Abstract

The optical and dielectric constants of Cs have been obtained above the plasma frequency. The measurements were made on Cs films evaporated on a plane surface of quartz and CaF2 semicylindrical substrates, at 10−6 torr. The refractive index n is determined from the critical angle for total internal reflection at the Cs–substrate interface. The absorption coefficient k is determined from the slope of the curve at the critical angle. The real part of the complex dielectric constant 1 differs from the value predicted by the nearly free-electron model. The effect is attributed to the existence of transitions from inner shells at higher photon energies and to interband transitions and plasmon-assisted transitions at lower energies. The derived parameters in this energy region are 4πnoα = 0.37±0.01, meff = 1.05±0.05 m, and ℏωp = 2.87±0.07 eV.

© 1971 Optical Society of America

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References

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  1. J. C. Sutherland, R. N. Hamm, and E. T. Arakawa, J. Opt. Soc. Am. 59, 1581 (1969).
    [Crossref]
  2. H. Mayer and B. Hietel, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966).
  3. N. V. Smith, Phys. Rev. B 2, 2840 (1970).
    [Crossref]
  4. M. H. Cohen, Phil. Mag. 3, 762 (1958).
    [Crossref]
  5. U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
    [Crossref]
  6. B. I. Lundqvist and C. Lydén, in Proceedings of the Electronic Density of States Symposium, Natl. Bur. Std. (U. S.) (U. S. Govt. Printing Office, Washington, D. C., 1969), p. 50.
  7. R. Janow and N. Tzoar, Bull. Am. Phys. Soc. 15, 368 (1970).
  8. H. E. Ives and H. B. Briggs, J. Opt. Soc. Am. 27, 395 (1937).
    [Crossref]
  9. J. C. Sutherland and E. T. Arakawa, J. Opt. Soc. Am. 58, 1080 (1968).
    [Crossref]
  10. U. S. Whang, T. A. Callcott, and E. T. Arakawa, Oak Ridge National Laboratory Report ORNL-TM-2622 (1970). The best films as judged by color (gold tint) and stability with time after evaporation were those formed in 10 s or less.
  11. L. Holland, The Properties of Glass Surfaces (Wiley, New York, 1964), p. 290.
  12. R. N. Hamm, R. A. MacRae, and E. T. Arakawa, J. Opt. Soc. Am. 55, 1460 (1965).
    [Crossref]
  13. V. G. Horton, E. T. Arakawa, R. N. Hamm, and M. W. Williams, Appl. Opt. 8, 1734 (1969).
    [Crossref]
  14. W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
    [Crossref]
  15. P. N. Butcher, J. Phys. A 64, 765 (1951).
  16. J. J. Hopfield, Phys. Rev. 139, A 419 (1965).
    [Crossref]
  17. N. V. Smith, Phys. Rev. 183, 634 (1969).
    [Crossref]
  18. J. J. Lander and J. Morrison, Surface Sci. 14, 465 (1969).
    [Crossref]
  19. C. Kunz, Z. Physik,  196, 311 (1966).
    [Crossref]
  20. B. M. Hartley, Phys. Letters 24A, 396 (1967).
  21. J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967)
    [Crossref]

1970 (3)

N. V. Smith, Phys. Rev. B 2, 2840 (1970).
[Crossref]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
[Crossref]

R. Janow and N. Tzoar, Bull. Am. Phys. Soc. 15, 368 (1970).

1969 (4)

1968 (1)

1967 (2)

B. M. Hartley, Phys. Letters 24A, 396 (1967).

J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967)
[Crossref]

1966 (1)

C. Kunz, Z. Physik,  196, 311 (1966).
[Crossref]

1965 (2)

1964 (1)

1958 (1)

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

1951 (1)

P. N. Butcher, J. Phys. A 64, 765 (1951).

1937 (1)

Arakawa, E. T.

