Abstract

Reflection and transmission filters have been constructed by the evaporation process, and their properties have been measured and shown to conform with the theory developed in Part I of this paper. A more extended set of curves of the reflection and transmission coefficients and the phase shift angles of a single metal film are given. From these curves, and from measurements made on the transmission filter, the optical constants of silver films are deduced and shown to be in agreement with other published data. A typical spectrogram of an infra-red reflection filter is also given, showing a minimum reflection coefficient of less than one percent at the odd overtones of the fundamental frequency.

© 1948 Optical Society of America

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References

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  1. L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 36, 451 (1947).
    [Crossref]
  2. L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
    [Crossref]
  3. H. Levinstein, doctoral thesis, University of Michigan, January1947.
  4. H. Murmann, Zeits. f. Physik 101, 643 (1936).
    [Crossref]
  5. These films were prepared by F. Goos (Zeits. f. Physik 100, 95 (1936)) by sputtering in a hydrogen atmosphere at a pressure of 0.1-mm Hg. The deposits were made on quartz. The thickness was determined by weighing the film with a quartz torsion microbalance, and assuming bulk density.
    [Crossref]

1947 (1)

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 36, 451 (1947).
[Crossref]

1945 (1)

L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
[Crossref]

1936 (2)

H. Murmann, Zeits. f. Physik 101, 643 (1936).
[Crossref]

These films were prepared by F. Goos (Zeits. f. Physik 100, 95 (1936)) by sputtering in a hydrogen atmosphere at a pressure of 0.1-mm Hg. The deposits were made on quartz. The thickness was determined by weighing the film with a quartz torsion microbalance, and assuming bulk density.
[Crossref]

Crittenden, E. C.

L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
[Crossref]

Dennison, D. M.

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 36, 451 (1947).
[Crossref]

Goos, F.

These films were prepared by F. Goos (Zeits. f. Physik 100, 95 (1936)) by sputtering in a hydrogen atmosphere at a pressure of 0.1-mm Hg. The deposits were made on quartz. The thickness was determined by weighing the film with a quartz torsion microbalance, and assuming bulk density.
[Crossref]

Hadley, L. N.

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 36, 451 (1947).
[Crossref]

Levinstein, H.

H. Levinstein, doctoral thesis, University of Michigan, January1947.

Murmann, H.

H. Murmann, Zeits. f. Physik 101, 643 (1936).
[Crossref]

Olsen, L. O.

L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
[Crossref]

Smith, C. F.

L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
[Crossref]

J. App. Phys. (1)

L. O. Olsen, C. F. Smith, and E. C. Crittenden, “Techniques for evaporation of metals,” J. App. Phys. 16, 425 (1945).
[Crossref]

J. Opt. Soc. Am. (1)

L. N. Hadley and D. M. Dennison, J. Opt. Soc. Am. 36, 451 (1947).
[Crossref]

Zeits. f. Physik (2)

H. Murmann, Zeits. f. Physik 101, 643 (1936).
[Crossref]

These films were prepared by F. Goos (Zeits. f. Physik 100, 95 (1936)) by sputtering in a hydrogen atmosphere at a pressure of 0.1-mm Hg. The deposits were made on quartz. The thickness was determined by weighing the film with a quartz torsion microbalance, and assuming bulk density.
[Crossref]

Other (1)

H. Levinstein, doctoral thesis, University of Michigan, January1947.

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Figures (22)

Fig. 1
Fig. 1

Diagram of experimental arrangement used in obtaining reflection coefficient of reflection filter.

Fig. 2
Fig. 2

Reflection and transmission coefficients of a metal film sandwiched between two dielectric layers whose indices of refraction are 1.5. The thickness ratio of the film is s/λ=0.02. R and T are given as functions of the extinction coefficient κ, with the index of refraction η of the metal film as a parameter which takes on the values 0, 1, 2, 3, 5.

Fig. 3
Fig. 3

Same as Fig. 2 except for the thickness ratio of the film—s/λ=0.04.

Fig. 4
Fig. 4

Same as Fig. 2 except for the thickness ratio of the film—s/λ=0.06.

Fig. 5
Fig. 5

Same as Fig. 2 except for the thickness ratio of the film—s/λ=0.10.

Fig. 6
Fig. 6

Same as Fig. 2 except for the thickness ratio of the film—s/λ=0.04 and the fact that R and T as functions of κ are given over only a limited range. The parameter η takes the values 0, 0.2, 0.4.

Fig. 7
Fig. 7

Same as Fig. 6 except for the thickness ratio of the film—s/λ=0.06.

Fig. 8
Fig. 8

Same as Fig. 6 except for the thickness ratio of the film—s/λ=0.08.

Fig. 9
Fig. 9

Same as Fig. 6 except for the thickness ratio of the film—s/λ=0.10.

Fig. 10
Fig. 10

The phase shift angle, at reflection y0, of a metal film sandwiched between two dielectric layers whose indices of refraction are 1.5. The thickness ratio of the film is s/λ=0.02. y0 is given as a function of κ, with the parameter η taking the values 0, 1, 2, 3, 5.

