Abstract

In this simulator the amplitude and phase of a light wave are represented by the amplitude and phase of an ac voltage. Each layer in the film is simulated by a four-terminal network containing adjustable attenuators and an adjustable phase shifter. The network obeys the same difference equation [See: Lord Rayleigh, Proc. Roy. Soc. (London) 93, 565 ( 1917); P. Rouard, Ann. Phys., Ser. 11 , 7, 291 ( 1937); W. Pfister and O. H. Roth, Hochfrequenztechnik und Elektroakustik 51, 156 ( 1938); S. M. MacNeille, U. S. Patent No. 2 403 731; A. Vasicek, J. Opt. Soc. Am. 37, 623 ( 1947); D. Caballero, J. Opt. Soc. Am. 37, 176 ( 1947)] as that which relates the reflectance of n+1 interference layers to the separate reflectances of the first n layers taken together and of the n+1th layer. With these networks connected in sequence and the circuit parameters adjusted to correspond to the optical constants of the various layers of the film, either the reflectance or transmittance of the multilayer can be read directly on a meter. Since the circuit parameters correspond to (1) reflectance at the interface between layers, (2) phase retardation, and (3) attenuation with passage through the layer, the instrument can treat problems involving oblique as well as normal incidence, polarization, and absorption.

© 1954 Optical Society of America

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References

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  1. J. phys. 11, 305–480 (1950) has an extensive review and bibliography.
  2. Lord Rayleigh, Proc. Roy. Soc. (London) 93, 565–577 (1917).
    [Crossref]
  3. R. V. Subrahmanian, Proc. Indian Acad. Sci. A,  16, 467–482 (1941).
  4. G. N. Ramachandran, Proc. Indian Acad. Sci. A,  16, 336–348 (1942).
  5. P. Cotton, Ann. Phys. Series 12 2, 209–232 (1947).

1950 (1)

J. phys. 11, 305–480 (1950) has an extensive review and bibliography.

1947 (1)

P. Cotton, Ann. Phys. Series 12 2, 209–232 (1947).

1942 (1)

G. N. Ramachandran, Proc. Indian Acad. Sci. A,  16, 336–348 (1942).

1941 (1)

R. V. Subrahmanian, Proc. Indian Acad. Sci. A,  16, 467–482 (1941).

1917 (1)

Lord Rayleigh, Proc. Roy. Soc. (London) 93, 565–577 (1917).
[Crossref]

Cotton, P.

P. Cotton, Ann. Phys. Series 12 2, 209–232 (1947).

Ramachandran, G. N.

G. N. Ramachandran, Proc. Indian Acad. Sci. A,  16, 336–348 (1942).

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) 93, 565–577 (1917).
[Crossref]

Subrahmanian, R. V.

R. V. Subrahmanian, Proc. Indian Acad. Sci. A,  16, 467–482 (1941).

Ann. Phys. Series 12 (1)

P. Cotton, Ann. Phys. Series 12 2, 209–232 (1947).

J. phys. (1)

J. phys. 11, 305–480 (1950) has an extensive review and bibliography.

Proc. Indian Acad. Sci. A (2)

R. V. Subrahmanian, Proc. Indian Acad. Sci. A,  16, 467–482 (1941).

G. N. Ramachandran, Proc. Indian Acad. Sci. A,  16, 336–348 (1942).

Proc. Roy. Soc. (London) (1)

Lord Rayleigh, Proc. Roy. Soc. (London) 93, 565–577 (1917).
[Crossref]

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Figures (6)

F. 1
F. 1

Schematic diagram showing derivation of fundamental difference equation.

F. 2
F. 2

Block diagram of one section of analog computer representing one layer of interference film.

F. 3
F. 3

Circuit diagram of one section of analog computer representing one layer of interference film.

F. 4
F. 4

Computer for six layers.

F. 5
F. 5

Calculated and computer curves for a three-layer film suggested by B. S. Blaisse. η is index, ηd optical thickness, of a layer. λ0 is the wavelength scale factor so the abscissa phase angle corresponding to any wavelength λ is θ = π0/λ).

F. 6
F. 6

Series of curves for six-layer films in which the thickness of the third layer is varied as shown while the thicknesses of the other layers are held equal and constant. The r’s represent amplitude reflectances at the interfaces with appropriate signs to indicate phase; ηd is the optical thickness of a layer expressed in terms of λ0 the wavelength scale factor.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

1 R 2 r 2 t 2 e i θ / 2 R 1 = R 2 r 2 t 2 e i θ / 2 .
( 1 R 2 r 2 ) e i θ R 1 + r 2 = R 2 = r 2 + R 1 e i θ 1 + r 2 R 1 e i θ .
R j + 1 = ( 1 R j + 1 r j + 1 ) e i θ j R j + r j + 1 .
r 1 = r 2 = r 3 = r 4 = , θ 1 = θ 3 = θ 5 = θ 7 =
θ 2 = θ 4 = θ 6 = θ 8 =
R j + 1 = ( 1 r j + 1 R j + 1 ) e i θ j R j + r j + 1 .