Abstract

The design of mirrors composed of multilayer stacks of dielectric films is considered. High reflectance over an extended spectral range is attained by positioning the stacks so that on a wavelength scale their high-reflectance bands are either contiguous or overlapping. Certain precautions must be taken in the choice of stacks to avoid deep-reflectance minima from developing within the extended high-reflectance region. Some of these are discussed and illustrated with both computional and experimental curves. The techniques of extending the high-reflectance regions are applicable not only to mirrors, but also to low- and high-pass cutoff filters and to multilayer polarizers.

© 1966 Optical Society of America

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References

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  1. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 69.
  2. See ref. 1, p. 61.
  3. F. Abelès, Ann. phys. 5, 604 (1950).
  4. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  5. J. S. Seeley, S. D. Smith, Appl. Opt. 5, 81 (1966).
    [CrossRef] [PubMed]
  6. F. A. Jenkins, J. Phys. Radium 19, 301 (1958).
    [CrossRef]
  7. H. H. Schroeder, A. F. Turner, J. Soc. Motion Picture Television Engrs. 69, 351 (1960).
  8. P. W. Baumeister, Handbook of Optical Design (U. S. Defense Documentation Center, Philadelphia, Pennsylvania1963), Chap. 20, p. 20–8.
  9. S. M. MacNeille, U.S. Patent2,403,731 (9July1946).
  10. R. S. Sokolova, T. N. Krylova, Opt. Spectry. (USSR) (English Transl.) 14, 213 (1963).
  11. S. D. Smith, J. Opt. Soc. Am. 48, 43 (1958).
    [CrossRef]

1966 (1)

1963 (1)

R. S. Sokolova, T. N. Krylova, Opt. Spectry. (USSR) (English Transl.) 14, 213 (1963).

1960 (1)

H. H. Schroeder, A. F. Turner, J. Soc. Motion Picture Television Engrs. 69, 351 (1960).

1958 (2)

F. A. Jenkins, J. Phys. Radium 19, 301 (1958).
[CrossRef]

S. D. Smith, J. Opt. Soc. Am. 48, 43 (1958).
[CrossRef]

1952 (1)

1950 (1)

F. Abelès, Ann. phys. 5, 604 (1950).

Abelès, F.

F. Abelès, Ann. phys. 5, 604 (1950).

Baumeister, P. W.

P. W. Baumeister, Handbook of Optical Design (U. S. Defense Documentation Center, Philadelphia, Pennsylvania1963), Chap. 20, p. 20–8.

Epstein, L. I.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 69.

Jenkins, F. A.

F. A. Jenkins, J. Phys. Radium 19, 301 (1958).
[CrossRef]

Krylova, T. N.

R. S. Sokolova, T. N. Krylova, Opt. Spectry. (USSR) (English Transl.) 14, 213 (1963).

MacNeille, S. M.

S. M. MacNeille, U.S. Patent2,403,731 (9July1946).

Schroeder, H. H.

H. H. Schroeder, A. F. Turner, J. Soc. Motion Picture Television Engrs. 69, 351 (1960).

Seeley, J. S.

Smith, S. D.

Sokolova, R. S.

R. S. Sokolova, T. N. Krylova, Opt. Spectry. (USSR) (English Transl.) 14, 213 (1963).

Turner, A. F.

H. H. Schroeder, A. F. Turner, J. Soc. Motion Picture Television Engrs. 69, 351 (1960).

Ann. phys. (1)

F. Abelès, Ann. phys. 5, 604 (1950).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Phys. Radium (1)

F. A. Jenkins, J. Phys. Radium 19, 301 (1958).
[CrossRef]

J. Soc. Motion Picture Television Engrs. (1)

H. H. Schroeder, A. F. Turner, J. Soc. Motion Picture Television Engrs. 69, 351 (1960).

Opt. Spectry. (USSR) (English Transl.) (1)

R. S. Sokolova, T. N. Krylova, Opt. Spectry. (USSR) (English Transl.) 14, 213 (1963).

Other (4)

P. W. Baumeister, Handbook of Optical Design (U. S. Defense Documentation Center, Philadelphia, Pennsylvania1963), Chap. 20, p. 20–8.

