Abstract

The various methods for the synthesis of optical thin film systems with prescribed properties are reviewed. One general approach is to refine numerically the properties of an initial system. In many problems, however, the choice of a suitable starting design for refinement is not at all obvious. The present paper describes a computer program for the completely automatic design of optical thin film systems by evolution which does not require a starting design. Apart from the specification of the desired optical properties of the system, the only input data necessary are the refractive indexes of the substrate, the medium, and the thin film materials that may be employed for the construction of the coating. Optical properties that may be specified at present include transmittance, reflectance, phase changes on transmission and reflection, and the first and second derivatives of these quantities, with respect to wavenumber and angle of incidence. Several examples are given to illustrate the performance of this program. Ways are indicated in which this automatic design program can be improved further in the future.

© 1965 Optical Society of America

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References

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  1. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).
  2. H. Mayer, Physik Dünner Schichten (Wissenschaftliche Verlagsgesellshaft, Stuttgart, 1950).
  3. P. W. Baumeister, “Applications of Thin Film Coatings” in Optical Design, MIL-HDBK-141, (DOD, Washington, D.C., 1962).
  4. A. Thelen, J. Opt. Soc. Am. 53, 1266 (1963).
    [CrossRef]
  5. J. J. Vera, Optica Acta 11, 315 (1964).
    [CrossRef]
  6. A. Herpin, Compt. Rend. 225, 182 (1947).
  7. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  8. S. D. Smith, J. Opt. Soc. Am. 48, 43 (1958).
    [CrossRef]
  9. P. H. Berning, J. Opt. Soc. Am. 52, 431 (1962).
    [CrossRef]
  10. H. Schröder, Z. Angew. Phys. 3, 53 (1951).
  11. H. Pohlack, Jenaer Jahrbuch (Zeiss, Jena, 1952), p. 181.
  12. R. G. Pegis, J. Opt. Soc. Am. 51, 1255 (1961).
    [CrossRef]
  13. P. G. Kard, Opt. i Spektroskopiya 16, 914 (1964);Opt. Spectry. 16, 497 (1964).
  14. G. Tricoles, J. Phys. 25, 262 (1964).
    [CrossRef]
  15. L. Young, J. Opt. Soc. Am. 51, 967 (1961).
    [CrossRef]
  16. J. Seeley, Proc. Phys. Soc. (London) 78, 998 (1961).
    [CrossRef]
  17. S. Fujiwara, J. Opt. Soc. Am. 53, 880, 1317 (1963).
    [CrossRef]
  18. R. Jacobsson, J. O. Martensson, Proc. Kyoto Meeting on Photographic and Spectroscopic Optics, 1964.
  19. P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
    [CrossRef]
  20. P. W. Baumeister, J. Opt. Soc. Am. 51, 1149 (1962).
    [CrossRef]
  21. R. T. MacIntyre, J. Opt. Soc. Am. 52, 1310 (1960).
  22. A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).
  23. N. Kimura, Oyo Buturi 31, 739 (1962).*
  24. N. Kimura, Oyo Buturi 32, 119 (1963).*
  25. Z. Knittl, M. Král, Optica Acta 9, 295 (1962).
    [CrossRef]
  26. Z. Knittl, Proc. 2nd Optical Conference of the Hungarian Society for Optics, Acoustics and Film Technics, Budapest, 1963.
  27. Z. Knittl, J. Phys. 25, 245 (1964).
    [CrossRef]
  28. J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475 (1961).
  29. Z. N. Elsner, Opt. i Spektroskopiya 17, 446 (1964);Opt. Spectry. 17, 238 (1964).
  30. A. V. Shatilov, L. P. Tyutikova, Opt. i Spektroskopiya 14, 426 (1963);Opt. Spectry. 14, 227 (1963).
  31. J. A. Dobrowolski, J. Opt. Soc. Am. 54, 1387 (1964).
  32. W. Weinstein, Vacuum 4, 3 (1954).
    [CrossRef]

1964 (6)

J. J. Vera, Optica Acta 11, 315 (1964).
[CrossRef]

Z. Knittl, J. Phys. 25, 245 (1964).
[CrossRef]

Z. N. Elsner, Opt. i Spektroskopiya 17, 446 (1964);Opt. Spectry. 17, 238 (1964).

J. A. Dobrowolski, J. Opt. Soc. Am. 54, 1387 (1964).

P. G. Kard, Opt. i Spektroskopiya 16, 914 (1964);Opt. Spectry. 16, 497 (1964).

G. Tricoles, J. Phys. 25, 262 (1964).
[CrossRef]

1963 (4)

A. Thelen, J. Opt. Soc. Am. 53, 1266 (1963).
[CrossRef]

S. Fujiwara, J. Opt. Soc. Am. 53, 880, 1317 (1963).
[CrossRef]

A. V. Shatilov, L. P. Tyutikova, Opt. i Spektroskopiya 14, 426 (1963);Opt. Spectry. 14, 227 (1963).

N. Kimura, Oyo Buturi 32, 119 (1963).*

1962 (5)

Z. Knittl, M. Král, Optica Acta 9, 295 (1962).
[CrossRef]

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).

