Abstract

The behavior of a symmetrical nonabsorbing multilayer in the region where the component film thicknesses are small compared with the wavelength closely approximates the behavior of a homogeneous single film. The index of the equivalent film can be made to take any value intermediate to the index values of the constituent films; and by adding together multiple periods of the basic combination, the equivalent thickness can be made as large as desired. Such combinations are shown to have useful application in the construction of wide-range antireflection coatings for high-index infrared optical materials.

© 1962 Optical Society of America

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References

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  1. L. Ivan Epstein, J. Opt. Soc. Am.,  42, 806 (1952).
    [CrossRef]
  2. Weinstein, Vacuum 4, 1, 3 (1954).
    [CrossRef]
  3. G. Hass and A. F. Turner, Ergebnisse der Hochvacuumtechnik und der Physik dünner Schichten (Wissenschaftliche Verlags-gesellschaft, Stuttgart, 1957).
  4. J. T. Cox, G. Hass, and G. F. Jacobus, J. Opt. Soc. Am. 51, 714 (1961).
    [CrossRef]

1961 (1)

1954 (1)

Weinstein, Vacuum 4, 1, 3 (1954).
[CrossRef]

1952 (1)

Cox, J. T.

Hass, G.

J. T. Cox, G. Hass, and G. F. Jacobus, J. Opt. Soc. Am. 51, 714 (1961).
[CrossRef]

G. Hass and A. F. Turner, Ergebnisse der Hochvacuumtechnik und der Physik dünner Schichten (Wissenschaftliche Verlags-gesellschaft, Stuttgart, 1957).

Ivan Epstein, L.

Jacobus, G. F.

Turner, A. F.

G. Hass and A. F. Turner, Ergebnisse der Hochvacuumtechnik und der Physik dünner Schichten (Wissenschaftliche Verlags-gesellschaft, Stuttgart, 1957).

Weinstein,

Weinstein, Vacuum 4, 1, 3 (1954).
[CrossRef]

J. Opt. Soc. Am. (2)

Vacuum (1)

Weinstein, Vacuum 4, 1, 3 (1954).
[CrossRef]

Other (1)

G. Hass and A. F. Turner, Ergebnisse der Hochvacuumtechnik und der Physik dünner Schichten (Wissenschaftliche Verlags-gesellschaft, Stuttgart, 1957).

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Figures (9)

Fig. 1
Fig. 1

Concept of equivalence as applied to symmetrical three-layer film combinations.

Fig. 2
Fig. 2

Concept of equivalence extended to multiple periods of a symmetrical three-layer film combination.

Fig. 3
Fig. 3

Equivalent phase thickness γ as a function of the combined phase thicknesses of the component layers of the combination: { ( 1 2 L ) H ( 1 2 L )}; nL=1.35, nH=4.0.

Fig. 4
Fig. 4

Equivalent index N of a symmetrical three-layer film combination: { ( 1 2 q L ) H ( 1 2 q L )} as a function of the equivalent phase thickness γ for various ratios q; nL=1.35, nH=4.0.

Fig. 5
Fig. 5

Equivalent index N of a symmetrical three-layer film combination: { ( 1 2 q H ) L ( 1 2 q H )} as a function of the equivalent phase thickness γ for various ratios q; nL=1.35, nH=4.0.

Fig. 6
Fig. 6

Comparison of calculated reflectance of the combinations A { ( 1 16 L ) ( 1 8 H ) ( 1 16 L ) } 4 G (solid) A(1.15H′)G (dashed); nL=1.35, nH=4.0, nH′=2.32, nG=1.50.

Fig. 7
Fig. 7

Calculated reflectance as a function of wavelength of a three-layer antireflection coating on germanium (solid curve) and a nine-layer equivalent coating (dashed curve).

Fig. 8
Fig. 8

Calculated transmittance as a function of wavelength of the equivalent antireflection coating in Fig. 7.

Fig. 9
Fig. 9

Calculated reflectance of an equivalent twenty-layer linearly step-graded-index film on germanium.

Tables (1)

Tables Icon

Table I Structure of ideal and equivalent linearly step-graded-index films on germanium.

Equations (5)

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N 2 = n 1 2 { sin q σ 1 + q cos σ 1 + q + 1 2 ( n 1 n 2 + n 2 n 1 ) cos q σ 1 + q sin σ 1 + q - 1 2 ( n 1 n 2 - n 2 n 1 ) sin σ 1 + q sin q σ 1 + q cos σ 1 + q + 1 2 ( n 1 n 2 + n 2 n 1 ) cos q σ 1 + q sin σ 1 + q + 1 2 ( n 1 n 2 - n 2 n 1 ) sin σ 1 + q } ,
cos γ = cos q σ 1 + q cos σ 1 + q - 1 2 ( n 1 n 2 + n 2 n 1 ) sin q σ 1 + q sin σ 1 + q ,
sin 2 γ = [ sin q σ 1 + q cos σ 1 + q + 1 2 ( n 1 n 2 + n 2 n 1 ) cos q σ 1 + q sin σ 1 + q ] 2 - 1 4 [ ( n 1 n 2 - n 2 n 1 ) sin σ 1 + q ] 2 ,
N n 1 ( q + n 2 / n 1 q + n 1 / n 2 ) 1 2 ,
γ σ ( 1 + ( n 1 - n 2 ) 2 q n 1 n 2 ( 1 + q ) 2 ) 1 2 .