Abstract

Empirically derived formulas are given that allow the thin-film designer to estimate in advance the number of layers needed to meet various thin-film optical performance requirements. The estimation of peak optical density and width of higher-order blocker bands and their suppression are also discussed.

© 1996 Optical Society of America

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References

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  1. R. R. Willey, “Predicting achievable design performance of broadband antireflection coatings,” Appl. Opt. 32, 5447–5451 (1993).
    [CrossRef] [PubMed]
  2. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658 (1996).
    [CrossRef] [PubMed]
  3. A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
    [CrossRef]
  4. L. Young, “Multilayer interference filters with narrow stop bands,” Appl. Opt. 6, 297–315 (1967).
    [CrossRef] [PubMed]
  5. J. A. Dobrowolski, “Subtractive method of optical thin-film interference filter design,” Appl. Opt. 12, 1885–1893 (1973).
    [CrossRef] [PubMed]
  6. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988), Chap. 7.
  7. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (MacMillan, New York, 1986), p. 171.
  8. P. Baumeister, Military Standardization Handbook, Optical Design, MIL-HDBK-141 (Defense Supply Agency, Washington, D.C., 1962), Chap. 20, p. 45.

1996 (1)

1993 (1)

1973 (1)

1971 (1)

1967 (1)

Baumeister, P.

P. Baumeister, Military Standardization Handbook, Optical Design, MIL-HDBK-141 (Defense Supply Agency, Washington, D.C., 1962), Chap. 20, p. 45.

Dobrowolski, J. A.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (MacMillan, New York, 1986), p. 171.

Sullivan, B. T.

Thelen, A.

A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
[CrossRef]

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988), Chap. 7.

Tikhonravov, A. V.

Trubetskov, M. K.

Verly, P. G.

Willey, R. R.

Young, L.

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Figures (6)

Fig. 1
Fig. 1

Example with different numbers of layer pairs with indices of 2.3 and 1.46 plotted on a linear frequency scale that also illustrates that the peak OD increases almost linearly with additional layer pairs after the first few pairs. The values calculated from the approximation, cos0.5(1.315δgg) are plotted on the right-hand side of the 9 PAIRS curve.

Fig. 2
Fig. 2

Higher-order reflectance bands for one QWOT each of high- and low-index material per pair (equal thicknesses) showing that the block band repeats at each odd multiple of a QWOT and has an equal width of the band in Δg. The first cycle of the curve generated by approximation (5) for this case is superimposed on the plot.

Fig. 3
Fig. 3

Reflectance bands with a 3:1 ratio between the overall thickness of the layer pairs to the thinnest layer of the pair, which adds the second and fourth harmonics but suppresses the third and multiples of it, such as the sixth, etc. The first cycle of the curve generated by approximation (5) for this case is superimposed on the plot.

Fig. 4
Fig. 4

Reflectance bands as seen in Fig. 3 but with a 4:1 ratio, which also adds the second harmonic but suppresses the fourth, eighth, etc. The first cycle of the curve generated by approximation (5) for this case is superimposed on the plot.

Fig. 5
Fig. 5

Illustration that shows that approximation (5) gives the correct results for an A of 4.75, where the reflectance goes to zero at g = 4.75. The first cycle of the curve generated by approximation (5) for this case is superimposed on the plot.

Fig. 6
Fig. 6

Illustration that shows that approximation (5) gives the correct results even for a smaller value of A such as 1.5, where the reflectance goes to zero at g = 1.5. The first cycle of the curve generated by approximation (5) for this case is superimposed on the plot.

Equations (6)

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Δ g = 2 π arcsin ( n H - n L n H + n L )
OD P 2 log 1 / 2 [ ( n H n L ) p + ( n L n H ) p ] .
Δ OD 2 log ( n H n L ) .
ODBWP 1.57 Δ g Δ OD 2 log ( n H n L ) arcsin ( n H - n L n H + n L ) .
OD N OD E sin 1.2 ( π N g A ) ,             N = 1 , 2 , .
d g 2 3 ( Δ g OD P 1.74 ) .

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