Abstract

The index of refraction, n, of sodium films evaporated onto quartz substrates has been determined in the spectral region from 420 to 2000 Å from interference patterns observed in the reflected beam and from the critical angle marking the onset of “total reflection.” The growth of an oxide layer on the surface of a film is shown not to alter appreciably the position of interference maxima and minima. The real part of the dielectric constant was consistent with a nearly-free-electron model. The effective volume–plasmon energy was found to be 5.69±0.06 eV, in agreement with the values determined from electron-energy-loss experiments.

© 1967 Optical Society of America

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References

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  1. R. W. Wood, Phil. Mag. 38,(1919).
  2. R. W. Wood, Phys. Rev. 44, 353 (1933).
    [Crossref]
  3. C. Zener, Nature 132, 968 (1933).
    [Crossref]
  4. R. DeL Kronig, Nature 133, 211 (1934).
    [Crossref]
  5. R. W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
    [Crossref]
  6. H. E. Ives and H. B. Briggs, J. Opt. Soc. Am. 27, 181 (1937).
  7. J. N. Hodgson, J. Phys. Chem. Solids 24, 1213 (1963).
    [Crossref]
  8. B. Hietel, Ph.D. thesis, Clausthal (1965).
  9. H. Mayer and B. Hietel, in Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North–Holland Publishing Co., Amsterdam, 1966).
  10. Spectrophotometry revealed 0.28% potassium in an evaporated sample. All oxide was removed from the sodium immediately before the system was evacuated.
  11. W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
    [Crossref]
  12. R. P. Madden, L. R. Canfield, and G. Hass, J. Opt. Soc. Am. 53, 620 (1963).
    [Crossref]
  13. R. N. Hamm, R. A. MacRae, and E. T. Arakawa, J. Opt. Soc. Am. 55, 1460 (1965).
    [Crossref]
  14. M. H. Cohen, Phil. Mag. 3, 762 (1958).
    [Crossref]
  15. M. Siegbahn and T. Magnusson, Z. Physik 87, 291 (1934).
    [Crossref]
  16. H. W. B. Skinner, Phil. Trans. Roy. Soc. (London) 239, 95 (1940).
    [Crossref]
  17. F. S. Ham, Phys. Rev. 128, 82 (1962).
    [Crossref]
  18. J. L. Robins and P. E. Best, Proc. Phys. Soc. (London) 79110 (1962).
    [Crossref]
  19. J. B. Swan, Phys. Rev. 135, A1467 (1964).
    [Crossref]
  20. C. Kunz, Phys. Letters 15, 312 (1965).
    [Crossref]
  21. O. Sueoka, J. Phys. Soc. Japan 20, 2249 (1965).
    [Crossref]
  22. C. J. Powell, Proc. Phys. Soc. 76, 593 (1960).
    [Crossref]
  23. J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
    [Crossref]
  24. M. Born and W. Heisenberg, Z. Physik 23, 388 (1924).
    [Crossref]
  25. K. Fajans and G. Joos, Z. Physik 23, 1 (1924).
    [Crossref]
  26. L. Pauling, Proc. Roy. Soc. (London) A114, 191 (1927).

1965 (3)

R. N. Hamm, R. A. MacRae, and E. T. Arakawa, J. Opt. Soc. Am. 55, 1460 (1965).
[Crossref]

C. Kunz, Phys. Letters 15, 312 (1965).
[Crossref]

O. Sueoka, J. Phys. Soc. Japan 20, 2249 (1965).
[Crossref]

1964 (2)

1963 (2)

1962 (2)

F. S. Ham, Phys. Rev. 128, 82 (1962).
[Crossref]

J. L. Robins and P. E. Best, Proc. Phys. Soc. (London) 79110 (1962).
[Crossref]

1960 (1)

C. J. Powell, Proc. Phys. Soc. 76, 593 (1960).
[Crossref]

1958 (1)

M. H. Cohen, Phil. Mag. 3, 762 (1958).
[Crossref]

1953 (1)

J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
[Crossref]

1940 (1)

H. W. B. Skinner, Phil. Trans. Roy. Soc. (London) 239, 95 (1940).
[Crossref]

1937 (1)

