Abstract

A method for calculating the optical properties of amorphous metals is described. When the reflectivity at low photon energies is well represented by the Hagen-Rubens equation, the Kramers-Kronig relation can be expressed in terms of a ratio reflectance, and the optical phase so obtained has much greater accuracy than when obtained by the regular approach. As an example, the optical properties of amorphous Fe80B20 are derived.

© 1990 Optical Society of America

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References

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  1. E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
    [CrossRef]
  2. J. M. Ziman, Principles of the Theory of Solids (Cambridge U. P., London, 1965), pp. 237–241.
  3. S. Ray, J. Tauc, “Optical and Magneto-Optical Properties of Metallic Glass,” Solid State Commun. 34, 769–772 (1980).
    [CrossRef]
  4. F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 299–408 (1965).
    [CrossRef]
  5. G. A. N. Connell, D. Bloomberg, “Amorphous Rare-Earth Transition-Metal Alloys,” in Physics of Disordered Materials, D. Adler, H. Fritzsche, S. R. Ovshinsky, Eds. (Plenum, New York, 1985), pp. 739–752.
    [CrossRef]

1980 (1)

S. Ray, J. Tauc, “Optical and Magneto-Optical Properties of Metallic Glass,” Solid State Commun. 34, 769–772 (1980).
[CrossRef]

1979 (1)

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

1965 (1)

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 299–408 (1965).
[CrossRef]

Bloomberg, D.

G. A. N. Connell, D. Bloomberg, “Amorphous Rare-Earth Transition-Metal Alloys,” in Physics of Disordered Materials, D. Adler, H. Fritzsche, S. R. Ovshinsky, Eds. (Plenum, New York, 1985), pp. 739–752.
[CrossRef]

Connell, G. A. N.

G. A. N. Connell, D. Bloomberg, “Amorphous Rare-Earth Transition-Metal Alloys,” in Physics of Disordered Materials, D. Adler, H. Fritzsche, S. R. Ovshinsky, Eds. (Plenum, New York, 1985), pp. 739–752.
[CrossRef]

Hauser, E.

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Hauser, J. J.

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Nagel, S. R.

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Ray, S.

S. Ray, J. Tauc, “Optical and Magneto-Optical Properties of Metallic Glass,” Solid State Commun. 34, 769–772 (1980).
[CrossRef]

Stern, F.

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 299–408 (1965).
[CrossRef]

Tauc, J.

S. Ray, J. Tauc, “Optical and Magneto-Optical Properties of Metallic Glass,” Solid State Commun. 34, 769–772 (1980).
[CrossRef]

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Ziman, J. M.

J. M. Ziman, Principles of the Theory of Solids (Cambridge U. P., London, 1965), pp. 237–241.

Zirke, R. J.

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Phys. Rev. B (1)

E. Hauser, R. J. Zirke, J. Tauc, J. J. Hauser, S. R. Nagel, “Optical Properties of Amorphous Metallic Gold-Silicon Alloys,” Phys. Rev. B 19, 6331–6336 (1979).
[CrossRef]

Solid State Commun. (1)

S. Ray, J. Tauc, “Optical and Magneto-Optical Properties of Metallic Glass,” Solid State Commun. 34, 769–772 (1980).
[CrossRef]

Solid State Phys. (1)

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 299–408 (1965).
[CrossRef]

Other (2)

G. A. N. Connell, D. Bloomberg, “Amorphous Rare-Earth Transition-Metal Alloys,” in Physics of Disordered Materials, D. Adler, H. Fritzsche, S. R. Ovshinsky, Eds. (Plenum, New York, 1985), pp. 739–752.
[CrossRef]

J. M. Ziman, Principles of the Theory of Solids (Cambridge U. P., London, 1965), pp. 237–241.

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Figures (3)

Fig. 1
Fig. 1

Reflectance of amorphous Fe80B20 for photon energies up to 6 eV divided by the Hagen-Rubens reflectance for σ0 = 7.5 × 1015 s−1.

Fig. 2
Fig. 2

Measured reflectance of amorphous Fe80B20 (solid line) for photon energies up to 6 eV. The Drude fit (dashed line) deviates at ~2.5 eV.

Fig. 3
Fig. 3

Calculated dielectric function of amorphous Fe80B20 for photon energies up to 6 eV. The accuracy of the analysis varies with energy as indicated by the shaded areas. The Drude fit (dashed lines) deviates above 3.5 eV.

Equations (12)

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θ ( ω ) = ω Π 0 ln R ( ω ) - ln R ( ω ) ω 2 - ω 2 d ω ,
R H = exp [ ( - 2 ω Π σ H ) 1 / 2 ] ,
θ H ( ω ) = ( ω 2 Π σ H ) 1 / 2 .
R R ( ω ) = R ( ω ) R H ( ω )
θ ( ω ) = θ H ( ω ) + ω Π 0 ln R R ( ω ) - ln R R ( ω ) ω 2 - ω 2 d ω .
R ( ω ) = R H ( ω )             ω ω min ,
R ( ω ) = R ( ω max ) ( ω max ω ) p             ω ω max .
θ ( ω ) = ω Π 0 ω max ln R R ( ω ) - ln R R ( ω ) ω 2 - ω 2 d ω + 1 2 Π ln ω max + ω ω max - ω [ ln R R ( ω ) R R ( ω max ) + ( 2 Π σ H ) 1 / 2 ( ω max 1 / 2 - ω 1 / 2 ) ] + p Π n = 1 ( 2 n + 1 ) - 2 ( ω ω max ) 2 n + 1 + ( ω 2 Π 3 σ H ) 1 / 2 × { 2 tan - 1 ( ω max ω ) 1 / 2 + ln 1 + ω max ω [ 1 + ( ω max ω ) 1 / 2 ] 2 } ,
n = 1 - [ R ( ω ) ] 1 / 2 1 + R ( ω ) - 2 [ R ( ω ) ] 1 / 2 cos θ ( ω ) ,
k = 2 [ R ( ω ) ] 1 / 2 sin θ ( ω ) 1 + R ( ω ) - 2 [ R ( ω ) ] 1 / 2 cos θ ( ω ) ,
ɛ 1 = n 2 - k 2 ,
ɛ 2 = 2 n k .

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