Abstract

Infrared optical constants collected from the literature are tabulated. The data for the noble metals and Al, Pb, and W can be reasonably fit using the Drude model. It is shown that 1(ω)=2(ω)ωp2/(2ωτ2) at the damping frequency ω = ωτ. Also −1(ωτ) ≃ −(½) 1(0), where the plasma frequency is ωp.

© 1983 Optical Society of America

I. Introduction

Many measurements of the optical constants of metals have been made, primarily at near IR, visible, and UV wavelengths. Brandli and Sievers[1] have measured Au and Pb in the far IR. For the near and far IR we have compiled these data and have tabulated the real and imaginary parts of the dielectric function, 1 and 2, respectively, the index of refraction n and the extinction index k for each metal. Drude model[2] parameters giving a reasonable fit to the data are given for Au, Ag, Cu, Al, Pb, and W. In general, the Drude model is not expected to be appropriate for transition metals in the near and middle IR, but a good fit can be obtained for W with a Drude model dielectric function.

Weaver et al.[3] have compiled extensive tables or optical properties of metals which have been recently published. Most of their tables do not extend beyond 12-μm wavelength, while our compilation extends to the longest wavelength for which data are available. Another standard compilation is that of Haas and Hadley in the AMERICAN INSTITUTE OF PHYSICS HANDBOOK.[4] However, this includes data only up to 1967. Except for a few cases, the data presented here are more recent.

Bennett and Bennett[5] have shown that the Drude model fits the measured reflectance of gold, silver, and aluminum in the 3–30-μm wavelength range with one adjustable parameter; i.e., the Drude model parameters were obtained from the dc resistivity and fitted with one free electron per atom for gold and silver and 2.6 free electrons per atom for aluminum. Brandli and Sievers have shown that the Drude model is an excellent fit to their far IR measurements on lead and provides a good fit for gold with no adjustable parameters.

II. Definitions and Equations

In keeping with IR spectroscopic notation, all frequencies will be expressed in cm−1. The complex dielectric function c and the complex index of refraction nc are defined as

c1+i2nc2(n+ik)2.

The Drude model dielectric function is

c=ωp2ω2+iωωτ,

where ω, ωp, and ωτ have units of cm−1. Separating the real and imaginary parts yields

1=ωp2ω2+ωτ2,
2=ωp2ωτω3+ωωτ2.

In these equations, the plasma frequency[6] is

ωp(cm1)=12πc(4πNe2m*)1/2,

where N is the free electron density, e is the electron charge, m* is the effective mass of the electrons, and is the high frequency dielectric constant. The damping frequency ωτ expressed in cm−1 is

ωτ(cm1)=12πcτ,

where τ is the electron lifetime in seconds and c is the velocity of light. Note that for low frequencies

1(0)(ωpωτ)2.

The dc conductivity σ0 is related to ωp and ωτ by

σ0=ωp2/(4πωτ)

with σ0 having units of cm−1. This can be expressed in terms of the dc resistivity ρ0:

σ0(cm1)=1/[2πcρo(s)]=(9×1011)/[2πcρ0(Ωcm)].

To analyze the data of Brandli, and Sievers[1] it is convenient to write the surface impedance Z(ω) for the Drude model[2]:

Z(ω)R(ω)+iX(ω)=4πc(1+i)(ωωτ2ωp2)1/2(1+iωωτ)1/2.

We shall need only R(ω):

R(ω)=4πc(ωωτ2ωp2)1/2[ωωτ+(1+ω2ωτ2)1/2]1/2.

III. Determination of Drude Model Parameters

All data in the form of n and k were changed to 1 and 2. Equations (3) and (4) were solved for ωτ, eliminating ωp:

ωτ=ω2(11).

This equation was solved to determine ωτ using 1 and 2 at some frequency ω. Then ωp was obtained from

ωp2=(11)(ω2+ωτ2).

This was done for several values of ω to obtain several pairs of ωτ and ωp, which produce the curve with the best eyeball fit to the data.

The one exception to this process was the measurements of Brandli and Sievers[1] for Au and Pb. They reported values of R(ω)/Z0 where Z0 = (4π)/c. For the far IR, Eq. (11) reduces to

R(ω)Z0=(ωωτ2ωp2)1/2.