Fig. 11
Fig. 11

Same as Fig. 10 except for the thickness ratio of the film—s/λ=0.04.

Fig. 12
Fig. 12

Same as Fig. 10 except for the thickness ratio of the film—s/λ=0.06.

Fig. 13
Fig. 13

Same as Fig. 10 except for the thickness ratio of the film—s/λ=0.10.

Fig. 14
Fig. 14

The difference δy between the phase shift angles at reflection at oblique incidence. θ=45°, s/λ=0.02 δy is given as a function of b with a as a parameter taking on the values 0, 1, 2, 3, 5.

Fig. 15
Fig. 15

Same as Fig. 14 except for the thickness ratio of the film—s/λ=0.04.

Fig. 16
Fig. 16

Same as Fig. 14 except for the thickness ratio of the film—s/λ=0.06.

Fig. 17
Fig. 17

Same as Fig. 14 except for the thickness ratio of the film—s/λ=0.10.

Fig. 18
Fig. 18

Spectrograph record of transmission filter No. 21. The upper curve gives the variation in intensity of the tungsten source as a function of wave-length, with a clear glass plate in place of the filter. The two nearly identical curves at the lower part of the figure give the variation in intensity of light transmitted through each of the silver films of the filter, taken separately. The center curve gives the variation in intensity of light transmitted through the filter. The transmission coefficient for any of the three lower curves is obtained by taking the ratio of any of their ordinates to the corresponding ordinate on the upper curve.

Fig. 19
Fig. 19

Analysis of data for filter No. 21. η, κ, y0, [δy/(πy0)]30° and [δy/(πy0)]45° are given as functions of s/λ.

Fig. 20
Fig. 20

Optical constants of silver films as determined by measurements on transmission filters. Points marked with a cross (×) are for thicknesses s between 200 and 400A. Points marked with a circle are for s between 400 and 500A. Points marked with a plus (+) are for s between 500 and 600A. Points marked with a square are taken from Murmann’s data for his calculated thickness of 294A. Note that values of 5η rather than η are plotted.

Fig. 21
Fig. 21

Reflection coefficient of typical reflection filter in the neighborhood of the fundamental frequency. λ0=8.1μ. Resistance of semiconducting layer is approximately 400 Ω/□. The solid curve is the theoretical reflection coefficient for a filter in which n=1.6, and the resistance of the semiconducting layer is 377 Ω/□.

Fig. 22
Fig. 22

Spectrograph record for filter of Fig. 21. The minima shown are for the third, fifth, seventh, ninth, and eleventh overtones. The upper curve is the reflection from an aluminum mirror in place of the filter. Reflection coefficient of filter is the ratio of ordinate on lower curve to corresponding ordinate on upper curve.

Tables (6)

Tables Icon

Table I Data taken from grating spectroscope for filter No. 21.

Tables Icon

Table II Values for the parameters of filter No. 21 as deduced from the curves of Figs. 2 through 17.

Tables Icon

Table III Experimental values of reflection and transmission coefficients and band widths obtained for a series of transmission filters.

Tables Icon

Table IV Experimental values of wave-length of transmission band for angles of incidence 0°, 30°, and 45°.

Tables Icon

Table V Values of the parameters η, κ, s, n3, and Δ as determined for the silver films of a group of transmission filters.

Tables Icon

Table VI The product of wave-length at minimum reflection coefficient by overtone number for the filter shown in Figs. 21 and 22.

Equations (13)

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T F = T 2 ( 1 - R L ) 2 + 4 R L sin 2 [ 2 π Δ ( n 3 2 - sin 2 θ ) 1 2 λ + y L ] .
R F = ( 1 - f ) 2 + n 2 cot 2 ( 2 π n Δ / λ ) ( 1 + f ) 2 + n 2 cot 2 ( 2 π n Δ / λ ) .
R L = 1 - ( T / T 0 1 2 ) .
( 2 π Δ n 3 / λ 0 ) - y 0 L = [ 2 π Δ ( n 3 2 - sin 2 θ ) 1 2 / λ θ ] - y θ L = [ 2 π Δ ( n 3 2 - sin 2 θ ) 1 2 / λ θ ] - y θ L = m π .
y 0 L y θ L y θ L .
( y θ L + y θ L ) / 2 = y 0 L
2 π Δ n 3 / λ 0 = 2 π Δ ( n 3 2 - sin 2 θ ) 1 2 / λ Av .
n 3 = sin θ / ( 1 - λ Av 2 / λ 0 2 ) 1 2 .
δ λ / λ Av = δ y / ( m π - y 0 ) .
T = 0.048 ,             W = 224 A , T 0 = 0.386 ,             R calc = 0.923.
R R = [ ( n 1 2 / p ) - ( n 3 2 / q ) - f ] 2 / [ ( n 1 2 / p ) + ( n 3 2 / q ) + f ] 2
T R = [ 4 n 1 2 n 3 2 / p q ] / [ ( n 1 2 / p ) + ( n 3 2 / q ) + f ] 2
A R = [ 4 n 1 2 f / p ] / [ ( n 1 2 / p ) + ( n 3 2 / q ) + f ] 2 .