Abstract

Fresnel diffraction patterns produced by slits in semitransparent metal and dielectric films show a fringed structure which depends upon the index of refraction and the thickness of the film. Intensity distributions calculated on the basis of scalar diffraction theory compare well with the experimental results.

© 1966 Optical Society of America

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References

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  1. N. Ananthanarayanan, Proc. Indian Acad. Sci. A14, 85 (1941); and Proc. Indian Acad. Sci. A10, 477 (1939).
  2. A. H. Pfund, J. Opt. Soc. Am. 24, 121 (1934).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 428.
  4. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 61.
  5. L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, Ltd., London, 1958).

1941 (1)

N. Ananthanarayanan, Proc. Indian Acad. Sci. A14, 85 (1941); and Proc. Indian Acad. Sci. A10, 477 (1939).

1934 (1)

Ananthanarayanan, N.

N. Ananthanarayanan, Proc. Indian Acad. Sci. A14, 85 (1941); and Proc. Indian Acad. Sci. A10, 477 (1939).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 428.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 61.

Holland, L.

L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, Ltd., London, 1958).

Pfund, A. H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 428.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 61.

J. Opt. Soc. Am. (1)

Proc. Indian Acad. Sci. (1)

N. Ananthanarayanan, Proc. Indian Acad. Sci. A14, 85 (1941); and Proc. Indian Acad. Sci. A10, 477 (1939).

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 428.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed., p. 61.

L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, Ltd., London, 1958).

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Figures (6)

Fig. 1
Fig. 1

Coordinates of a point in the plane of the slit.

Fig. 2
Fig. 2

Relation of coordinates in the plane of the slit to coordinates in the plane of observation, where the approximation that r′ and s′ are normal distances to screen has been made.

Fig. 3
Fig. 3

The complete optical system.

Fig. 4
Fig. 4

The observed and calculated diffraction patterns of the 66-μ-wide slit in a zinc sulfide film 88.4 mμ thick and the calculated patterns for the 110-μ-wide slit in a silver film 162 mμ thick.

Fig. 5
Fig. 5

Graph of the approximate phase change on passing through a zinc sulfide film 88.4 mμ thick vs wavelength.

Fig. 6
Fig. 6

A spectrogram in the region of the silver pass band at 320 mμ for which a diffraction pattern due to a slit in a silver film was adjusted to fall along the slit of a stigmatic spectrograph.

Tables (3)

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Table I Values of n2 and κn2.

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Table II Measured film thicknesses.

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Table III Real and imaginary components of the transmittance i.

Equations (52)