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
[Crossref]

J. C. Sutherland, R. N. Hamm, and E. T. Arakawa, J. Opt. Soc. Am. 59, 1581 (1969).
[Crossref]

V. G. Horton, E. T. Arakawa, R. N. Hamm, and M. W. Williams, Appl. Opt. 8, 1734 (1969).
[Crossref]

J. C. Sutherland and E. T. Arakawa, J. Opt. Soc. Am. 58, 1080 (1968).
[Crossref]

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

U. S. Whang, T. A. Callcott, and E. T. Arakawa, Oak Ridge National Laboratory Report ORNL-TM-2622 (1970). The best films as judged by color (gold tint) and stability with time after evaporation were those formed in 10 s or less.

Bearden, J. A.

J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967)
[Crossref]

Briggs, H. B.

Burr, A. F.

J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967)
[Crossref]

Butcher, P. N.

P. N. Butcher, J. Phys. A 64, 765 (1951).

Callcott, T. A.

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
[Crossref]

U. S. Whang, T. A. Callcott, and E. T. Arakawa, Oak Ridge National Laboratory Report ORNL-TM-2622 (1970). The best films as judged by color (gold tint) and stability with time after evaporation were those formed in 10 s or less.

Cohen, M. H.

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

Hamm, R. N.

Hartley, B. M.

B. M. Hartley, Phys. Letters 24A, 396 (1967).

Hietel, B.

H. Mayer and B. Hietel, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966).

Holland, L.

L. Holland, The Properties of Glass Surfaces (Wiley, New York, 1964), p. 290.

Hopfield, J. J.

J. J. Hopfield, Phys. Rev. 139, A 419 (1965).
[Crossref]

Horton, V. G.

Hunter, W. R.

Ives, H. E.

Janow, R.

R. Janow and N. Tzoar, Bull. Am. Phys. Soc. 15, 368 (1970).

Kunz, C.

C. Kunz, Z. Physik,  196, 311 (1966).
[Crossref]

Lander, J. J.

J. J. Lander and J. Morrison, Surface Sci. 14, 465 (1969).
[Crossref]

Lundqvist, B. I.

B. I. Lundqvist and C. Lydén, in Proceedings of the Electronic Density of States Symposium, Natl. Bur. Std. (U. S.) (U. S. Govt. Printing Office, Washington, D. C., 1969), p. 50.

Lydén, C.

B. I. Lundqvist and C. Lydén, in Proceedings of the Electronic Density of States Symposium, Natl. Bur. Std. (U. S.) (U. S. Govt. Printing Office, Washington, D. C., 1969), p. 50.

MacRae, R. A.

Mayer, H.

H. Mayer and B. Hietel, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966).

Morrison, J.

J. J. Lander and J. Morrison, Surface Sci. 14, 465 (1969).
[Crossref]

Smith, N. V.

N. V. Smith, Phys. Rev. B 2, 2840 (1970).
[Crossref]

N. V. Smith, Phys. Rev. 183, 634 (1969).
[Crossref]

Sutherland, J. C.

Tzoar, N.

R. Janow and N. Tzoar, Bull. Am. Phys. Soc. 15, 368 (1970).

Whang, U. S.

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
[Crossref]

U. S. Whang, T. A. Callcott, and E. T. Arakawa, Oak Ridge National Laboratory Report ORNL-TM-2622 (1970). The best films as judged by color (gold tint) and stability with time after evaporation were those formed in 10 s or less.

Williams, M. W.

Appl. Opt. (1)

Bull. Am. Phys. Soc. (1)

R. Janow and N. Tzoar, Bull. Am. Phys. Soc. 15, 368 (1970).

J. Opt. Soc. Am. (5)

J. Phys. A (1)

P. N. Butcher, J. Phys. A 64, 765 (1951).

Phil. Mag. (1)

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

Phys. Letters (1)

B. M. Hartley, Phys. Letters 24A, 396 (1967).

Phys. Rev. (2)

J. J. Hopfield, Phys. Rev. 139, A 419 (1965).
[Crossref]

N. V. Smith, Phys. Rev. 183, 634 (1969).
[Crossref]

Phys. Rev. B (1)

N. V. Smith, Phys. Rev. B 2, 2840 (1970).
[Crossref]

Phys. Rev. Letters (1)