1934 (2)

R. DeL Kronig, Nature 133, 211 (1934).
[Crossref]

M. Siegbahn and T. Magnusson, Z. Physik 87, 291 (1934).
[Crossref]

1933 (2)

R. W. Wood, Phys. Rev. 44, 353 (1933).
[Crossref]

C. Zener, Nature 132, 968 (1933).
[Crossref]

1927 (1)

L. Pauling, Proc. Roy. Soc. (London) A114, 191 (1927).

1924 (2)

M. Born and W. Heisenberg, Z. Physik 23, 388 (1924).
[Crossref]

K. Fajans and G. Joos, Z. Physik 23, 1 (1924).
[Crossref]

1919 (1)

R. W. Wood, Phil. Mag. 38,(1919).

1913 (1)

R. W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Arakawa, E. T.

Best, P. E.

J. L. Robins and P. E. Best, Proc. Phys. Soc. (London) 79110 (1962).
[Crossref]

Born, M.

M. Born and W. Heisenberg, Z. Physik 23, 388 (1924).
[Crossref]

Briggs, H. B.

Canfield, L. R.

Cohen, M. H.

M. H. Cohen, Phil. Mag. 3, 762 (1958).
[Crossref]

DeL Kronig, R.

R. DeL Kronig, Nature 133, 211 (1934).
[Crossref]

Duncan, R. C.

R. W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Duncan, R. W.

R. W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Fajans, K.

K. Fajans and G. Joos, Z. Physik 23, 1 (1924).
[Crossref]

Ham, F. S.

F. S. Ham, Phys. Rev. 128, 82 (1962).
[Crossref]

Hamm, R. N.

Hass, G.

Heisenberg, W.

M. Born and W. Heisenberg, Z. Physik 23, 388 (1924).
[Crossref]

Hietel, B.

H. Mayer and B. Hietel, in Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North–Holland Publishing Co., Amsterdam, 1966).

B. Hietel, Ph.D. thesis, Clausthal (1965).

Hodgson, J. N.

J. N. Hodgson, J. Phys. Chem. Solids 24, 1213 (1963).
[Crossref]

Hunter, W. R.

Ives, H. E.

Joos, G.

K. Fajans and G. Joos, Z. Physik 23, 1 (1924).
[Crossref]

Kahn, A. H.

J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
[Crossref]

Kunz, C.

C. Kunz, Phys. Letters 15, 312 (1965).
[Crossref]

MacRae, R. A.

Madden, R. P.

Magnusson, T.

M. Siegbahn and T. Magnusson, Z. Physik 87, 291 (1934).
[Crossref]

Mayer, H.

H. Mayer and B. Hietel, in Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North–Holland Publishing Co., Amsterdam, 1966).

Pauling, L.

L. Pauling, Proc. Roy. Soc. (London) A114, 191 (1927).

Powell, C. J.

C. J. Powell, Proc. Phys. Soc. 76, 593 (1960).
[Crossref]

Robins, J. L.

J. L. Robins and P. E. Best, Proc. Phys. Soc. (London) 79110 (1962).
[Crossref]

Siegbahn, M.

M. Siegbahn and T. Magnusson, Z. Physik 87, 291 (1934).
[Crossref]

Skinner, H. W. B.

H. W. B. Skinner, Phil. Trans. Roy. Soc. (London) 239, 95 (1940).
[Crossref]

Sockley, W.

J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
[Crossref]

Sueoka, O.

O. Sueoka, J. Phys. Soc. Japan 20, 2249 (1965).
[Crossref]

Swan, J. B.

J. B. Swan, Phys. Rev. 135, A1467 (1964).
[Crossref]

Tessman, J. R.

J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
[Crossref]

Wood, R. W.

R. W. Wood, Phys. Rev. 44, 353 (1933).
[Crossref]

R. W. Wood, Phil. Mag. 38,(1919).

Zener, C.

