Abstract

The reflectance R of a multilayer stack is changed as either the thickness t or refractive index n of any of the films in the stack is altered. An efficient method of computing the first partial derivatives ∂R/∂t and ∂R/∂n is presented. An example is cited in which these derivatives are employed in a relaxation process which is utilized to improve the design of a multilayer containing absorbing films, which is used as a reflection filter in the vacuum-ultraviolet spectral region.

© 1962 Optical Society of America

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References

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  1. A. W. Crook, J. Opt. Soc. Am. 38, 954 (1948).
    [Crossref] [PubMed]
  2. P. Rouard, Ann. phys. 11, 342 (1950).
  3. H. Schröder, Z. angew. Phys. 3, 53 (1951).
  4. J. J. Leurgans, J. Opt. Soc. Am. 41, 714 (1951).
    [Crossref]
  5. F. Abelès, Ann. phys. 5, 103 (1950).
  6. P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
    [Crossref]
  7. J. A. Dobrowolski, J. Opt. Soc. Am. 51, 1475(A) (1961).

1961 (1)

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

1958 (1)

1951 (2)

H. Schröder, Z. angew. Phys. 3, 53 (1951).

J. J. Leurgans, J. Opt. Soc. Am. 41, 714 (1951).
[Crossref]

1950 (2)

F. Abelès, Ann. phys. 5, 103 (1950).

P. Rouard, Ann. phys. 11, 342 (1950).

1948 (1)

Abelès, F.

F. Abelès, Ann. phys. 5, 103 (1950).

Baumeister, P. W.

Crook, A. W.

Dobrowolski, J. A.

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

Leurgans, J. J.

Rouard, P.

P. Rouard, Ann. phys. 11, 342 (1950).

Schröder, H.

H. Schröder, Z. angew. Phys. 3, 53 (1951).

Ann. phys. (2)

P. Rouard, Ann. phys. 11, 342 (1950).

F. Abelès, Ann. phys. 5, 103 (1950).

J. Opt. Soc. Am. (4)

Z. angew. Phys. (1)

H. Schröder, Z. angew. Phys. 3, 53 (1951).

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Figures (2)

Fig. 1
Fig. 1

The change in the computed reflectance per fractional change of thickness of the layers of a five-layer quarter-wave stack. The dashed line is the computed reflectance of the stack. The vertical-dashed line at λ0/λ=0.83 is the edge of the high-reflectance zone of the stack.

Fig. 2
Fig. 2

The computed reflectance as a function of the vacuum wave number, of the multilayers whose designs are shown in Table I.

Tables (3)

Tables Icon

Table I The design of the multilayers whose reflectance curves are shown in Fig. 2.

Tables Icon

Table II The change in reflectance per fractional change of thickness of the layers in the multilayer designated as Design I (in Table I).

Tables Icon

Table III The optical constants (as a function of wavelength) of the materials which were used in multilayers whose reflectance curves are shown in Fig. 2.

Equations (10)

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δ R ] σ 1 = ( R / t i ) δ t i + 1 2 ( 2 R / t i 2 ) ( δ t i ) 2 + higher-order terms .
M i = [ cos β i j sin β i / n i j n i sin β i cos β i ] ,
R = ( B 1 - B 3 ) 2 + ( B 2 - B 4 ) 2 ( B 1 + B 3 ) 2 + ( B 2 + B 4 ) 2 ,
M = [ C 1 j C 2 j C 3 C 4 ] ,
M = M l M l - 1 M i M 3 * M 2 M 1 ,
R / t i ( R - R ) / δ t i
R β i = n 0 R B 1 C 1 β i + n 0 n s R B 2 C 2 β i + n s R B 3 C 4 β i + R B 4 C 3 β i .
[ C 1 / β 4 j ( C 2 / β 4 ) j ( C 3 / β 4 ) C 4 / β 4 ] = M 6 M 5 M 4 M 3 M 2 M 1 ,
M 4 = ( - sin β 4 j 1 n 4 cos β 4 j n 4 cos β 4 - sin β 4 ) .
glass H L H L H glass ,