Abstract

Measurements of the optical constants of metals at submillimeter wavelengths are sparse. We have used a nonresonant cavity to measure, at room temperature, the angle averaged absorptance spectra P(ω) of aluminum, molybdenum, tantalum, titanium, tungsten, and iron in the 30–300-cm−1 wavenumber region. The real part of the normalized surface impedance spectrum, z(ω) = r(ω) + ix(ω), was determined from P(ω). Measurements were also made on iron from 400 to 4000 cm−1 using standard reflectance techniques. The r(ω) spectrum was combined with previous measurements by others at higher frequencies and Kramers-Kronig analyses of the resultant combined r(ω) spectra provided ɛ(ω) = ɛ1(ω) + iɛ2(ω) and N(ω) = n(ω) + ik(ω).

© 1988 Optical Society of America

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References

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  1. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  2. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).
  3. 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 (1985).
    [CrossRef] [PubMed]
  4. F. E. Pinkerton, A. J. Sievers, “Quantitative FIR Absorptivity Measurements of Metals with Dual Nonresonant Cavities,” Infrared Phys. 22, 377 (1982).
    [CrossRef]
  5. F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
    [CrossRef]
  6. G. Brandli, A. J. Sievers, “Absolute Measurement of the Far-Infrared Surface Resistance of Pb,” Phys. Rev. B 5, 3550 (1972).
    [CrossRef]
  7. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, M. R. Querry, “Optical Properties of Au, Ni, and Pb at Submillimeter Wavelengths,” Appl. Opt. 26, 744 (1987).
    [CrossRef] [PubMed]
  8. R. J. Bell, M. A. Ordal, R. W. Alexander, “Equations Linking Different Sets of Optical Properties for Nonmagnetic Materials,” Appl. Opt. 24, 3680 (1985).
    [CrossRef] [PubMed]
  9. 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]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).
  11. H. E. Bennett, J. M. Bennett, “Validity of the Drude Theory for Silver, Gold and Aluminum in the Infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175.
  12. L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

1987 (1)

1985 (2)

1984 (1)

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

1983 (1)

1982 (1)

F. E. Pinkerton, A. J. Sievers, “Quantitative FIR Absorptivity Measurements of Metals with Dual Nonresonant Cavities,” Infrared Phys. 22, 377 (1982).
[CrossRef]

1972 (1)

G. Brandli, A. J. Sievers, “Absolute Measurement of the Far-Infrared Surface Resistance of Pb,” Phys. Rev. B 5, 3550 (1972).
[CrossRef]

1971 (1)

L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

Alexander, R. W.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, “Validity of the Drude Theory for Silver, Gold and Aluminum in the Infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, “Validity of the Drude Theory for Silver, Gold and Aluminum in the Infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175.

Brandli, G.

G. Brandli, A. J. Sievers, “Absolute Measurement of the Far-Infrared Surface Resistance of Pb,” Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).

Kirillova, M. M.

L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).

Long, L. L.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).

Maple, M. B.

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

Nomerovannaya, L. V.

L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

Noskov, M. M.

L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

Ordal, M. A.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Pinkerton, F. E.

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

F. E. Pinkerton, A. J. Sievers, “Quantitative FIR Absorptivity Measurements of Metals with Dual Nonresonant Cavities,” Infrared Phys. 22, 377 (1982).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).

Querry, M. R.

Sales, B. C.

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

Sievers, A. J.

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

F. E. Pinkerton, A. J. Sievers, “Quantitative FIR Absorptivity Measurements of Metals with Dual Nonresonant Cavities,” Infrared Phys. 22, 377 (1982).
[CrossRef]

G. Brandli, A. J. Sievers, “Absolute Measurement of the Far-Infrared Surface Resistance of Pb,” Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).

Ward, C. A.

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).

Appl. Opt. (4)

Infrared Phys. (1)

F. E. Pinkerton, A. J. Sievers, “Quantitative FIR Absorptivity Measurements of Metals with Dual Nonresonant Cavities,” Infrared Phys. 22, 377 (1982).
[CrossRef]

Phys. Rev. B (2)

F. E. Pinkerton, A. J. Sievers, M. B. Maple, B. C. Sales, “Enhanced Far-Infrared Absorption in CdPd3 and YbCuSi2 Experiment,” Phys. Rev. B 29, 609 (1984).
[CrossRef]

G. Brandli, A. J. Sievers, “Absolute Measurement of the Far-Infrared Surface Resistance of Pb,” Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, “Optical Properties of Tungsten Monocrystals,” Sov. Phys. JETP 33, 405 (1971).