S. M. MacNeille, U.S. Patent2,403,731 (9July1946).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955), p. 69.

See ref. 1, p. 61.

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Figures (19)

Fig. 1
Fig. 1

Nomenclature for a multilayer stack.

Fig. 2
Fig. 2

Computed spectrophotometric curves of four multilayer stacks having the same basic period repeated 2, 3, 4, and 5 times. The abscissae are proportional to frequency. In the discussions of designs, the obvious substitutions of nH or nL are made for the nm. in Fig. 1 as well as nG and nA for the glass substrate and incident medium of air.

Fig. 3
Fig. 3

Measured reflectances of two low-pass stacks G[0.5H-(L)0.5H]4A on BaF2 substrates. G denotes the BaF2 and A air; H and L are films of stibnite and chiolite one quarter-wave thick at reference wavelength λ0 = 4.06 μ or 6.3 μ.

Fig. 4
Fig. 4

Measured reflectances of two high-pass stacks G[0.5L-(H)0.5L]4A on BaF2 substrates. G denotes the BaF2 and A air; H and L are films of stibnite and chiolite one quarter-wave thick at reference wavelength λ0 = 4.06 μ or 6.3 μ.

Fig. 5
Fig. 5

Computed spectrophotometric curves of two quarter-wave stacks; separately, dashed; and as a single coating; G[LH′]6[LH]6A, solid curve, where G denotes the substrate of index 1.52 and A is air. The film thickness ratio L′/L = H′/H = 0.72 makes the high-reflectance bands contiguous for nL = 1.38 and nH = 2.3.

Fig. 6
Fig. 6

Computed spectrophotometric curves of three contiguous low-pass stacks as a single coating: G[0.5H(L)0.5H]5 [0.69H(1.38L)0.69H]5 [0.95H(1.9L)0.95H]5A. nG = 1.52, nA = 1.0, nH = 2.3, and nL = 1.38.

Fig. 7
Fig. 7

Measured reflectances of two low-pass stacks G[0.5H-(L)0.5H]7A on fused quartz substrates. G denotes the SiO2 and A air. H and L are films of antimony trioxide and chiolite one quarter-wave thick at reference wavelength λ0 = 370 nm or 460 nm.

Fig. 8
Fig. 8

Measured reflectance of the two contiguous stacks of Fig. 7 superposed in a single coating for an extended high-reflectance region.

Fig. 9
Fig. 9

Measured reflectance of the two contiguous low-pass stacks of Fig. 3 superposed in a single coating for an extended high-reflectance region.

Fig. 10
Fig. 10

Measured reflectance of the two contiguous high-pass stacks of Fig. 4 superposed in a single coating for an extended high-reflectance region.

Fig. 11
Fig. 11

Computed spectrophotometric curves of a 2:1 stack G[LLH]6A, solid line; and a quarter-wave stack G[LH]6A, dashed line. nG = 1.52, nA = 1.0, nH = 2.3, and nL = 1.38.

Fig. 12
Fig. 12

Computed spectrophotometric curve of the two stacks of Fig. 11 superposed in a single coating G[LH]6 [LLH]6A. Since nH/nL < 2 deep interference minima form in the high-reflectance region

Fig. 13
Fig. 13

Measured reflectance of a high-pass stack G[L(2H)L]4A on a BaF2 substrate. G denotes BaF2 and A air. H and L are films of stibnite and chiolite one quarter-wave thick at reference wavelength λ0 = 3.1 μ.

Fig. 14
Fig. 14

Measured reflectance of a 2:1 stack G[L(4H)L]4A on a BaF2 substrate. G denotes BaF2 and A air. H and L are films of stibnite and chiolite one quarter-wave thick at reference wavelength λ0 = 3.1 μ.

Fig. 15
Fig. 15

Measured reflectance of the stacks of Figs. 13 and 14 superposed in a single coating G[L(2H)L]4 [L(4H)L]4A with contiguous high-reflectance bands giving an extended region of high reflectance with no deep minima.

Fig. 16
Fig. 16

Schematic construction of the MacNeille multilayer interference film polarizer with the Brewster angle condition at and L, H film-pair interface within the multilayer.