N. Kimura, Oyo Buturi 31, 739 (1962).*

P. H. Berning, J. Opt. Soc. Am. 52, 431 (1962).
[CrossRef]

P. W. Baumeister, J. Opt. Soc. Am. 51, 1149 (1962).
[CrossRef]

1961 (4)

R. G. Pegis, J. Opt. Soc. Am. 51, 1255 (1961).
[CrossRef]

L. Young, J. Opt. Soc. Am. 51, 967 (1961).
[CrossRef]

J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475 (1961).

J. Seeley, Proc. Phys. Soc. (London) 78, 998 (1961).
[CrossRef]

1960 (1)

R. T. MacIntyre, J. Opt. Soc. Am. 52, 1310 (1960).

1958 (2)

1954 (1)

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

1952 (1)

1951 (1)

H. Schröder, Z. Angew. Phys. 3, 53 (1951).

1947 (1)

A. Herpin, Compt. Rend. 225, 182 (1947).

Baumeister, P. W.

P. W. Baumeister, J. Opt. Soc. Am. 51, 1149 (1962).
[CrossRef]

P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
[CrossRef]

P. W. Baumeister, “Applications of Thin Film Coatings” in Optical Design, MIL-HDBK-141, (DOD, Washington, D.C., 1962).

Berning, P. H.

Dobrowolski, J. A.

J. A. Dobrowolski, J. Opt. Soc. Am. 54, 1387 (1964).

J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475 (1961).

Elsner, Z. N.

Z. N. Elsner, Opt. i Spektroskopiya 17, 446 (1964);Opt. Spectry. 17, 238 (1964).

Epstein, L. I.

Ermolaev, A. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).

Fujiwara, S.

S. Fujiwara, J. Opt. Soc. Am. 53, 880, 1317 (1963).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

Herpin, A.

A. Herpin, Compt. Rend. 225, 182 (1947).

Jacobsson, R.

R. Jacobsson, J. O. Martensson, Proc. Kyoto Meeting on Photographic and Spectroscopic Optics, 1964.

Kard, P. G.

P. G. Kard, Opt. i Spektroskopiya 16, 914 (1964);Opt. Spectry. 16, 497 (1964).

Kimura, N.

N. Kimura, Oyo Buturi 32, 119 (1963).*

N. Kimura, Oyo Buturi 31, 739 (1962).*

Knittl, Z.

Z. Knittl, J. Phys. 25, 245 (1964).
[CrossRef]

Z. Knittl, M. Král, Optica Acta 9, 295 (1962).
[CrossRef]

Z. Knittl, Proc. 2nd Optical Conference of the Hungarian Society for Optics, Acoustics and Film Technics, Budapest, 1963.

Král, M.

Z. Knittl, M. Král, Optica Acta 9, 295 (1962).
[CrossRef]

MacIntyre, R. T.

R. T. MacIntyre, J. Opt. Soc. Am. 52, 1310 (1960).

Martensson, J. O.

R. Jacobsson, J. O. Martensson, Proc. Kyoto Meeting on Photographic and Spectroscopic Optics, 1964.

Mayer, H.

H. Mayer, Physik Dünner Schichten (Wissenschaftliche Verlagsgesellshaft, Stuttgart, 1950).

Minkov, I. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).

Pegis, R. G.

Pohlack, H.

H. Pohlack, Jenaer Jahrbuch (Zeiss, Jena, 1952), p. 181.

Schröder, H.

H. Schröder, Z. Angew. Phys. 3, 53 (1951).

Seeley, J.

J. Seeley, Proc. Phys. Soc. (London) 78, 998 (1961).
[CrossRef]

Shatilov, A. V.

A. V. Shatilov, L. P. Tyutikova, Opt. i Spektroskopiya 14, 426 (1963);Opt. Spectry. 14, 227 (1963).

Smith, S. D.

Thelen, A.

Tricoles, G.

G. Tricoles, J. Phys. 25, 262 (1964).
[CrossRef]

Tyutikova, L. P.

A. V. Shatilov, L. P. Tyutikova, Opt. i Spektroskopiya 14, 426 (1963);Opt. Spectry. 14, 227 (1963).

Vera, J. J.

J. J. Vera, Optica Acta 11, 315 (1964).
[CrossRef]

Vlasov, A. G.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).

Weinstein, W.

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

Young, L.