ωτ was obtained from this data using ωn from the near IR fit. This value of ωτ was used for gold and lead rather than the ωτ obtained from the near IR fit.

We note from Eq. (12) the frequency for which −1(ω) = 2(ω) is very nearly ω = ωτ since −1 ≫ 1. With ω = ωτ both components (−1 and 2) of the dielectric function are ωp2/(2ωτ2). Thus the Drude parameters, ωτ and ωp, can be determined at the crossover from ω = ωτ and the value of the dielectric function. Note that 1(0)ωp2/ωτ2; so −½1(0) ≃ −1(ωτ).

IV. Data

Figures 112 are plots of −1(ω) and 2(ω) for the twelve metals. The high frequency termination occurs where the Drude model becomes invalid. The solid lines are calculated from the Drude model with the parameters listed in Table 13. Tables 112 present the collected values of 1, 2, n and k. Table 13 summarizes the Drude model parameters from our fit (for Ag, Au, Cu, Al, Pb, and W) as well as ωτ calculated from ωp and the AIP Handbook[19] values of the dc resistivity. Dielectric functions for all metals considered in this article except Pb have been tabulated by Weaver et al. for the UV, visible, and near IR.

Finally, we disclaim any physical signficance for the Drude model. The intent is only to parametrize the optical constants for these metals even when there is some question as to the physical meaning of the parameters. The transition metals show interband transitions and cannot be fit with a Drude model in the IR (with the exception of W). Even the noble metals in the IR can have small interband contributions to the dielectric constants.[20]

This work was partially supported by the U.S. Army, DAAK-11-82-C-0052. We gratefully acknowledge the valuable advice of Jean M. Bennett, David Begley, David Bryan, Kul Bhasin, and W. F. Parks.

Figures and Tables

 

Fig. 1 Aluminum: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. [7] are: Shiles et al., □ for both −1 and 2; Bennett and Bennett * for −1 and 2; Schulz, ⋄ for −1 and 2.

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Fig. 2 Copper: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. [8] are: Schulz, ⋄ for both −1 and 2; Lenham and Treherne, * for −1 and 2; Robusto and Braunstein, □ for both; Hageman et al., × for both; and Dold and Mecke, Δ for both.

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Fig. 3 Gold: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. [9] are: Bennett and Bennett, * for both −1 and 2; Schulz, ⋄ for both; Motulevich and Shubin, □ for both; Padalka and Shklyarevskii, ○ for both; Bolotin et al., × for both; Brandli and Sievers, + for both; Weaver et al., Δ for both.

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Fig. 4 Lead: −1(ω) and 2(ω) vs frequency. The solid line represents the Drude model. The data from Ref. [10] are: Brandli and Sievers, × for −1 and + for 2; and Golovashkin and Motulevich, Δ for −1 and □ for 2.

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Fig. 5 Silver: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. [11] are: Bennett and Bennett, * for both −1 and 2; Schulz, ⋄ for both; and Hagemann et al., × for both.

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Fig. 6 Colbalt: −1(ω) and 2(ω) vs frequency. The data from Ref. [12] are: Kirillova and Charikov, + for −1 and □ for 2; Johnson and Christy, ⋄ for −1 and ○ for 2; and Weaver et al, × for −1 and Δ for 2.

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Fig. 7 Iron: −1(ω) and 2(ω) vs frequency. The data from Ref. [13] are: Weaver et al., × for −1 and Δ for 2; Bolotin et al., ⋄ for −1 and ○ for 2.

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Fig. 8 Nickel: −1(ω) and 2(ω) vs frequency. The data from Ref. [14] are: Lynch et al., × for −1 and Δ for 2; Johnson and Christy, ⋄ for −1 and ○ for 2.

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Fig. 9 Palladium: −1(ω) and 2(ω) vs frequency. The data from Ref. [15] are: Weaver and Benbow, ⋄ for −1 and ○ for 2; Bolotin et al., + for −1 and □ for 2; Johnson and Christy, × for −1 and Δ for 2.