Fig. 17
Fig. 17

Computed percent polarization in transmission of a MacNeille polarizer, with two band-nested stacks to extend the useful spectral range: G[0.5H(L)0.5H]8[0.5H(2L)0.5H] G, where G denotes fused quartz prisms for ϕp = 48.1°, nG = 1.48, nL = 1.35, and nH = 1.91 = nL n H = 1.91 = n L 2.

Fig. 18
Fig. 18

Measured reflectances of two quarter-wave stacks with slightly overlapping high-reflectance bands. Individual stacks, solid curves: curve A, G[0.8(HLHLHLHLH)] A; curve B, G[1.2(HLHLHLHLH)] A. Combined in a single coating there is a minimum in the overlap region: curve C, dashed, G[0.8-(HLHLHLHLH)] [1.2(HLHLHLHLH)] A. Inserted L eliminates minimum: curve D, dotted, G[0.8(HLHLHLHLH)]-L[1.2(HLHLHLHLH)] A. G denotes glass substrate, nG = 1.52, and A air. H and L are films of stibnite and chiolite one quarter-wave thick at reference wavelength λ0 = 1.6 μ.

Fig. 19
Fig. 19

Computed reflectances of broad band mirror comprised of two overlapping high-pass stacks of m periods. High-reflectance band limits shown by vertical dot-dash and dashed lines with overlap cross-hatched.

Tables (2)

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Table I Effective Indices

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Table II The sign of a12–a21 in the high-reflectance band of quarter-wave and 2:1 stacks. a12 and a21 are elements of the characteristic matrix

Equations (30)

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M i = [ cos δ i j n i - 1 sin δ i j n i sin δ i cos δ i ] ,
T = 1 - R = 4 2 + n 0 n s - 1 C 11 2 + n s n 0 - 1 C 22 2 + n 0 - 1 n s - 1 C 21 2 + n 0 n s C 12 2 ,
M = [ C 11 j C 12 j C 21 C 22 ] ,
M = M 1 * M 2 * * M m ,
G [ LH ] m A ,
M 2 ,
G ( 0.5 H ) LHLH L ( 0.5 H ) A or G [ 0.5 H ( L ) 0.5 H ] m A .
G ( 0.5 L ) HLHL H ( 0.5 L ) A or G [ 0.5 L ( H ) 0.5 L ] m A .
Δ g = 2 π - 1 arcsin ( 1 - n L / n H ) / ( 1 + n L / n H ) ,
G [ LLH ] m A ,
cos 2 δ = ( G - 1 ) ( G + 1 ) - 1 ,
G = ½ ( n H n L - 1 + n H - 1 n L ) ,
cos δ cos 2 δ - G sin δ sin 2 δ = - 1.
G [ L ( 2 H ) L ] 4 A ,
G [ L ( 4 H ) L ] 4 A ,
δ ¯ L = 2 π σ n L t L cos θ L = δ L cos θ L .
n H / n L = ( n H cos θ H ) n L - 1 sec θ L = 2.0.
n H cos θ L = n L cos θ H .
f = ( T - T ) / ( T + T ) ,
f = ( R - R ) / [ 2 - ( R + R ) ]
g 2 / g 1 = θ L / ( 90 ° - θ L ) .
G [ LH ] m [ HL ] m G .
T max = T A T B / ( 1 - R A R B ) 2 ,
ρ A + ρ B = 2 K π ,
glass [ stack A ] [ stack B ] air .
M A = | A 11 j A 12 j A 21 A 22 | = | a 11 j a 12 j a 21 a 22 | m M B = | B 11 j B 12 j B 21 B 22 | = | b 11 j b 12 j b 21 b 22 | m .
M A = [ cosh m y j a 12 sinh y m sinh y j a 21 sinh y m sinh y cosh m y ] ,
C 11 2 = ( A 11 B 11 - A 12 B 21 ) 2 C 12 2 = ( A 11 B 12 + A 12 B 22 ) 2 C 21 2 = ( A 21 B 11 + A 22 B 21 ) 2 C 22 2 = ( - A 21 B 12 + A 22 B 22 ) 2 .
cross - product term = A 11 B 11 P 1 P 2 sinh m y sinh y sinh m y sinh y ,
P 1 = n 0 a 12 - a 21 / n 0 and P 2 = n s b 12 - b 21 / n s .

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