Abstract

The absorptance characteristics of bare silver aluminum, gold, copper, and molybdenum mirrors at angles of incidence from 0 to 89° are presented. The angle-dependent absorptance measurements are performed using a photoacoustic calorimetry technique. Absolute absorptance is determined using a laser energy ratiometer. Data are obtained for both s- and p-polarization light at two wavelengths, 0.5145 and 10.6 μm. It is found that the Fresnel theory for bare metal surfaces does not always reliably predict the measured absorptance at high angles of incidence.

© 1986 Optical Society of America

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References

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  1. B. E. Newnam, “Multifacet-All Metal Reflector Design for Soft X-Ray and XUV Free Electron Resonators,” at Seventeenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, CO., 28–30 Oct. 1985.
  2. J. F. Figueira, S. J. Thomas, “Damage Thresholds at Metal Surfaces for Short Pulse IR Lasers,” IEEE J. Quantum Electron. QE-18, 1381 (1982).
    [CrossRef]
  3. I. Goldstein, D. Bua, F. A. Horrigan, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., Natl. Bur. Stand. U.S. Spec. Publ. 435 (1976), pp. 41–48.
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 628–630.
  5. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Eds., Physics Data: Optical Properties of Metals, Cuts 1 and 2 (Fachinformationszentrum, Federal Republic of Germany, 1981).
  6. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “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 (1983).
    [CrossRef] [PubMed]
  7. H. J. Hagemann, W. Gudat, C. Kunz, “Optical Constants From the Far Infrared to the X-ray Region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” J. Opt. Soc. Am. 65, 742 (1975).
    [CrossRef]
  8. L. G. Schulz, “The Optical Constants of Silver, Gold, Copper, and Aluminum. I: The Absorption Coefficient k,” J. Opt. Soc. Am. 44, 357 (1954).
    [CrossRef]
  9. L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II: The Index of Refraction n,” J. Opt. Soc. Am. 44, 362 (1954).
    [CrossRef]
  10. E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum-Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
    [CrossRef]
  11. P. F. Robusto, R. Braunstein, “Optical Measurements of the Surface Plasmon of Copper,” Phys. Status Solidi 107, 443 (1981).
    [CrossRef]
  12. W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” to be published Rev. Sci. Instrum., Nov.1986.
    [CrossRef]
  13. A. Hordvik, H. Schlossberg, “Photoacoustic Technique for Determining Optical Absorption Coefficients in Solids,” Appl. Opt. 16, 101 (1977).
    [CrossRef] [PubMed]

1983 (1)

1982 (1)

J. F. Figueira, S. J. Thomas, “Damage Thresholds at Metal Surfaces for Short Pulse IR Lasers,” IEEE J. Quantum Electron. QE-18, 1381 (1982).
[CrossRef]

1981 (1)

P. F. Robusto, R. Braunstein, “Optical Measurements of the Surface Plasmon of Copper,” Phys. Status Solidi 107, 443 (1981).
[CrossRef]

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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

1977 (1)

1975 (1)

1954 (2)

Alexander, R. W.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 628–630.

Braunstein, R.

P. F. Robusto, R. Braunstein, “Optical Measurements of the Surface Plasmon of Copper,” Phys. Status Solidi 107, 443 (1981).
[CrossRef]

Bua, D.

I. Goldstein, D. Bua, F. A. Horrigan, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., Natl. Bur. Stand. U.S. Spec. Publ. 435 (1976), pp. 41–48.

Figueira, J. F.

J. F. Figueira, S. J. Thomas, “Damage Thresholds at Metal Surfaces for Short Pulse IR Lasers,” IEEE J. Quantum Electron. QE-18, 1381 (1982).
[CrossRef]

Ford, D. H.

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” to be published Rev. Sci. Instrum., Nov.1986.
[CrossRef]

Goldstein, I.

I. Goldstein, D. Bua, F. A. Horrigan, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., Natl. Bur. Stand. U.S. Spec. Publ. 435 (1976), pp. 41–48.

Gudat, W.

Hagemann, H. J.

Hordvik, A.

Horrigan, F. A.

I. Goldstein, D. Bua, F. A. Horrigan, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., Natl. Bur. Stand. U.S. Spec. Publ. 435 (1976), pp. 41–48.

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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Kimura, W. D.

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” to be published Rev. Sci. Instrum., Nov.1986.
[CrossRef]

Kunz, C.

Long, L. L.

Newnam, B. E.

B. E. Newnam, “Multifacet-All Metal Reflector Design for Soft X-Ray and XUV Free Electron Resonators,” at Seventeenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, CO., 28–30 Oct. 1985.

Ordal, M. A.

Robusto, P. F.

P. F. Robusto, R. Braunstein, “Optical Measurements of the Surface Plasmon of Copper,” Phys. Status Solidi 107, 443 (1981).
[CrossRef]

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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Schlossberg, H.

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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Tangherlini, F. R.

Thomas, S. J.