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Fig. 10 Platinum: −1(ω) and 2(ω) vs frequency. The data from Ref. [16] are Weaver et al., Δ for −1 and □ for 2.

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Fig. 11 Titanium: −1(ω) and 2(ω) vs frequency. The data from Ref. [17] are: Kirillova and Charikov, □ for both −1 and 2; Lynch et al., Δ for both; Johnson and Christy, ○ for both; Kirillova and Charikov, + for both; Bolotin et al., × for both.

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Fig. 12 Tungsten: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. [18] are: Nomerovannaya et al., □ for both −1 and 2; Weaver et al., Δ for both.

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Tables Icon

TABLE 1. Al, ALUMINUME. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980)

Tables Icon

H. E. Bennett and J. M. Bennett, Optical Properties and Electronics Structure of Metals and Alloys, ed. F. Abeles (North–Holland, 1966), p. 175.

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L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954) and 362 (1954).

Tables Icon

TABLE 2. Cu, COPPERL. G. Schulz, J. Opt. Am. 44, 357 and 362 (1954).

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A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966).

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P. F. Robusto and Braunstein, Phys. Stat. Sol. (b) 107, 443 (1981).

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H. J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

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B. Dold and R. Mecke, Optik 22, 435 (1965).

Tables Icon

TABLE 3. Au, GOLDH. E. Bennett and J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys edited by F. Abeles (North–Holland, Amsterdam, 1966), p. 175.

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L. G. Schulz, J. Opt. Soc. Am. 44, 357 and 362 (1954).

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G. P. Motulevich and A. A. Shubin, Soviet Phys. JETP 20, 560 (1965).

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V. G. Padalka and I. N. Shklyarevskii, Opt. Spectr. U.S.S.R. 11, 285 (1961).

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G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, and B. A. Charikov, Phys. Met. and Met. 13, 823 (1962).

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G. Brandli and A. J. Sievers, Phy. Rev. B 5, 3550 (1972).

Tables Icon

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch (with C. G. Olson), Physics Data, Optical Properties of Metals, (Fach–Information Zentrum, Kalsrube, FOR, 1981).

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TABLE 4. Pb, LEADG. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972).

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A. I. Golovashkin and G. P. Motulevich, Soviet Physics JETP 26, 881 (1968)

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TABLE 5. Ag, SILVERH. E. Bennett and J. M. Bennett in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abeles (North–Holland, Amsterdam, 1966), p. 175.

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L. G. Schulz, J. Opt. Soc. Am. 44, p. 357 and 362 (1954).

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H. J. Hageman, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

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TABLE 6. Co, COBALTM. M. Kirillova and B. A. Charikov, Opt. Spectry. 17, 134 (1964).

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P. B. Johnson and R. W. Christy, Phys. B 9, 5056 (1974).

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J. H. Weaver, E. Colavita, D. W. Lynch and R. Rosei, Phys. Rev. B 19, 3850 (1979).

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TABLE 7. Fe, IronJ. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys. Rev. B 19, 3850 (1979).

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G. A. Bolotin, M. M. Kirillova, and V. M. Mayevskiy, Phys. Met. Metall, 27(2) 31 (1969).

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TABLE 8. Ni, NICKELD. W. Lynch, R. Rosei and J. H. Weaver, Solid State Commun. 9, 2195 (1971).

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B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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TABLE 9. Pd, PalladiumJ. H. Weaver and R. L. Bendow, Phys. Rev. B 12, 3509 (1975).

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G. A. Bolotin, M. M. Kirilova, L. V. Nomerovannaya, and M. M. Noskov, Fiz. Metal. Metalloved 23, 463 (1967).

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P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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TABLE 10. Pt, PlatinumJ. H. Weaver, Phys. Rev. B 11, 1416 (1975).

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J. H. Weaver, D. W. Lynch, and C. G. Olson, Phys. Rev. B 10, 501 (1974).

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TABLE 11. Ti, TITANIUMM. M. Kirillova and B. A. Charikov, Opt. Spectry 17, 134 (1964).

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D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev. B 11, 3617 (1975).

Tables Icon

P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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M. M. Kirillova and B. A. Charikov, Phys. Met. 15, 138 (1963).

