

Z. Les, J. Kuros, Thin Solid Films 46, 117 (1977).
[CrossRef]

Les, Z.

Z. Les, J. Kuros, Thin Solid Films 46, 117 (1977).
[CrossRef]

Liddell, H. M.

H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Hilger, Bristol, UK, 1981).

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Moore, R.

Pegis, R. J.

Pelletier, E.

Rigler, A. K.

Rosenbluth, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Stolov, E. G.

E. G. Stolov, Sov. J. Opt. Technol. 43, 352 (1976).

Stone, R. E.

B. Aspvall, R. E. Stone, J. Algorithms 1, 1 (1980).
[CrossRef]

Tang, J. F.

Teller, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Viswanathan, V. K.

I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

Vogl, T. P.

Walsh, K.

Woodfin, G.

I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

Zheng, Q.

Zycha, H.

Appl. Opt. (6)

J. Algorithms (1)

B. Aspvall, R. E. Stone, J. Algorithms 1, 1 (1980).
[CrossRef]

J. Chem. Phys. (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953).
[CrossRef]

J. Opt. Soc. Am. (5)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

I. O. Bohachevsky, V. K. Viswanathan, G. Woodfin, Proc. Soc. Photo-Opt. Instrum. Eng. 485, 104 (1984).

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Sov. J. Opt. Technol. (1)

E. G. Stolov, Sov. J. Opt. Technol. 43, 352 (1976).

Thin Solid Films (1)

Z. Les, J. Kuros, Thin Solid Films 46, 117 (1977).
[CrossRef]

Other (3)

H. M. Liddell, Computer-Aided Techniques for the Design of Multilayer Filters (Hilger, Bristol, UK, 1981).

P. R. Adby, M. A. H. Dempster, Introduction to Optimization Methods (Chapman and Hall, London, 1974).

L. C. W. Dixon, G. P. Szegö, eds., Towards Global Optimization (North-Holland, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

First example. The optimized reflectance curve after 100 interations for the starting configuration of a seven-layer stack given in the text. The objective is to maximize R at λ = 1 μm, the reference wavelength. An additional low-index layer was added to the starting configuration of Ref. 1. The final layer thicknesses in full waves are indicated. Note that the extra-low-index layer thickness is forced to essentially zero while the remaining layers constitute approximately a quarter-wave stack.

Fig. 2
Fig. 2

Second example. Optimization after 100 iterations for the starting configuration of a three-layer stack given in the text. The line segment shows the target reflectance linear for the range 0.9 to 1.1 μm. The reference wavelength is 0.1 μm. The layer thickness in full waves are indicated.

Fig. 3
Fig. 3

Third example. Optimization after 250 iterations for the starting configuration of a 17-layer stack given in the text. The reference wavelength is 5 μm. Here maximum reflectance at 5 μm is desired, with zero reflectances at 4.5 and 5.5 μm. The final layer thicknesses in full waves are indicated.

Equations (4)

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M ( R ) = ( n = 1 p 1 w n R n 2 + m = 1 p 2 w m R m 2 ) 1 / 2
M ( R ) = [ n = 1 p w n ( R - R n ) 2 ] 1 / 2
G 0.6 H 0.4 L 0.6 H 1.2 L 0.8 H 1.6 L 1.6 H 0.4 L air ,
G A B C B 2 A B C B 2 A B C B 2 A B C B A air ,

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