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U ( P ) = B ( C + i S ) ,
C = b A cos [ π 2 ( u 2 + v 2 ) ] d u d v ,
S = b A sin [ π 2 ( u 2 + v 2 ) ] d u d v ,
π 2 u 2 = π λ ( 1 r + 1 s ) ξ 2 cos 2 δ ,
π 2 v 2 = π λ ( 1 r + 1 s ) η 2 ,
d = ξ 2 - ξ 1 ,
ξ ¯ = 1 2 ( ξ 1 + ξ 2 ) .
ξ 1 < ξ < ξ 2 , - < η < .
w 1 < u < w 2 - < v < ,
w = [ 2 λ ( 1 r + 1 s ) ] 1 2 ξ cos δ .
w = [ 2 λ ( 1 r + 1 s ) ] 1 2 ξ .
w 2 - w 1 = ( ξ 2 - ξ 1 ) [ 2 λ ( 1 r + 1 s ) ] 1 2 = d [ 2 λ ( 1 r + 1 s ) ] 1 2 ,
1 2 ( w 2 + w 1 ) + 1 2 ( w 2 - w 1 ) = w 2 ,
1 2 ( w 2 + w 1 ) - 1 2 ( w 2 - w 1 ) = w 1 .
1 2 ( w 2 + w 1 ) = w ¯
1 2 ( w 2 - w 1 ) = d w ,
w ¯ + d w = w 2 w ¯ - d w = w 1 .
w ¯ = ξ 1 + ξ 2 2 [ 2 λ ( 1 r + 1 s ) ] 1 2 ,
w ¯ = ξ ¯ [ 2 λ ( 1 r + 1 s ) ] 1 2 .
ξ 2 - ( d / 2 ) = r l / ( r + s ) .
ξ ¯ = [ r / ( r + s ) ] l .
w ¯ = r r + s [ 2 λ ( 1 r + 1 s ) ] 1 2 l
l = [ r + s r ( λ 2 r s r + s ) 1 2 ] w ¯ .
U ( P ) = F + T ,
and             F = B ( C + i S ) T = B ( C + i S ) t ,
t = D + i E .
U ( P ) = B ( C + i S + t C + i t S ) .
U ( P ) = B [ ( C + D C - E S ) + i ( S + E C + D S ) ] .
C = b w 1 w 2 d u - d v { cos [ π 2 ( u 2 + v 2 ) ] } S = b w 1 w 2 d u - d v { sin [ π 2 ( u 2 + v 2 ) ] } C = b ( - w 1 d u - d v { cos [ π 2 ( u 2 + v 2 ) ] } + w 2 d u - d v { cos [ π 2 ( u 2 + v 2 ) ] } ) S = b ( w 2 d u - d v { sin [ π 2 ( u 2 + v 2 ) ] } + w 2 d u - d v { sin [ π 2 ( u 2 + v 2 ) ] } ) ;
cos [ π 2 ( u 2 + v 2 ) ] = cos π 2 u 2 cos π 2 v 2 - sin π 2 u 2 sin π 2 v 2 sin [ π 2 ( u 2 + v 2 ) ] = sin π 2 u 2 cos π 2 v 2 + sin π 2 u 2 cos π 2 v 2 .
C = b w 1 w 2 d u ( cos π 2 u 2 - sin π 2 u 2 ) S = b w 1 w 2 d u ( sin π 2 u 2 + cos π 2 u 2 ) ,
C = b [ C ( w 2 ) - C ( w 1 ) ] - b [ S ( w 2 ) - S ( w 1 ) ] S = b [ S ( w 2 ) - S ( w 1 ) ] + b [ C ( w 2 ) - C ( w 1 ) ] .
C = b - w 1 d u { cos π 2 u 2 - sin π 2 u 2 } + b w 2 d u { cos π 2 u 2 - sin π 2 u 2 } S = b - w 1 d u { sin π 2 u 2 + cos π 2 u 2 } + b w 2 d u { sin π 2 u 2 + cos π 2 u 2 }
C = b [ C ( w 1 ) - C ( w 2 ) ] - b [ S ( w 1 ) - S ( w 2 ) ] S = b [ C ( w 1 ) - C ( w 2 ) ] + b [ S ( w 1 ) - S ( w 2 ) ] + 2 b .
Δ C = C ( w 2 ) - C ( w 1 ) Δ S = S ( w 2 ) - S ( w 1 ) ,
C = b ( Δ C - Δ S ) S = b ( Δ C + Δ S ) C = - b ( Δ C - Δ S ) S = - b ( Δ C + Δ S ) + 2 b .
U ( P ) = b B [ ( Δ C - Δ S - D Δ C + D Δ S + E Δ C + E Δ S - 2 E ) + i ( Δ C + Δ S - E Δ C + E Δ S - D Δ C - D Δ S + 2 D ) ] .
α = Δ C + E Δ S - D Δ C + D - E ,
β = Δ S - E Δ C - D Δ S + D + E ,
U ( P ) = b B [ ( α - β ) + i ( α + β ) ] .
U * U = I = 2 b 2 B 2 [ α 2 + β 2 ] .
α = 1 + E - D + E - E = 1 β = 1 - E - D + D + E = 1 ,
I 0 = 4 b 2 B 2 .
I / I 0 = 1 2 ( α 2 + β 2 ) .
t = t 12 t 23 e i β / ( 1 + r 12 r 23 e 2 i β ) ,
β = ( 2 π / λ 0 ) n ˆ 2 h ,
t 12 = 2 n ˆ 1 / ( n ˆ 1 + n ˆ 2 )             t 23 = 2 n ˆ 2 / ( n ˆ 2 + n ˆ 3 )
t 12 = ( n ˆ 1 - n ˆ 2 ) / ( n ˆ 1 + n ˆ 2 )             r 23 = ( n ˆ 2 - n ˆ 3 ) / ( n ˆ 2 + n ˆ 3 )
n ˆ = n + i ( κ n ) ,
t t 12 t 23 e i β .
β = ( 2 π / λ 0 ) n ˆ 2 h ,
Re β = ( 2 π / λ 0 ) n 2 h .