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G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, and B. A. Charikov, Phys. Met. and Met. 13, 823 (1962).

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TABLE 12. W, TUNGSTENL. V. Nomerovannaya, M. M. Kirillova, and M. M. Noskov, Opt. Spectry. 17, 134 (1964).

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J. H. Weaver, D. W. Lynch and C. G. Olson, Phys. Rev. B 12, 1293 (1975).

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Table 13. Optical Parameters Found using a Drude Model Fit of the Experimental Dielectric Functions for Six Metals for which the Dielectric Functions could be Fit; here ωf is the Frequency at which the Fit is Forced, and −1(0) is −1(ω) at dc; the Crossover Frequency Applies to −12.

References

1. G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972). [CrossRef]  

2. P. Drude, Theory of Optics (Longmans, Green, New York, 1922; Dover, New York, 1968). A more modern reference is F. Wooten, Optical Properties of Solids (Academic, New York, 1972), p. 52. For the Drude model and surface impedance see B. Donovan, Elementary Theory of Metals (Pergamon, New York, 1967), p. 220.

3. J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

4. G. Haas and L. Hadley, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–118.

5. H. E. Bennett and J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed., (North-Holland, Amsterdam; Wiley, New York, 1966), Sec. II.6, p. 175. For Ag, Au, and AL for ω, they estimated 145, 216, and 663 cm−1, respectively.

6. For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is (the contribution from the core electrons at high frequencies). Often m* = m and = 1 are assumed. For discussion see H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant. [CrossRef]  

7. Al: E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980); [CrossRef]  H. E. Bennett and J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954). [CrossRef]  

8. Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); [CrossRef]  A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966); [CrossRef]  P. F. Robusto and R. Braunstein, Phys. Status Solidi B 107, 443 (1981); [CrossRef]  H. J. Hageman, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975); [CrossRef]  B. Dold and R. Mecke, Optik 22, 435 (1965).

9. Au: H. E. Bennett and J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); [CrossRef]  G. P. Motulevich and A. A. Shubin, Sov. Phys. JETP 20, 560 (1965); V. G. Padalka and I. N. Shklyarevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N. Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, and B. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brändli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972). [CrossRef]  

10. Pb: G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972); [CrossRef]  A. I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).

11. Ag: H. E. Bennett and J. M. Bennett, in Optical Properties and Electronic Structure of Metals and AlloysF. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, and 362 (1954); [CrossRef]  H. J. Hagemann, W. Endat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975). [CrossRef]  

12. Co: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974); [CrossRef]  J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys. Rev. B 19, 3850 (1979). [CrossRef]  

13. Fe: J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys. Rev. B 19, 3850 (1979); [CrossRef]  G. A. Bolotin, M. M. Krillova, and V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).

14. Ni: D. W. Lynch, R. Rosei, and J. H. Weaver, Solid State Commun. 9, 2195 (1973); [CrossRef]  P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974). [CrossRef]  

15. Pd: J. H. Weaver and R. L. Benbow, Phys. Rev. B 12, 3509 (1975); [CrossRef]  G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, and M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974). [CrossRef]  

16. Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); [CrossRef]  J. H. Weaver, C. G. Olson, and D. W. Lynch, Phys. Rev. B 10, 501 (1974). [CrossRef]  

17. Ti: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev. B 11, 3617 (1975); [CrossRef]  P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974); [CrossRef]  M. M. Kirillova and B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, and B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).

18. W: L. V. Nomerovannaya, M. M. Kirillova, and M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, and C. G. Olson, Phys. Rev. B 12, 1293 (1975). [CrossRef]  