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Letters 25, 646 (1970).
[Crossref]

Rev. Mod. Phys. (1)

J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, 125 (1967)
[Crossref]

Surface Sci. (1)

J. J. Lander and J. Morrison, Surface Sci. 14, 465 (1969).
[Crossref]

Z. Physik (1)

C. Kunz, Z. Physik,  196, 311 (1966).
[Crossref]

Other (4)

B. I. Lundqvist and C. Lydén, in Proceedings of the Electronic Density of States Symposium, Natl. Bur. Std. (U. S.) (U. S. Govt. Printing Office, Washington, D. C., 1969), p. 50.

H. Mayer and B. Hietel, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966).

U. S. Whang, T. A. Callcott, and E. T. Arakawa, Oak Ridge National Laboratory Report ORNL-TM-2622 (1970). The best films as judged by color (gold tint) and stability with time after evaporation were those formed in 10 s or less.

L. Holland, The Properties of Glass Surfaces (Wiley, New York, 1964), p. 290.

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Figures (6)

F. 1
F. 1

Calculated reflectance vs angle of incidence for nrel = 0.7, θc = 44°26′, and various values of krel. Triangles are the positions of θm’s. The values are θm = 45°0′ for k = 0.02, θm = 45°54′ for k = 0.05, and θm = 49°26′ for k = 0.10.

F. 2
F. 2

Dependence of the slope of the reflectance at θm on nrel and P. (a) nrel = 0.62, P = 0.47, m = 2.92; (b) nrel = 0.65, P = 0.41, m = 2.84; (c) nrel = 0.65, P = 0.52, m = 2.84; (d) nrel = 0.67, P = 0.60, m = 2.84; (e) nrel = 0.67, P = 1.20, m = 2.82; (f) nrel = 0.69, P =1.20, m = 2.78, where m = (ΔRθ) (deg−1) represents the slope at θm.

F. 3
F. 3

Fitting of experimental reflectance at 1817 Å (○) and 2260 Å (△) to theoretical curves. Data are normalized at θ = 20° for both, at θ = 44° (◊) for λ = 1817 Å, and at θ = 48° (□) for λ = 2260 Å.

F. 4
F. 4

Optical conductivity vs photon energy. Data points are taken from present work (○), Smith (□), Mayer and Hietel (△). Broken curves represent contributions to the absorption of free carriers (· — ·), interband transitions (– – –), and collective effects (···).

F. 5
F. 5

1 vs λ2. Circles (●) are data points measured by authors. Data by (×) authors, (□) Smith, and (▲) Ives and Briggs plot 1δ∊1, the portion of 1 describing free-electron absorption in an NFE model. Solid straight line gives 4πn0α = 0.37, meff = 1.05 m, and ℏωP = 2.87 eV. Dashed line gives 4πn0α = 0.36, meff = 1.11 m, and ℏωP = 2.80 eV. Dotted line gives 4πn0α = 0.38, meff = m, and ℏωP = 2.94 eV.

F. 6
F. 6

δ∊2 and δ∊1+ 1 vs ℏω. δ∊2(I) and δ∊2(P) represent the contributions to 2 of the interband transitions and plasmon-assisted transitions, respectively. δ∊2(I) and δ∊2(P) represent contributions of the same mechanisms to 1. Separate contributions to 1 or 2 add algebraically.

Tables (1)

Tables Icon

Table I Optical and dielectric constants of Cs.

Equations (10)

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R ( θ ) = I ( θ ) / I 0 ,
n rel = sin θ c ,
n rel = sin θ m .
n = n s sin θ m and k = n s k rel ,
1 ( ω ) = 1 + 4 π n 0 α 0 ( ω a 2 / ω 2 ) + δ 1 ( ω ) ,
ω a 2 = 4 π n 0 e 2 / m eff .
δ 1 ( E 0 ) = 2 π 0 E δ 2 ( E ) E 2 E 0 2 d E ,
4 π n 0 α = 0.37 ± 0.01
ω p = 2.87 ± 0.07 eV .
m eff = 1.05 ± 0.05 m .