Abstract

The equivalent-layer concept is used to develop a method to design multilayer interference filters with relatively smooth high-transmittance regions on both sides of the rejection band. Most of the resulting designs have the interesting property of having low ripple in all high-transmittance regions. The characteristics of several typical designs are presented.

© 1971 Optical Society of America

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References

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  1. W. Geffcken, West German Patent No. 902 191, issued 15March1954.
  2. H. Schröder, Z. Angew. Physik 3, 53 (1951).
  3. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  4. L. Young, J. Opt. Soc. Am. 51, 967 (1961).
    [CrossRef]
  5. L. Young and E. G. Cristal, Appl. Opt. 5, 77 (1966).
    [CrossRef] [PubMed]
  6. A. Thelen, J. Opt. Soc. Am. 56, 1533 (1966).
    [CrossRef]
  7. P. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
    [CrossRef]
  8. J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475 (1961).
  9. H. A. Macleod, Thin-Film Optical Filters (Hilger, London; American Elsevier, New York, 1969).
  10. L. Young, Appl. Opt. 6, 297 (1967).
    [CrossRef] [PubMed]
  11. G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw–Hill, New York, 1964).
  12. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).
  13. A. Thelen, J. Opt. Soc. Am. 53, 1266 (1963).
    [CrossRef]

1967 (1)

1966 (2)

1963 (1)

1961 (2)

L. Young, J. Opt. Soc. Am. 51, 967 (1961).
[CrossRef]

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

1958 (1)

1952 (1)

1951 (1)

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

Baumeister, P.

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

Cristal, E. G.

Dobrowolski, J. A.

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

Epstein, L. I.

Geffcken, W.

W. Geffcken, West German Patent No. 902 191, issued 15March1954.

Jones, E. M. T.

G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw–Hill, New York, 1964).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Hilger, London; American Elsevier, New York, 1969).

Matthaei, G. L.

G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw–Hill, New York, 1964).

Schröder, H.

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

Thelen, A.

Young, L.

L. Young, Appl. Opt. 6, 297 (1967).
[CrossRef] [PubMed]

L. Young and E. G. Cristal, Appl. Opt. 5, 77 (1966).
[CrossRef] [PubMed]

L. Young, J. Opt. Soc. Am. 51, 967 (1961).
[CrossRef]

G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw–Hill, New York, 1964).

Appl. Opt. (2)

J. Opt. Soc. Am. (6)

Z. Angew. Physik (1)

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

Other (4)

W. Geffcken, West German Patent No. 902 191, issued 15March1954.

H. A. Macleod, Thin-Film Optical Filters (Hilger, London; American Elsevier, New York, 1969).

G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw–Hill, New York, 1964).

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

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Figures (12)

F. 1
F. 1

Transmittance of the quarter-wave stack 1.56|H (LH)9| 1.56 with nH = 2.34 and nL = 1.56.

F. 2
F. 2

Normalized equivalent index of the structure A/2 B A/2 for three index ratios ρ = n B / n A = 3 2, 4 3, 7/6. The junction of the dotted line with the respective equivalent index curve is the point where the equivalent thickness is 3λ0/8.

F. 3
F. 3

Two thin-film structures with equal transmittance.

F. 4
F. 4

Transmittance of the design 1.56 |(A/2 B2 A/2)2 (A/2 B1 A/2)6 (A/2 B2 A/2)2| 1.56 with nA = 1.56, nB1 = 2.34, and nB2 = 1.91.

F. 5
F. 5

Transmittance of the design 1.56 |(A/2 B3 A/2) (A/2 B2 A/2) (A/2 B1 A/2)6 (A/2 B2 A/2) (A/2 B3 A/2)| 1.56 with nA = 1.56, nB1 = 2.34, nB2 = 1.95, and nB3 = 1.86 (solid curve) compared to the design of Fig. 4 (dotted curve) and the design of Fig. 6 (line–dot–line curve) in the high-transmittance region.

F. 6
F. 6

Transmittance of the design 1.56 |(A/2 B5 A/2) (A/2 B4 A/2) (A/2 B3 A/2) (A/2 B2 A/2) (A/2 B1 A/2)6 (A/2 B2 A/2) (A/2 B3 A/2) (A/2 B4 A/2) (A/2 B5 A/2)| 1.56 with nA = 1.56, nB1 = 2.34, nB2 = 2.10, nB3 = 2.02, nB4 = 1.85, nB5 = 1.74.

F. 7
F. 7

Transmittance of the design 4.00|(A/2 B5 A/2) (A/2 B4 A/2) (A/2 B3 A/2) (A/2 B2 A/2) (A/2 B1 A/2)6 (A/2 B2 A/2) (A/2 B3 A/2) (A/2 B4 A/2) (A/2 B5 A/2)| 4.00 with nA = 4.00, nB1 =1.80, nB2 = 1.99, nB3 = 2.35, nB4 = 2.96, and nB5 = 3.61.

F. 8
F. 8

Transmittance of the design 1.52 |(3B2 3A)2 (3B1 3A)6 (3B2 3A)2 2B2 B3| 1.00 with nA = 1.56, nB1 = 2.34, nB2 = 1.91, nB3 = 1.38, and λ0 = 530 nm.

F. 9
F. 9

Normalized equivalent index of the structure A B A for three index ratios, ρ = n B / n A = 3 2, 4 3, 7/6.

F. 10
F. 10

Transmittance of the design 1.56 |(A B5 A) (A B4 A) (A B3 A) (A B2 A) (A B1 A)6 (A B2 A) (A B3 A) (A B4 A) (A B5 A)| 1.56 with nA = 1.56, nB1 = 2.34, nB2 = 2.184, nB3 = 2.028, nB4 = 1.872, and nB5 = 1.716.

F. 11
F. 11

Normalized equivalent index of the structures aA/2 bB aA/2 with nB/nA = const = 1.5 and ξ = (ba)/(b + a) = 0, 0.2, 0.4, 0.6, 0.8.

F. 12
F. 12

Transmittance of the design 1.56 |(a1A/2 b1B a1A/2) (a2A/2 b2B a2A/2) ⋯ (a10A/2 b10B a10A/2)6 ⋯ (a1A/2 b1B a1A/2)| 1.56 with nA = 1.56, nB = 2.34, and a1 = 1.90, a2 = 1.80, ⋯ a10 = 1.00, and b1 = 0.10, b2 = 0.20, ⋯ b10 = 1.00.

Equations (6)

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N / n A = [ cos π λ 0 2 λ 1 n B / n A 1 + n B / n A cos π λ 0 2 λ + 1 n B / n A 1 + n B / n A ] 1 2
Γ = λ 0 π arcos ( 1 ( 1 + n B / n A ) 2 2 n B / n A sin 2 π λ 0 2 λ ) .
N ( λ 0 / λ ) n A = n A N ( 2 λ 0 / λ ) or N ( λ 0 / λ ) = n A 2 N ( 2 λ 0 / λ )
T R B 4 ( n S n M / n A 2 ) ( n B / n A ) 2 ν n A > n B
T R B 4 ( n A 2 / n S n M ) ( n A / n B ) 2 ν n B > n A .
N ( n A , n B 2 ) = [ n A N ( n A , n B 1 ) ] 1 2 ,