Other (4)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physics Data, Optical Properties of Metals, Part I: the Transition Metals and Physics Data, Optical Properties of Metals, Part II: the Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides (Fachinformationszentrum, 7514 Eggenatein-Leopoldshafen 2, Karlsruhe, F.R. Germany, 1981).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U.P., New York, 1986).

H. E. Bennett, J. M. Bennett, “Validity of the Drude Theory for Silver, Gold and Aluminum in the Infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175.

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Figures (12)

Fig. 1
Fig. 1

Normalized surface impedance of aluminum. Dots with error bars were measured with a nonresonant cavity. The dash–dot line is from Shiles et al. (tabulated in Ref. 2) and the dashed line is from Bennett and Bennett.11

Fig. 2
Fig. 2

ɛ1 and ɛ2 for aluminum derived from the Kramers-Kronig analysis as described in the text.

Fig. 3
Fig. 3

Normalized surface impedance of iron. Dots with error bars were measured with a nonresonant cavity. The dash–dot line is from our reflectance measurements. The dotted line is from the measurements of Bolotin et al. and the short–long dash line is from the measurements of Weaver (both tabulated in Ref. 2).

Fig. 4
Fig. 4

ɛ1 and ɛ2 for iron. The solid curve is from the Kramers-Kronig analysis as described in the text. The dash–dot line is from Weaver et al. (tabulated in Ref. 2). The dotted line represents the results of Bolotin et al. (tabulated in Ref. 2).

Fig. 5
Fig. 5

Normalized surface impedance of titanium. The dots with error bars are from the nonresonant cavity measurements. The dash–dot line represents the measurements of Lynch, Olson, and Weaver (tabulated in Ref. 2).

Fig. 6
Fig. 6

ɛ1 and ɛ2 of titanium. The solid line is from the Kramers-Kronig analysis as described in the text. The dash–dot line is from the measurements of Lynch, Olson, and Weaver (tabulated in Ref. 2).

Fig. 7
Fig. 7

Normalized surface impedance of tantalum. The dots with error bars are from the nonresonant cavity measurements. The dash–dot line represents the measurements of Weaver et al. (tabulated in Ref. 2).

Fig. 8
Fig. 8

ɛ1 and ɛ2 of tantalum from the Kramers-Kronig analysis as described in the text.

Fig. 9
Fig. 9

Normalized surface impedance for tungsten. The dots with error bars are the nonresonant cavity measurements. The dash–dot line represents the results of Weaver, Lynch, and Olson (tabulated in Ref. 2). The dotted line is the results of Nomerovannaya et al.12

Fig. 10
Fig. 10

ɛ1 and ɛ2 of tungsten. The solid line is from the Kramers-Kronig analysis described in the text. The dash–dot line is the data of Weaver, Lynch, and Olson (tabulated in Ref. 2). The dotted curve is the data of Nomerovannaya et al.12

Fig. 11
Fig. 11

Normalized surface impedance for molybdenum. The dots with error bars are the nonresonant cavity results. The dash–dot curve displays the results of Lynch and Hunter (tabulated in Ref. 2).

Fig. 12
Fig. 12

ɛ1 and ɛ2 of molybdenum from the Kramers-Kronig analysis described in the text.

Tables (6)

Tables Icon

Table I Optical Constants of Aluminum

Tables Icon

Table II Optical Constants of Iron

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Table III Optical Constants of Titanium

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Table IV Optical Constants of Tantalum

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Table V Optical Constants of Tungsten

Tables Icon

Table VI Optical Constants of Molybdenum

Equations (2)

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I s ( ω ) I r ( ω ) [ 2 S 1 + ( S 2 + S 3 ) P r ( ω ) ] + S 4 P r ( ω ) [ 2 S 1 + ( S 2 + S 3 ) P r ( ω ) ] + S 4 P s ( ω ) = 0 ,
P ( ω ) 4 r ( [ 1 + 1 r 2 ( 1 + ξ ) 2 ] [ r + 1 r 3 ( 1 + ξ ) 2 ] × ln [ 1 + 2 r + r 2 ( 1 + ξ 2 ) ] + r ln [ r 2 ( 1 + ξ 2 ) ] + ( 1 ξ 2 ξ ) { r tan 1 [ ξ 1 + r ( 1 + ξ 2 ) ] + 1 r 3 ( 1 + ξ 2 ) 2 tan 1 ( r ξ 1 + r ) } ) .

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