Abstract

A simple extension of techniques used in designing conventional single-peak narrow-band filters permits the design of filters having two or more peaks. The design procedure and monitoring techniques are discussed. An example of an actual filter produced by using this technique is presented.

© 1982 Optical Society of America

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References

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  1. A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 50, 1533–1538 (1966).
    [Crossref]
  2. C. Jacobs, “Dielectric square bandpass design,” Appl. Opt. 20, 1039–1042 (1981).
    [Crossref] [PubMed]
  3. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
    [Crossref]
  4. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
    [Crossref]
  5. H. A. MacLeod and D. Richmond, “The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 21, 429–443 (1974).
    [Crossref]

1981 (1)

1974 (1)

H. A. MacLeod and D. Richmond, “The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 21, 429–443 (1974).
[Crossref]

1972 (2)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
[Crossref]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

1966 (1)

A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 50, 1533–1538 (1966).
[Crossref]

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Fornier, A.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Jacobs, C.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

MacLeod, H. A.

H. A. MacLeod and D. Richmond, “The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 21, 429–443 (1974).
[Crossref]

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
[Crossref]

Pelletier, E.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Richmond, D.

H. A. MacLeod and D. Richmond, “The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 21, 429–443 (1974).
[Crossref]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Thelen, A.

A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 50, 1533–1538 (1966).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 50, 1533–1538 (1966).
[Crossref]

Opt. Acta (2)

H. A. MacLeod and D. Richmond, “The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 21, 429–443 (1974).
[Crossref]

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
[Crossref]

Thin Solid Films (1)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the auto-correlation of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Equivalent admittance and phase thickness plotted against g for the symmetrical period HLHLHLH. (H indicates a quarter wave of index 2.52, L of 1.30.)

Fig. 2
Fig. 2

Calculated performance of the design: glass/(HLHLHLH)3/glass and glass/(HLHLHLH)4/glass, where H and L are defined in Fig. 1 and the index of glass is 1.52.

Fig. 3
Fig. 3

Calculated performance of the design: glass/HL(HLHLHLH)3LH/glass and glass/H(HLHLHLH)3H/glass with indices as in Figs. 1 and 2, showing (a) the decrease in half-width produced by reflection from additional coatings added to the basic three-period structure and (b) the increase produced by reflection-reducing coatings.

Fig. 4
Fig. 4

A double-cavity double-peak filter formed by coupling two of the cavities of Fig. 2(a): glass/(HLHLHLH)3L(HLHLHLH)3L/glass.

Fig. 5
Fig. 5

The computed performance of the design: glass/(HLHLH)3/glass, with reference wavelength 420 nm and indices including dispersion, as given in the text.

Fig. 6
Fig. 6

The effect of random errors of 2.5% standard deviation in the turning-value monitoring of the filter shown in Fig. 5, assuming that all layers are monitored on the same substrate and at the reference wavelength, 420 nm. The scatter is so great that only parts of the filter characteristic can be seen.

Fig. 7
Fig. 7

The effects of random errors of 2.5% standard deviation in the turning-value monitoring of the filter of Figs. 5 and 6. All layers are assumed to be deposited on the same substrate, but the monitoring wavelength is switched from 420 to 436 nm at the start of the ninth layer.

Fig. 8
Fig. 8

The measured transmittance of an experimental version of the filter of Figs. 57, produced by the technique of Fig. 7 involving a monitoring-wavelength change at the ninth layer. The mercury spectrum is also shown for comparison with the positions of the two peaks.

Tables (3)

Tables Icon

Table 1 Scheme for Producing Number and Positions of Multiple Peaks

Tables Icon

Table 2 Possible Monitoring Scheme for the Two-Peak Mercury-Line Filter

Tables Icon

Table 3 Theoretical Thicknesses Using the Two Monitoring Schemes Finally Chosen

Equations (23)

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

2 π D / λ = m π ,
D = m λ / 2 ,
R = ( n m - n n m + n ) 2 ,
Δ λ = ( 1 - R ) m π R λ p .
2 D [ 1 m - 1 ( m + 1 ) ] = 2 D m ( m + 1 ) .
2 D / ( m + 1 ) = λ 1
2 D / m = λ 2 ,
1 2 D = 1 λ 1 - 1 λ 2 .
n E = n A n C n M n B n D n L
ϕ E = q π 2 ,
n E = n H ( q + 1 ) / 2 n L ( q - 1 ) / 2
n E = n L ( q + 1 ) / 2 n H ( q - 1 ) / 2 ,
ϕ E = q π 2
Δ g = Δ λ λ 0 = 4 ( n H - n L ) n L ( q - 1 ) / 2 π n H ( q + 1 ) / 2
( H L H L H H ) 3
( H L ) q ( H L H L H H ) 3 ( L H ) q ,
H ( H L H L H H ) 3 H .
n = A + ( B / λ 2 ) + ( C / λ 4 )             ( zinc sulfide ) ,
A = 2.2524 , B = 0.1575 × 10 5 , C = 0.5422 × 10 10 ,
n = 1.3000 ( cryolite ) , n = 1.5200 ( substrate ) .
glass / ( H L H L H ) 3 / glass ,
( H L H L H ) 3
( H L H L H ) 3 L ( H L H L H ) 3 .