19. J. Babiskin and J. R. Anderson, in American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 9–39.

20. G. R. Parkins, W. E. Lawrence, and R. W. Christy, Phys. Rev. B 23, 6408 (1981). [CrossRef]  

References

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  1. G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
    [CrossRef]
  2. P. Drude, Theory of Optics (Longmans, Green, New York, 1922; Dover, New York, 1968). A more modern reference is F. Wooten, Optical Properties of Solids (Academic, New York, 1972), p. 52. For the Drude model and surface impedance see B. Donovan, Elementary Theory of Metals (Pergamon, New York, 1967), p. 220.
  3. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).
  4. G. Haas, L. Hadley, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–118.
  5. H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed., (North-Holland, Amsterdam; Wiley, New York, 1966), Sec. II.6, p. 175. For Ag, Au, and AL for ω, they estimated 145, 216, and 663 cm−1, respectively.
  6. For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is ∊∞ (the contribution from the core electrons at high frequencies). Often m* = m and ∊∞ = 1 are assumed. For discussion see H. Ehrenreich, M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant.
    [CrossRef]
  7. Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
    [CrossRef]
  8. Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P. Lenham, D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966); P. F. Robusto, R. Braunstein, Phys. Status Solidi B 107, 443 (1981); H. J. Hageman, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975); B. Dold, R. Mecke, Optik 22, 435 (1965).
    [CrossRef]
  9. Au: H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); G. P. Motulevich, A. A. Shubin, Sov. Phys. JETP 20, 560 (1965); V. G. Padalka, I. N. Shklyarevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N. Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, B. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brändli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
    [CrossRef]
  10. Pb: G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A. I. Golovashkin, G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).
    [CrossRef]
  11. Ag: H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and AlloysF. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, and 362 (1954); H. J. Hagemann, W. Endat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
    [CrossRef]
  12. Co: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979).
    [CrossRef]
  13. Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
    [CrossRef]
  14. Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
    [CrossRef]
  15. Pd: J. H. Weaver, R. L. Benbow, Phys. Rev. B 12, 3509 (1975); G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
    [CrossRef]
  16. Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C. G. Olson, D. W. Lynch, Phys. Rev. B 10, 501 (1974).
    [CrossRef]
  17. Ti: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, J. H. Weaver, Phys. Rev. B 11, 3617 (1975); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); M. M. Kirillova, B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).
    [CrossRef]
  18. W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
    [CrossRef]
  19. J. Babiskin, J. R. Anderson, in American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 9–39.
  20. G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
    [CrossRef]

1981

G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
[CrossRef]

1980

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

1979

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

1975

Pd: J. H. Weaver, R. L. Benbow, Phys. Rev. B 12, 3509 (1975); G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C. G. Olson, D. W. Lynch, Phys. Rev. B 10, 501 (1974).
[CrossRef]

1973

Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

1972

Pb: G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A. I. Golovashkin, G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).
[CrossRef]

G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

1964

Co: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979).
[CrossRef]

Ti: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, J. H. Weaver, Phys. Rev. B 11, 3617 (1975); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); M. M. Kirillova, B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).
[CrossRef]

W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
[CrossRef]

1959

For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is ∊∞ (the contribution from the core electrons at high frequencies). Often m* = m and ∊∞ = 1 are assumed. For discussion see H. Ehrenreich, M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant.
[CrossRef]

1954

Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P. Lenham, D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966); P. F. Robusto, R. Braunstein, Phys. Status Solidi B 107, 443 (1981); H. J. Hageman, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975); B. Dold, R. Mecke, Optik 22, 435 (1965).
[CrossRef]

Anderson, J. R.

J. Babiskin, J. R. Anderson, in American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 9–39.

Babiskin, J.

J. Babiskin, J. R. Anderson, in American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 9–39.

Benbow, R. L.

Pd: J. H. Weaver, R. L. Benbow, Phys. Rev. B 12, 3509 (1975); G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Bennett, H. E.

Ag: H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and AlloysF. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, and 362 (1954); H. J. Hagemann, W. Endat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
[CrossRef]

Au: H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); G. P. Motulevich, A. A. Shubin, Sov. Phys. JETP 20, 560 (1965); V. G. Padalka, I. N. Shklyarevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N. Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, B. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brändli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed., (North-Holland, Amsterdam; Wiley, New York, 1966), Sec. II.6, p. 175. For Ag, Au, and AL for ω, they estimated 145, 216, and 663 cm−1, respectively.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed., (North-Holland, Amsterdam; Wiley, New York, 1966), Sec. II.6, p. 175. For Ag, Au, and AL for ω, they estimated 145, 216, and 663 cm−1, respectively.

