Abstract

The refining method described in this paper is based, unlike the methods known up to now, on the combination of a special relaxation algorithm and a broad-band interpolation with respect to the layer parameters. It is shown that this combination is an essential requirement for the excellent convergence provided by this method, which is therefore applicable to rather complicated filter functions and gives useful solutions even for very rough initial filter designs. This algorithm is employed in the program package CALMIC (Calculation of Multilayer Interference Coatings) with considerable success. Two examples of applications illustrate the efficiency of the program.

© 1973 Optical Society of America

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References

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  1. P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958)
    [CrossRef]
  2. P. W. Baumeister, J. Opt. Soc. Am. 52, 1149 (1962)
    [CrossRef]
  3. J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475 (1961)
  4. J. A. Dobrowolski, Appl. Opt. 4, 937 (1965).
    [CrossRef]
  5. S. D. Smith, J. Opt. Soc. Am. 48, 43 (1958)
    [CrossRef]
  6. A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].
  7. L. Young, Appl. Opt. 4, 366 (1965)
    [CrossRef]
  8. H. Anders, Optik 25, 7 (1967)
  9. A. Thelen, J. Opt. Soc. Am. 61, 365 (1971)
    [CrossRef]
  10. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952)
    [CrossRef]
  11. H. Schröder, Z. Angew. Phys. 3, 53 (1951)
  12. A. Thelen in Physics of Thin Films, (G. Hass, Ed. (Academic Press, New York, 1969), Vol. 5, p. 58

1971 (1)

1967 (1)

H. Anders, Optik 25, 7 (1967)

1965 (2)

1962 (2)

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].

P. W. Baumeister, J. Opt. Soc. Am. 52, 1149 (1962)
[CrossRef]

1961 (1)

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

1958 (2)

1952 (1)

1951 (1)

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

Anders, H.

H. Anders, Optik 25, 7 (1967)

Baumeister, P. W.

Dobrowolski, J. A.

J. A. Dobrowolski, Appl. Opt. 4, 937 (1965).
[CrossRef]

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

Epstein, L. I.

Ermolaev, A. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].

Minkov, I. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].

Schröder, H.

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

Smith, S. D.

Thelen, A.

A. Thelen, J. Opt. Soc. Am. 61, 365 (1971)
[CrossRef]

A. Thelen in Physics of Thin Films, (G. Hass, Ed. (Academic Press, New York, 1969), Vol. 5, p. 58

Vlasov, A. G.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].

Young, L.

Appl. Opt. (2)

J. Opt. Soc. Am. (6)

Opt. Spektrosk. (1)

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962) [Opt. Spectrosc. 13, 142 (1962)].

Optik (1)

H. Anders, Optik 25, 7 (1967)

Z. Angew. Phys. (1)

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

Other (1)

A. Thelen in Physics of Thin Films, (G. Hass, Ed. (Academic Press, New York, 1969), Vol. 5, p. 58

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Figures (3)

Fig. 1
Fig. 1

Transmittance of an improved eighteen layer blocking filter. The starting design is represented by a dashed line, the first iteration by a dotted line, and the final design (third iteration) by a solid line. The construction parameters are given in Table I.

Fig. 2
Fig. 2

Decrease of the merit function D for successive steps (from layer to layer) of the first iteration of the refining process applied to the blocking filter whose transmittance and construction parameters are shown in Fig. 1 and Table I, respectively. Note that only layers 1, 2, 3 and 16, 17, 18 have been subjected to the refining procedure.

Fig. 3
Fig. 3

Transmittance of a minus filter that has been developed by evolution using a eight-layer stack (dashed line) found by automatic synthesis as a starting system. Two such systems brought into interferential contact and refined give the performance shown by the dotted line. Four such systems, finally, yield the filter curve shown by the solid line. The corresponding construction parameters are given in Table II.

Tables (2)

Tables Icon

Table I Physical Thickness of Each Layer of the Dielectric Stack Whose Transmittance is Shown in Fig. 1, Corresponding to the Various Stages of the Refining Process.

Tables Icon

Table II Physical Thickness of Each Layer of the Dielectric Stack Whose Transmittance is Shown in Fig. 3, Corresponding to the Various Stages of the Evolution.

Equations (4)

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R = 1 - { 1 / [ a 0 + a 1 · cos ( φ + 4 π n t / λ ) ] } .
D lin = 1 L i = 1 L [ T ( λ i ) - T d ( λ i ) - Δ T ( λ i ) Δ T ( λ i ) ] 2 ,
D a v = j = 1 N [ 1 λ 2 j - λ 1 j | λ 1 j λ 2 j [ T ( λ ) - T d ( λ ) ] d λ | - Δ T j ¯ Δ T j ¯ ] 2
R = 1 - ( 1 / m = 0 M a m · cos α m ) .

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