Abstract

A method is described for determining the optical constants of a thin film deposited on a nonabsorbing window using a single set of transmittances over an absorption band. The method depends on the fact that the phase shift of the transmitted radiation can be determined from the transmittances by a Kramers–Kronig transform. No assumption of a physical model or band shape is required. Practical implementation of the method is numerically complicated, and the use of a digital computer is essential.

© 1966 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
    [Crossref]
  2. O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press Inc., New York, 1955).
  3. Note that we use the opposite sign convention from Ref. 2 in defining n so that the exponentials in Eq. (2) will also have opposite signs from Ref. 2.
  4. P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
    [Crossref]
  5. P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
    [Crossref]
  6. S. Maeda and P. N. Schatz, J. Chem. Phys. 36, 571 (1962).
    [Crossref]
  7. H. Yamada and W. B. Person, J. Chem. Phys. 40, 309 (1964).
    [Crossref]

1964 (1)

H. Yamada and W. B. Person, J. Chem. Phys. 40, 309 (1964).
[Crossref]

1963 (2)

S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[Crossref]

P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
[Crossref]

1962 (1)

S. Maeda and P. N. Schatz, J. Chem. Phys. 36, 571 (1962).
[Crossref]

1961 (1)

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

Dows, D. A.

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press Inc., New York, 1955).

Hollenberg, J. L.

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

Kozima, K.

P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
[Crossref]

Maeda, S.

P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
[Crossref]

S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[Crossref]

S. Maeda and P. N. Schatz, J. Chem. Phys. 36, 571 (1962).
[Crossref]

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

Person, W. B.

H. Yamada and W. B. Person, J. Chem. Phys. 40, 309 (1964).
[Crossref]

Schatz, P. N.

P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
[Crossref]

S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[Crossref]

S. Maeda and P. N. Schatz, J. Chem. Phys. 36, 571 (1962).
[Crossref]

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

Thyagarajan, G.

S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[Crossref]

Yamada, H.

H. Yamada and W. B. Person, J. Chem. Phys. 40, 309 (1964).
[Crossref]

J. Chem. Phys. (5)

P. N. Schatz, S. Maeda, and K. Kozima, J. Chem. Phys. 38, 2658 (1963).
[Crossref]

P. N. Schatz, S. Maeda, J. L. Hollenberg, and D. A. Dows, J. Chem. Phys. 34, 175 (1961).
[Crossref]

S. Maeda and P. N. Schatz, J. Chem. Phys. 36, 571 (1962).
[Crossref]

H. Yamada and W. B. Person, J. Chem. Phys. 40, 309 (1964).
[Crossref]

S. Maeda, G. Thyagarajan, and P. N. Schatz, J. Chem. Phys. 39, 3474 (1963).
[Crossref]

Other (2)

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press Inc., New York, 1955).

Note that we use the opposite sign convention from Ref. 2 in defining n so that the exponentials in Eq. (2) will also have opposite signs from Ref. 2.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Phase shift of transmitted radiation as a function of frequency. The solid curve is the correct result. The broken line is the result of an oversimplified treatment, and the circles show the results after corrections are applied.

Fig. 2
Fig. 2

Absorption coefficient of solid CS2 (on AgCl) as a function of frequency. The solid line is the experimental curve and the broken line is the calculated true curve.

Fig. 3
Fig. 3

Calculated optical constants of solid CS2 as a function of frequency. The solid curve is κ and the broken curve is n.

Equations (13)

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

I = I 0 ϕ T 2 ( 1 - R w ) ( 1 - R w R i ) - 1 ,
T = t 1 t 2 exp ( i γ ) 1 + r 1 r 2 exp ( 2 i γ ) ,
t 1 = 2 ( 1 + n ) - 1 , t 2 = 2 n ( n + ϕ ) - 1 , r 1 = ( 1 - n ) ( 1 + n ) - 1 , r 2 = ( n - ϕ ) ( n + ϕ ) - 1 , γ = 2 π n d / λ .
T = T exp ( i θ ) ,
ln T = ln T + i θ .
θ ( ν 0 ) = - 2 ν 0 π P 0 ln T ( ν ) d ν ν 2 - ν 0 2 + 2 π ν 0 d ,
T = 4 [ ( n 2 + κ 2 ) / ( C 2 + D 2 ) ] 1 2 ,
θ = arc tan [ ( κ C + n D ) / ( n C - κ D ) ] ,
C = e M [ P cos N + Q sin N ] + e - M [ L cos N - H sin N ] , D = e M [ P sin N - Q cos N ] - e - M [ L sin N + H cos N ] ,
P = ( 1 + n ) ( n + ϕ ) - κ 2 , Q = κ ( 1 + 2 n + ϕ ) , L = ( 1 - n ) ( n - ϕ ) + κ 2 , H = κ ( 1 - 2 n + ϕ ) , N = 2 π ν n d , M = 2 π ν κ d .
T 2 = ( I / I 0 ϕ ) [ ( 1 - R i R w ) / ( 1 + R w ) ] .
( 1 - R i R w ) / ( 1 + R w ) = ( 1 - R w ) .
n ( ν ) - n = ( c / 2 π 2 ) [ A i / ( ν i 2 - ν 2 ) ] .