Abstract

It is shown that the transmission of light through a thin dielectric film under conditions of frustrated total reflection can be used to measure the refractive index and thickness of the film. The refractive index and thickness have been measured for each of several magnesium fluoride films. The thickness was checked in each case by multiple beam interference and the refractive index compared with the results obtained by other authors for similar films. It appears that many present concepts on which the theory of the optical properties of thermally evaporated films is based are inadequate for the problems involved.

© 1958 Optical Society of America

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References

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  1. Handbook of Chemistry and Physics (The Chemical Rubber Publishing Company, Cleveland, 1953–1954), thirty-fifth edition.
  2. J. Bannon, Nature 157, 446 (1946).
    [CrossRef]
  3. J. L. Rood, J. Opt. Soc. Am. 39, 854 (1949).
    [CrossRef]
  4. J. F. Hall and W. F. Ferguson, J. Opt. Soc. Am. 45, 74 (1955).
    [CrossRef]
  5. N. Morita, J. Phys. Soc. (Japan) 11, 957 (1956).
  6. Coleman, Turner, and Ullrich, J. Opt. Soc. Am. 37, 521 (1947).
  7. F. Abelès, J. Phys. radium 11, 310 (1950).
    [CrossRef]
  8. Mattuck, Petti, and Bateman, J. Opt. Soc. Am. 46, 782 (1956).
    [CrossRef]
  9. O. S. Heavens and S. D. Smith, J. Opt. Soc. Am. 47, 469 (1957).
    [CrossRef]
  10. L. G. Schulz and E. J. Schreiber, J. Opt. Soc. Am. 40, 761 (1950).
    [CrossRef]
  11. P. Bousquet, Optica Acta 3, 153 (1956).
    [CrossRef]
  12. A. F. Turner, J. Phys. radium 11, 444 (1950).
    [CrossRef]
  13. A. E. Gee and H. D. Polster, J. Opt. Soc. Am. 39, 1044 (1949).
    [CrossRef]
  14. E. E. Hall, Phys. Rev. 15, 73 (1902).
  15. H. Arzelies, Compt. rend. 226, 478 (1948).

1957 (1)

1956 (3)

Mattuck, Petti, and Bateman, J. Opt. Soc. Am. 46, 782 (1956).
[CrossRef]

N. Morita, J. Phys. Soc. (Japan) 11, 957 (1956).

P. Bousquet, Optica Acta 3, 153 (1956).
[CrossRef]

1955 (1)

1950 (3)

L. G. Schulz and E. J. Schreiber, J. Opt. Soc. Am. 40, 761 (1950).
[CrossRef]

A. F. Turner, J. Phys. radium 11, 444 (1950).
[CrossRef]

F. Abelès, J. Phys. radium 11, 310 (1950).
[CrossRef]

1949 (2)

1948 (1)

H. Arzelies, Compt. rend. 226, 478 (1948).

1947 (1)

Coleman, Turner, and Ullrich, J. Opt. Soc. Am. 37, 521 (1947).

1946 (1)

J. Bannon, Nature 157, 446 (1946).
[CrossRef]

1902 (1)

E. E. Hall, Phys. Rev. 15, 73 (1902).

Abelès, F.

F. Abelès, J. Phys. radium 11, 310 (1950).
[CrossRef]

Arzelies, H.

H. Arzelies, Compt. rend. 226, 478 (1948).

Bannon, J.

J. Bannon, Nature 157, 446 (1946).
[CrossRef]

Bateman,

Bousquet, P.

P. Bousquet, Optica Acta 3, 153 (1956).
[CrossRef]

Coleman,

Coleman, Turner, and Ullrich, J. Opt. Soc. Am. 37, 521 (1947).

Ferguson, W. F.

Gee, A. E.

Hall, E. E.

E. E. Hall, Phys. Rev. 15, 73 (1902).

Hall, J. F.

Heavens, O. S.

Mattuck,

Morita, N.

N. Morita, J. Phys. Soc. (Japan) 11, 957 (1956).

Petti,

Polster, H. D.