C. Zener, Nature 132, 968 (1933).
[Crossref]

J. Opt. Soc. Am. (4)

J. Phys. Chem. Solids (1)

J. N. Hodgson, J. Phys. Chem. Solids 24, 1213 (1963).
[Crossref]

J. Phys. Soc. Japan (1)

O. Sueoka, J. Phys. Soc. Japan 20, 2249 (1965).
[Crossref]

Nature (2)

C. Zener, Nature 132, 968 (1933).
[Crossref]

R. DeL Kronig, Nature 133, 211 (1934).
[Crossref]

Phil. Mag. (2)

R. W. Wood, Phil. Mag. 38,(1919).

M. H. Cohen, Phil. Mag. 3, 762 (1958).
[Crossref]

Phil. Trans. Roy. Soc. (London) (1)

H. W. B. Skinner, Phil. Trans. Roy. Soc. (London) 239, 95 (1940).
[Crossref]

Phys. Letters (1)

C. Kunz, Phys. Letters 15, 312 (1965).
[Crossref]

Phys. Rev. (5)

J. B. Swan, Phys. Rev. 135, A1467 (1964).
[Crossref]

F. S. Ham, Phys. Rev. 128, 82 (1962).
[Crossref]

R. W. Wood, Phys. Rev. 44, 353 (1933).
[Crossref]

R. W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

J. R. Tessman, A. H. Kahn, and W. Sockley, Phys. Rev. 92, 890 (1953).
[Crossref]

Proc. Phys. Soc. (1)

C. J. Powell, Proc. Phys. Soc. 76, 593 (1960).
[Crossref]

Proc. Phys. Soc. (London) (1)

J. L. Robins and P. E. Best, Proc. Phys. Soc. (London) 79110 (1962).
[Crossref]

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

L. Pauling, Proc. Roy. Soc. (London) A114, 191 (1927).

Z. Physik (3)

M. Born and W. Heisenberg, Z. Physik 23, 388 (1924).
[Crossref]

K. Fajans and G. Joos, Z. Physik 23, 1 (1924).
[Crossref]

M. Siegbahn and T. Magnusson, Z. Physik 87, 291 (1934).
[Crossref]

Other (3)

B. Hietel, Ph.D. thesis, Clausthal (1965).

H. Mayer and B. Hietel, in Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North–Holland Publishing Co., Amsterdam, 1966).

Spectrophotometry revealed 0.28% potassium in an evaporated sample. All oxide was removed from the sodium immediately before the system was evacuated.

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Figures (6)

Fig. 1
Fig. 1

Reflectance R of a sodium film vs angle of incidence θ for 1580-Å radiation. The angle of maximum slope θm is 44°. Interference fringes appear for θ less than θm.

Fig. 2
Fig. 2

Reflectance R of a sodium film vs angle of incidence θ for 836-Å radiation.

Fig. 3
Fig. 3

Cross section of a sodium film on a quartz substrate.

Fig. 4
Fig. 4

Sin2 θ vs N2 for three sets of order numbers.

Fig. 5
Fig. 5

Reflectance R of a sodium film vs angle of incidence θ for 1216-Å radiation. Measurements were made 20 min, 3 h, and 24 h after evaporation.

Fig. 6
Fig. 6

Real part of the dielectric constant of sodium, 1, vs λ for wavelengths between 420 and 2000 Å. Present work ●, Wood ×. For wavelengths from 950 Å to 1850 Å, the points in the figure represent the average of the values of 1 given by the critical-angle and interference methods.

Tables (2)

Tables Icon

Table I Index of refraction of Na.

Tables Icon

Table II Polarizabilities, effective electron masses, and the plasma energy of sodium.

Equations (9)

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

n = sin θ m .
N λ = P λ + 2 T ( n 2 - sin 2 θ ) 1 2 ,
sin 2 θ = n 2 - ( λ / 2 T ) 2 ( N - P ) 2 .
1 = n 2 - k 2 .
1 = 1 + 4 π N α 0 - ( λ 2 / λ a 2 ) + δ ( λ ) ,
λ a 2 = π c 2 m a / N c e 2 ,
1 = 1 + 4 π N α T - ( λ 2 / λ a 2 ) .
1 = 1 + 4 π N α 1 - ( λ 2 / λ b 2 ) ,
λ b 2 = ( π c 2 / N c e 2 ) m opt .