Au: H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); G. P. Motulevich, A. A. Shubin, Sov. Phys. JETP 20, 560 (1965); V. G. Padalka, I. N. Shklyarevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N. Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, B. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brändli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Ag: H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and AlloysF. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, and 362 (1954); H. J. Hagemann, W. Endat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
[CrossRef]

Brandli, G.

Pb: G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A. I. Golovashkin, G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).
[CrossRef]

G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Charikov, B. A.

Co: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979).
[CrossRef]

Ti: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, J. H. Weaver, Phys. Rev. B 11, 3617 (1975); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); M. M. Kirillova, B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).
[CrossRef]

Christy, R. W.

G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
[CrossRef]

Cohen, M. H.

For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is ∊∞ (the contribution from the core electrons at high frequencies). Often m* = m and ∊∞ = 1 are assumed. For discussion see H. Ehrenreich, M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant.
[CrossRef]

Colavita, E.

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

Drude, P.

P. Drude, Theory of Optics (Longmans, Green, New York, 1922; Dover, New York, 1968). A more modern reference is F. Wooten, Optical Properties of Solids (Academic, New York, 1972), p. 52. For the Drude model and surface impedance see B. Donovan, Elementary Theory of Metals (Pergamon, New York, 1967), p. 220.

Ehrenreich, H.

For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is ∊∞ (the contribution from the core electrons at high frequencies). Often m* = m and ∊∞ = 1 are assumed. For discussion see H. Ehrenreich, M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant.
[CrossRef]

Haas, G.

G. Haas, L. Hadley, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–118.

Hadley, L.

G. Haas, L. Hadley, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–118.

Inokuti, M.

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

Kirillova, M. M.

W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
[CrossRef]

Ti: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, J. H. Weaver, Phys. Rev. B 11, 3617 (1975); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); M. M. Kirillova, B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).
[CrossRef]

Co: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979).
[CrossRef]

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

Lawrence, W. E.

G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
[CrossRef]

Lynch, D. W.

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

Nomerovannaya, L. V.

W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
[CrossRef]

Noskov, M. M.

W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
[CrossRef]

Parkins, G. R.

G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
[CrossRef]

Rosei, R.

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Sasaki, T.

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

Schulz, L. G.

Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P. Lenham, D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966); P. F. Robusto, R. Braunstein, Phys. Status Solidi B 107, 443 (1981); H. J. Hageman, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975); B. Dold, R. Mecke, Optik 22, 435 (1965).
[CrossRef]

Shiles, E.

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

Sievers, A. J.

Pb: G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A. I. Golovashkin, G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).
[CrossRef]

G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Smith, D. Y.

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

Weaver, J. H.

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C. G. Olson, D. W. Lynch, Phys. Rev. B 10, 501 (1974).
[CrossRef]

Pd: J. H. Weaver, R. L. Benbow, Phys. Rev. B 12, 3509 (1975); G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

J. Opt. Soc. Am.

Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P. Lenham, D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966); P. F. Robusto, R. Braunstein, Phys. Status Solidi B 107, 443 (1981); H. J. Hageman, W. Gudat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975); B. Dold, R. Mecke, Optik 22, 435 (1965).
[CrossRef]

Opt. Spectrosc.

Co: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979).
[CrossRef]

Ti: M. M. Kirillova, B. A. Charikov, Opt. Spectrosc. 17, 134 (1964); D. W. Lynch, C. G. Olson, J. H. Weaver, Phys. Rev. B 11, 3617 (1975); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974); M. M. Kirillova, B. A. Charikov, Phys. Met. 15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov, A. V. Sokolov, B. A. Charikov, Phys. Met. Metallogr. USSR 13, 823 (1962).
[CrossRef]

W: L. V. Nomerovannaya, M. M. Kirillova, M. M. Noskov, Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, C. G. Olson, Phys. Rev. B 12, 1293 (1975).
[CrossRef]

Phys. Rev.