Rood, J. L.

Schreiber, E. J.

Schulz, L. G.

Smith, S. D.

Turner,

Coleman, Turner, and Ullrich, J. Opt. Soc. Am. 37, 521 (1947).

Turner, A. F.

A. F. Turner, J. Phys. radium 11, 444 (1950).
[CrossRef]

Ullrich,

Coleman, Turner, and Ullrich, J. Opt. Soc. Am. 37, 521 (1947).

Compt. rend. (1)

H. Arzelies, Compt. rend. 226, 478 (1948).

J. Opt. Soc. Am. (7)

J. Phys. radium (2)

F. Abelès, J. Phys. radium 11, 310 (1950).
[CrossRef]

A. F. Turner, J. Phys. radium 11, 444 (1950).
[CrossRef]

J. Phys. Soc. (Japan) (1)

N. Morita, J. Phys. Soc. (Japan) 11, 957 (1956).

Nature (1)

J. Bannon, Nature 157, 446 (1946).
[CrossRef]

Optica Acta (1)

P. Bousquet, Optica Acta 3, 153 (1956).
[CrossRef]

Phys. Rev. (1)

E. E. Hall, Phys. Rev. 15, 73 (1902).

Other (1)

Handbook of Chemistry and Physics (The Chemical Rubber Publishing Company, Cleveland, 1953–1954), thirty-fifth edition.

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Figures (4)

Fig. 1
Fig. 1

The refractive index of thermally evaporated magnesium fluoride films as measured by various authors; 1. Bulk indexes; 2. Bannon; 3. Rood; 4. Hall and Ferguson; 5. Morita; 6. Coleman, Turner, and Ullrich; 7. Abelès; 8. Mattuck, Petti, and Bateman; 9. Heavens and Smith; 10. Schulz and Schreiber; compared with 0, the results of this paper. The range of index in each case includes experimental error.

Fig. 2
Fig. 2

The basic experimental assembly.

Fig. 3
Fig. 3

The complete experimental assembly.

Fig. 4
Fig. 4

A typical graph for the solution of the optical constants of a thin film which are given by the point of intersection of the two lines and is shown above in the case of film 2.

Tables (1)

Tables Icon

Table I The refractive index and thickness, A, of three films of MgF2. The thickness, B, is that measured by multiple beam interference.

Equations (6)

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| E 3 E 1 | 2 = 4 cos 2 ϕ ( sin 2 ϕ - n 1 2 ) sinh 2 u ( 1 - n 1 2 ) 2 + 4 cos 2 ϕ ( sin 2 ϕ - n 1 2 ) ,
| E 3 E 1 | 2 = 4 cos 2 ϕ ( sin 2 ϕ - n 1 2 ) { ( cos ϕ + n 1 n 2 cos θ ) 2 ( sin 2 ϕ - n 1 2 ) + sinh 2 u ( sin 2 ϕ + n 1 2 n 2 2 cos 2 θ - n 1 2 ) ( 1 - n 1 2 ) } ,
| E 3 E 1 | 2 = 4 n 2 cos 2 ϕ ( cos θ + n cos ϕ ) 2 ,
T s = | E 3 E 3 | 2 = ( sin 2 α - n 2 n 1 2 ) [ cos α + ( n 2 - sin 2 α ) 1 2 ] 2 { n 2 ( 1 - n 2 n 1 2 ) ( 1 - n 1 2 ) sinh 2 u + ( sin 2 α - n 2 n 1 2 ) [ cos α + ( n 2 - sin 2 α ) 1 2 ] 2 } ,
u = 2 π d ( sin 2 α - n 2 n 1 2 ) 1 2 ( n n 1 λ 2 ) - 1 .
sinh 2 u = ( sin 2 α - n 2 n 1 2 ) [ cos α + ( n 2 - sin 2 α ) 1 2 ] 2 ( 1 - T s ) n 2 ( 1 - n 2 n 1 2 ) ( 1 - n 1 2 ) T s .