Abstract

Any arbitrary generalized gradient-index interference coating (including homogeneous and inhomogeneous layers) possesses a digital configuration (sequence of thin high- or low-index layers), which is spectrally equivalent at all wavelengths. Such digital configurations are found directly from arbitrary-index profiles by using a prescribed two-layer high-low equivalent to a thin layer of arbitrary index. Digital configurations may be designed directly from given spectral requirements by using a flip-flop optimization scheme.

© 1985 Optical Society of America

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References

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  1. L. I. Epstein, “The Design of Optical Filters,” J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  2. P. H. Berning, “Use of Equivalent Films in the Design of Infrared Multilayer Antireflection Coatings,” J. Opt. Soc. Am. 52, 431 (1962).
    [CrossRef]
  3. W. H. Southwell, “Gradient-Index Antireflection Coatings,” Opt. Lett. 8, 584 (1983).
    [CrossRef] [PubMed]
  4. H. Sankur, W. H. Southwell, “Broadband Gradient-Index Antireflection Coating for ZnSe,” Appl. Opt. 23, 2770 (1984).
    [CrossRef] [PubMed]
  5. C. G. Snedaker, “New Numerical Thin-Film Synthesis Technique,” J. Opt. Soc. Am. 72, 1732A (1982).

1984 (1)

1983 (1)

1982 (1)

C. G. Snedaker, “New Numerical Thin-Film Synthesis Technique,” J. Opt. Soc. Am. 72, 1732A (1982).

1962 (1)

1952 (1)

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Figures (4)

Fig. 1
Fig. 1

Gradient-index antireflection coating and its 68-layer high–low digital equivalent. In the upper curve the ZnSe substrate is on the right and air on the left. The performances of the two configurations are almost identical.

Fig. 2
Fig. 2

Three-layer antireflection coating design where one layer of intermediate index is replaced by thin high–low equivalent pairs.

Fig. 3
Fig. 3

One hundred-layer flip-flop antireflection coating design. Intially all sublayers had high index. Convergence was reached in four passes.

Fig. 4
Fig. 4

One hundred-layer “flip-flop” antireflection coating design starting from an alternating high–low configuration. Convergence was achieved in two passes.

Equations (9)

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M = ( cos ϕ i N sin ϕ , i N sin ϕ cos ϕ ) ,
ϕ = 2 π λ N T ,
N T λ ,
M = ( 1 i 2 π T λ i 2 π λ N 2 T 1 ) .
M = [ 1 i 2 π λ ( t H + t L ) i 2 π λ ( n H 2 t H + n L 2 t L ) 1 ] .
T = t H + t L ,
N 2 = n H 2 t H + n L 2 t L t H + t L .
t H = ( N 2 n L 2 ) ( n H 2 n L 2 ) T ,
t L = T t H .

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