J. F. Figueira, S. J. Thomas, “Damage Thresholds at Metal Surfaces for Short Pulse IR Lasers,” IEEE J. Quantum Electron. QE-18, 1381 (1982).
[CrossRef]

Ward, C. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 628–630.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

J. F. Figueira, S. J. Thomas, “Damage Thresholds at Metal Surfaces for Short Pulse IR Lasers,” IEEE J. Quantum Electron. QE-18, 1381 (1982).
[CrossRef]

J. Opt. Soc. Am. (3)

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: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Phys. Status Solidi (1)

P. F. Robusto, R. Braunstein, “Optical Measurements of the Surface Plasmon of Copper,” Phys. Status Solidi 107, 443 (1981).
[CrossRef]

Other (5)

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” to be published Rev. Sci. Instrum., Nov.1986.
[CrossRef]

B. E. Newnam, “Multifacet-All Metal Reflector Design for Soft X-Ray and XUV Free Electron Resonators,” at Seventeenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, CO., 28–30 Oct. 1985.

I. Goldstein, D. Bua, F. A. Horrigan, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds., Natl. Bur. Stand. U.S. Spec. Publ. 435 (1976), pp. 41–48.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 628–630.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Eds., Physics Data: Optical Properties of Metals, Cuts 1 and 2 (Fachinformationszentrum, Federal Republic of Germany, 1981).

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Figures (21)

Fig. 1
Fig. 1

Schematic of glancing incidence measurement apparatus.

Fig. 2
Fig. 2

Absorptance characteristics of the bare silver mirror at 0.5145 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Hagemann et al.7

Fig. 3
Fig. 3

Absorptance characteristics of the bare silver mirror at 10.6 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Hagemann et al.7

Fig. 4
Fig. 4

Absorptance characteristics of the bare silver mirror discussed in Figs. 2 and 3 between 80 and 90° angle of incidence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light. The bare metal theoretical curves use values for n and k given by Hagemann et al.7

Fig. 5
Fig. 5

Fractional deviation of bare silver mirror absorptance data from theoretical cosine dependence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light.

Fig. 6
Fig. 6

Absorptance characteristics of the bare aluminum mirror at 0.5145 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Shiles et al.10

Fig. 7
Fig. 7

Absorptance characteristics of the bare aluminum mirror at 10.6 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Shiles et al.10

Fig. 8
Fig. 8

Absorptance characteristics of the bare aluminum mirror discussed in Figs. 6 and 7 between 80 and 90° angle of incidence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light. The bare metal theoretical curves use values for n and k given by Shiles et al.10

Fig. 9
Fig. 9

Fractional deviation of bare aluminum mirror absorptance data from theoretical cosine dependence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light.

Fig. 10
Fig. 10

Absorptance characteristics of the bare gold mirror at 0.5145 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Weaver.5

Fig. 11
Fig. 11

Absorptance characteristics of the bare gold mirror at 10.6 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Weaver.5

Fig. 12
Fig. 12

Absorptance characteristics of the bare gold mirror discussed in Figs. 10 and 11 between 80 and 90° angle of incidence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light. The bare metal theoretical curves use value for n and k given by Weaver.5

Fig. 13
Fig. 13

Fractional deviation of bare gold mirror absorptance data from theoretical cosine dependence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light.

Fig. 14
Fig. 14

Absorptance characteristics of the bare copper mirror at 0.5145 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Robusto and Braunstein.11

Fig. 15
Fig. 15

Absorptance characteristics of the bare copper mirror at 10.6 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Robusto and Braunstein.11

Fig. 16
Fig. 16

Absorptance characteristics of the bare copper mirror discussed in Figs. 14 and 15 between 80 and 90° angle of incidence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light. The bare metal theoretical curves use values for n and k given by Robusto and Braunstein.11

Fig. 17
Fig. 17

Fractional deviation of bare copper mirror absorptance data from theoretical cosine dependence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light.

Fig. 18
Fig. 18

Absorptance characteristics of the bare molybdenum mirror at 0.5145 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Weaver.5

Fig. 19
Fig. 19

Absorptance characteristics of the bare molybdenum mirror at 10.6 μm: (a) s-polarized light; (b) p-polarized light. The bare metal theoretical curves use values for n and k given by Weaver.5

Fig. 20
Fig. 20

Absorptance characteristics of the bare molybdenum mirror discussed in Figs. 18 and 19 between 80 and 90° angle of incidence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light. The bare metal theoretical curves use values for n and k given by Weaver.5

Fig. 21
Fig. 21

Fractional deviation of bare molybdenum mirror absorptance data from theoretical cosine dependence for s-polarized light: (a) 0.5145-μm light; (b) 10.6-μm light.

Equations (5)

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n ( λ ) = n ( λ ) + i k ( λ ) ,
ρ 2 = ( cos θ - u ) 2 + v 2 ( cos θ + u ) 2 + v 2 ,
ρ 2 = [ ( n 2 - k 2 ) cos θ - u ] 2 + ( 2 n k cos θ - v ) 2 [ ( n 2 - k 2 ) cos θ + u ] 2 + ( 2 n k cos θ + v ) 2 ,
2 u 2 = ( n 2 - k 2 ) - sin 2 θ + { [ ( n 2 - k 2 ) - sin 2 θ ] 2 + 4 n 2 k 2 } 1 / 2 , 2 v 2 = - ( n 2 - k 2 ) + sin 2 θ + { [ ( n 2 - k 2 ) - sin 2 θ ] 2 + 4 n 2 k 2 } 1 / 2 .
A ( θ ) - A ( 0 ) cos θ A ( 0 ) cos θ ,

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