Abstract

Considerable broadening of the reflectance band of a multilayer stack may be obtained by staggering the layer thicknesses in such a way that they form either an arithmetic or geometric progression. Results are shown for asymmetric and symmetric filters of 15, 25, and 35 layers. The presence of the narrowband transmission peaks exhibited by the symmetric filters is explained, and the advantages of the use of this type of filter as an interference filter is discussed.

© 1966 Optical Society of America

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References

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  1. W. Weinstein, Vacuum 4, 3 (1954).
    [CrossRef]
  2. P. W. Baumeister, J. M. Stone, J. Opt. Soc. Am. 46, 228 (1956).
    [CrossRef]
  3. S. Penselin, A. Steudel, Z. Physik 142, 21 (1955).
    [CrossRef]
  4. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth Scientific Publications, Ltd., London, 1955).
  5. P. W. Baumeister, F. A. Jenkins, J. Opt. Soc. Am. 47, 57 (1957).
    [CrossRef]
  6. P. W. Baumeister, F. A. Jenkins, M. A. Jeppersen, J. Opt. Soc. Am. 49, 1188 (1959).
    [CrossRef]
  7. P. Giacomo, P. W. Baumeister, F. A. Jenkins, Proc. Phys. Soc. 73, 480 (1959).
    [CrossRef]

1959

P. W. Baumeister, F. A. Jenkins, M. A. Jeppersen, J. Opt. Soc. Am. 49, 1188 (1959).
[CrossRef]

P. Giacomo, P. W. Baumeister, F. A. Jenkins, Proc. Phys. Soc. 73, 480 (1959).
[CrossRef]

1957

1956

1955

S. Penselin, A. Steudel, Z. Physik 142, 21 (1955).
[CrossRef]

1954

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

Baumeister, P. W.

Giacomo, P.

P. Giacomo, P. W. Baumeister, F. A. Jenkins, Proc. Phys. Soc. 73, 480 (1959).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth Scientific Publications, Ltd., London, 1955).

Jenkins, F. A.

Jeppersen, M. A.

Penselin, S.

S. Penselin, A. Steudel, Z. Physik 142, 21 (1955).
[CrossRef]

Steudel, A.

S. Penselin, A. Steudel, Z. Physik 142, 21 (1955).
[CrossRef]

Stone, J. M.

Weinstein, W.

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

J. Opt. Soc. Am.

Proc. Phys. Soc.

P. Giacomo, P. W. Baumeister, F. A. Jenkins, Proc. Phys. Soc. 73, 480 (1959).
[CrossRef]

Vacuum

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

Z. Physik

S. Penselin, A. Steudel, Z. Physik 142, 21 (1955).
[CrossRef]

Other

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth Scientific Publications, Ltd., London, 1955).

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Figures (8)

Fig. 1
Fig. 1

Thicknesses of the layers for each type of filter: (a) asymmetric geometric; (b) asymmetric arithmetic; (c) symmetric geometric; (d) symmetric arithmetic.

Fig. 2
Fig. 2

15-layer asymmetric geometric filter. Reflectance (continuous curve) and phase change on reflection (broken curve).

Fig. 3
Fig. 3

25-layer asymmetric geometric filter. Reflectance (continuous curve) and phase change on reflection (broken curve).

Fig. 4
Fig. 4

35-layer asymmetric geometric filter. Reflectance (continuous curve) and phase change on reflection (broken curve).

Fig. 5
Fig. 5

25-layer symmetric geometric filter. Reflectance.

Fig. 6
Fig. 6

35-layer symmetric geometric filter. Reflectance.

Fig. 7
Fig. 7

Graph showing intersections of curves of ψ (σ) and 2πntσ vs σ/σ0 for 25-layer symmetric geometric filter.

Fig. 8
Fig. 8

Graph showing intersections of curves of ψ(σ) and 2ϕntσ vs σ/σ0 for 35-layer symmetric geometric filter.

Tables (1)

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Table I Comparison of Bandwidths for Various Types of Broad-Band Reflecting Filters

Equations (6)

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Δ σ σ 0 = 4 π arcsin ( n H - n L n H + n L ) ,
4 π n t σ - 2 ψ = 2 m π ,
T ( σ ) = T 0 ( σ ) 1 1 + F ( σ ) sin 2 θ ( σ ) ,
T 0 ( σ ) = [ 1 - R 1 ( σ ) ] [ 1 - R 2 ( σ ) ] [ 1 - R ( σ ) ] 2
F ( σ ) = 4 R ( 1 - R ) 2 , R = ( R 1 R 2 ) 1 / 2 , θ = 2 π n t σ - ψ ( σ ) .
Δ σ = 1 - R R 1 / 2 1 ( 2 π n t σ - ψ / σ ) .

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