Abstract

Using four different fitting methods, the applicability of the Lorentz-Drude (LD) model has been investigated for calculating the reflection coefficients of the laser light of wavelengths of λ(0.22 μm,200 μm) from the surface of aluminum. The applicability of the LD model has been established not only in the IR region but also in the visible and UV regions. The values of plasma frequency ωp and damping frequency Γ have been determined. The values of the reflection coefficients calculated by the LD model have been compared with corresponding experimental values. It has been established that in both the far and medium IR region as well as in both visible and UV, discrepancies are smaller than 3%. The maximum discrepancy is smaller than 7% occurs in a narrow region (~λ = 0.825 μm), where aluminum strongly absorbs caused by band—band and transitions.

© 1990 Optical Society of America

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References

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  1. H. E. Bennett, J. M. Bennett, “Title,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (Wiley, New York, 1966).
  2. L. G. Schulz, “The Optical Constants of Silver, Gold, Copper and Aluminum. I. The Absorption Coefficient k,” J. Opt. Soc. Am. 44, 357–362 (1954); L. G. Schulz, F. R. Tangherlini, “The Optical Constants of Silver, Gold, Copper and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am. 44, 362–368 (1954).
    [Crossref]
  3. G. Hass, “Filmed Surfaces for Reflecting Optics,” J. Opt. Soc. Am. 45, 945–952 (1955).
    [Crossref]
  4. E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
    [Crossref]
  5. M. A. Ordal, R. J. Bell, R. W. Alexander, L. A. Newquist, M. R. Querry, “Optical Properties of Al, Fe, Ti, Ta, W, and Mo at Submillimeter Wavelengths,” Appl. Opt. 27, 1203–1209(1988).
    [Crossref] [PubMed]
  6. M. A. Ordal et al., “Optical Properties of the Metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the Infrared and Far Infrared,” Appl. Opt. 22, 1099–1119 (1983).
    [Crossref] [PubMed]
  7. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, M. R. Querry, “Optical Properties of Fourteen Metals in the Infrared and Far Infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24, 4493–4499 (1985).
    [Crossref] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).
  9. A. V. Sokolov, Opticheskie svoistva metallov, Moskva: Gosudarstvennoe izdateljstvo fiziko-matematicheskoi literature (1961).
    [PubMed]
  10. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  11. M. F. von Almen, “Coupling of Laser Radiation to Metals and Semiconductors,” in Physical Processes in Laser Material Interactions, M. Bertollotti, Ed. (Plenum, New York, 1983), pp. 49–75.

1988 (1)

1985 (1)

1983 (1)

1980 (1)

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

1961 (1)

A. V. Sokolov, Opticheskie svoistva metallov, Moskva: Gosudarstvennoe izdateljstvo fiziko-matematicheskoi literature (1961).
[PubMed]

1955 (1)

1954 (1)

Alexander, R. W.

Bell, R. J.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, “Title,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (Wiley, New York, 1966).

Bennett, J. M.

H. E. Bennett, J. M. Bennett, “Title,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (Wiley, New York, 1966).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Hass, G.

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Long, L. L.

Newquist, L. A.

Ordal, M. A.

Querry, M. R.

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

Schulz, L. G.

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

Smith, D. Y.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

Sokolov, A. V.

A. V. Sokolov, Opticheskie svoistva metallov, Moskva: Gosudarstvennoe izdateljstvo fiziko-matematicheskoi literature (1961).
[PubMed]

von Almen, M. F.

M. F. von Almen, “Coupling of Laser Radiation to Metals and Semiconductors,” in Physical Processes in Laser Material Interactions, M. Bertollotti, Ed. (Plenum, New York, 1983), pp. 49–75.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Opticheskie svoistva metallov, Moskva: Gosudarstvennoe izdateljstvo fiziko-matematicheskoi literature (1)

A. V. Sokolov, Opticheskie svoistva metallov, Moskva: Gosudarstvennoe izdateljstvo fiziko-matematicheskoi literature (1961).
[PubMed]

Phys. Rev. B (1)

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Application to Aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[Crossref]

Other (4)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

M. F. von Almen, “Coupling of Laser Radiation to Metals and Semiconductors,” in Physical Processes in Laser Material Interactions, M. Bertollotti, Ed. (Plenum, New York, 1983), pp. 49–75.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

H. E. Bennett, J. M. Bennett, “Title,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (Wiley, New York, 1966).

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Figures (2)

Fig. 1
Fig. 1

Real and imaginary parts of the dielectric function of Al, (−r1), and r2 as a function of wavenumber from 101 to 105 cm−1. The solid lines are the Lorentz-Drude model fit. Data points are: ◒, Bennett and Bennett1; ●, Schulz2; ⊙, Ordal et al.5 for both (−r1) and r2.

Fig. 2
Fig. 2

Reflection coefficient of Al as a function of wavenumber from 101 to 105 cm−1. The solid line is the Lorentz-Drude model fit. Data points shown are: ◒, Bennett and Bennett1; ●, Schulz2; ◇, Hass3; and ⊙, Ordal et al.5

Tables (2)

Tables Icon

Table I Optical Parameters of Aluminum Obtained by the Lorentz-Drude Model Fit

Tables Icon

Table II Experimental Re and Calculated Rc Values of Reflectivity vs ω, or λ, and Adequate Relative Discrepancies for R

Equations (15)

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r = r 1 + i r 2 = 1 - ω p 2 ω 2 + i Γ ω ,
ω p 2 = N e 2 m 0 ,
r 1 = 1 - ω p 2 ω 2 + Γ 2 ,
r 2 = ω p 2 Γ ω ( ω 2 + Γ 2 ) .
n 2 = ( n + i k ) 2 = r μ r ,
n = μ r 2 ( r 1 2 + r 2 2 + r 1 ) ,
k = μ r 2 ( r 1 2 + r 2 2 - r 1 ) .
R = | n - 1 n + 1 | 2 = ( n - 1 ) 2 + k 2 ( n + 1 ) 2 + k 2 ,
σ = σ 0 ω r 2 ,
σ 0 = σ ( ω ) | ω = 0 = N e 2 m · Γ ω 2 + Γ 2 | ω = 0 = N e 2 m Γ .
Γ = N e 2 m σ 0 .
ω p = ω ( 1 - r 1 ) 2 + r 2 2 1 - r 1 ,
Γ = ω r 2 1 - r 1 .
P · W + T = E ,
- r 1 ( ω ) r 2 ( ω ) ,

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