Compt. Rend. (1)

A. Herpin, Compt. Rend. 225, 182 (1947).

J. Opt. Soc. Am. (12)

J. Phys. (2)

Z. Knittl, J. Phys. 25, 245 (1964).
[CrossRef]

G. Tricoles, J. Phys. 25, 262 (1964).
[CrossRef]

Opt. i Spektroskopiya (4)

P. G. Kard, Opt. i Spektroskopiya 16, 914 (1964);Opt. Spectry. 16, 497 (1964).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. i Spektroskopiya 13, 259 (1962);Opt. Spectry. 13, 142 (1962).

Z. N. Elsner, Opt. i Spektroskopiya 17, 446 (1964);Opt. Spectry. 17, 238 (1964).

A. V. Shatilov, L. P. Tyutikova, Opt. i Spektroskopiya 14, 426 (1963);Opt. Spectry. 14, 227 (1963).

Optica Acta (2)

Z. Knittl, M. Král, Optica Acta 9, 295 (1962).
[CrossRef]

J. J. Vera, Optica Acta 11, 315 (1964).
[CrossRef]

Oyo Buturi (2)

N. Kimura, Oyo Buturi 31, 739 (1962).*

N. Kimura, Oyo Buturi 32, 119 (1963).*

Proc. Phys. Soc. (London) (1)

J. Seeley, Proc. Phys. Soc. (London) 78, 998 (1961).
[CrossRef]

Vacuum (1)

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

Z. Angew. Phys. (1)

H. Schröder, Z. Angew. Phys. 3, 53 (1951).

Other (6)

H. Pohlack, Jenaer Jahrbuch (Zeiss, Jena, 1952), p. 181.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

H. Mayer, Physik Dünner Schichten (Wissenschaftliche Verlagsgesellshaft, Stuttgart, 1950).

P. W. Baumeister, “Applications of Thin Film Coatings” in Optical Design, MIL-HDBK-141, (DOD, Washington, D.C., 1962).

Z. Knittl, Proc. 2nd Optical Conference of the Hungarian Society for Optics, Acoustics and Film Technics, Budapest, 1963.

R. Jacobsson, J. O. Martensson, Proc. Kyoto Meeting on Photographic and Spectroscopic Optics, 1964.

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Figures (7)

Fig. 1
Fig. 1

Block diagram of the flow of calculations in the main program.

Fig. 2
Fig. 2

Synthesis of a system simulating the properties of a seven-layer λ/4 stack. Curves 0–4 represent the performance of the designs at the start and after the first, second, third, and fourth iteration, respectively.

Fig. 3
Fig. 3

Synthesis of a narrow band transmission filter. The curves represent the performance at the start (0) and the first, third, fourth, fifth, and seventh iterations.

Fig. 4
Fig. 4

Synthesis of an achromatized semireflecting beam splitter with a transmittance of 50% for normal incidence of light. The curves represent the performance of the designs described in Table III.

Fig. 5
Fig. 5

Filter in which the reflectance varies linearly with wavelength.

Fig. 6
Fig. 6

First attempt at the synthesis of an achromatized antireflection coating for wide-angle use. Performance of an uncoated glass surface and a two-layer coating for several angles of incidence.

Fig. 7
Fig. 7

Shatilov and Tyutikova's problem. Curve 1, Shatilov and Tyutikova's system. Curve 2, performance of the eleven-layer design obtained after nine iterations with the present program.

Tables (4)

Tables Icon

Table I Synthesis of a System Simulating the Properties of a Seven-Layer λ/4 Stack

Tables Icon

Table II Synthesis of a Narrow Band Transmission Filter

Tables Icon

Table III Achromatic Beam Splitter with a 50% Transmittance for Normal Incidence of Light

Tables Icon

Table IV Optical Thicknesses (in μ) and Refractive Indexes of the Multilayer Systems described in Sections D–F

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

R , d R d σ , d R d θ , d 2 R d σ 2 , d 2 R d θ 2 , d 2 R d θ d σ , T , d T d σ , d T d θ , d 2 T d σ 2 , d 2 T d θ 2 , d 2 T d θ d σ , Δ R , d Δ R d σ , d Δ R d θ , d 2 Δ R d σ 2 , d 2 Δ R d θ 2 , d 2 Δ R d θ d σ , Δ T , d Δ T d σ , d Δ T d θ , d 2 Δ T d σ 2 , d 2 Δ T d θ 2 , d 2 Δ T d θ d σ .
M = M ( n 1 , t 1 ; n 2 , t 2 ; . . . n i , t i ; . . . n L , t L ) .
δ p i = M p i / 2 M p i 2 .
M = M ( p + k Δ p )
( n t ) = ( n t ) i + ( n t ) i + 1 ,
n = [ ( n t ) i + ( n t ) i + 1 ] / ( t i + t i + 1 ) ,
M = [ 1 m i = 1 m ( | P i D P i | T i ) k ] 1 / k .

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