For a single carrier type (electrons) the plasma frequency ωp is as given in Eq. (5) where the dielectric constant is ∊∞ (the contribution from the core electrons at high frequencies). Often m* = m and ∊∞ = 1 are assumed. For discussion see H. Ehrenreich, M. H. Cohen, Phys. Rev. 115, 786 (1959); the last paragraph on p. 790 is most relevant.
[CrossRef]

Phys. Rev. B

Al: E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, Phys. Rev. B 22, 1612 (1980); H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
[CrossRef]

G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

Pd: J. H. Weaver, R. L. Benbow, Phys. Rev. B 12, 3509 (1975); G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, M. M. Noskov, Fiz. Met. Mettalloved. 23, 463 (1967); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C. G. Olson, D. W. Lynch, Phys. Rev. B 10, 501 (1974).
[CrossRef]

Fe: J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, Phys. Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, V. M. Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
[CrossRef]

Pb: G. Brandli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A. I. Golovashkin, G. P. Motulevich, Sov. Phys. JETP 26, 881 (1968).
[CrossRef]

G. R. Parkins, W. E. Lawrence, R. W. Christy, Phys. Rev. B 23, 6408 (1981).
[CrossRef]

Solid State Commun.

Ni: D. W. Lynch, R. Rosei, J. H. Weaver, Solid State Commun. 9, 2195 (1973); P. B. Johnson, R. W. Christy, Phys. Rev. B 9, 5056 (1974).
[CrossRef]

Other

Ag: H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and AlloysF. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt. Soc. Am. 44, 357, and 362 (1954); H. J. Hagemann, W. Endat, C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
[CrossRef]

J. Babiskin, J. R. Anderson, in American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 9–39.

P. Drude, Theory of Optics (Longmans, Green, New York, 1922; Dover, New York, 1968). A more modern reference is F. Wooten, Optical Properties of Solids (Academic, New York, 1972), p. 52. For the Drude model and surface impedance see B. Donovan, Elementary Theory of Metals (Pergamon, New York, 1967), p. 220.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Part 1: The Transition Metals,” “Part 2, Noble Metals, Aluminum, Scandium, Yttrium, the Lanthanides, and the Actinides,” in Physics Data, Optical Properties of Metals (Fachinformationszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Federal Republic of Germany, 1981).

G. Haas, L. Hadley, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p. 6–118.

H. E. Bennett, J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed., (North-Holland, Amsterdam; Wiley, New York, 1966), Sec. II.6, p. 175. For Ag, Au, and AL for ω, they estimated 145, 216, and 663 cm−1, respectively.

Au: H. E. Bennett, J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); G. P. Motulevich, A. A. Shubin, Sov. Phys. JETP 20, 560 (1965); V. G. Padalka, I. N. Shklyarevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N. Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, B. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brändli, A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Aluminum: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. 7 are: Shiles et al., □ for both −1 and 2; Bennett and Bennett * for −1 and 2; Schulz, ⋄ for −1 and 2.

Fig. 2
Fig. 2

Copper: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. 8 are: Schulz, ⋄ for both −1 and 2; Lenham and Treherne, * for −1 and 2; Robusto and Braunstein, □ for both; Hageman et al., × for both; and Dold and Mecke, Δ for both.

Fig. 3
Fig. 3

Gold: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. 9 are: Bennett and Bennett, * for both −1 and 2; Schulz, ⋄ for both; Motulevich and Shubin, □ for both; Padalka and Shklyarevskii, ○ for both; Bolotin et al., × for both; Brandli and Sievers, + for both; Weaver et al., Δ for both.

Fig. 4
Fig. 4

Lead: −1(ω) and 2(ω) vs frequency. The solid line represents the Drude model. The data from Ref. 10 are: Brandli and Sievers, × for −1 and + for 2; and Golovashkin and Motulevich, Δ for −1 and □ for 2.

Fig. 5
Fig. 5

Silver: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. 11 are: Bennett and Bennett, * for both −1 and 2; Schulz, ⋄ for both; and Hagemann et al., × for both.

Fig. 6
Fig. 6

Colbalt: −1(ω) and 2(ω) vs frequency. The data from Ref. 12 are: Kirillova and Charikov, + for −1 and □ for 2; Johnson and Christy, ⋄ for −1 and ○ for 2; and Weaver et al, × for −1 and Δ for 2.

Fig. 7
Fig. 7

Iron: −1(ω) and 2(ω) vs frequency. The data from Ref. 13 are: Weaver et al., × for −1 and Δ for 2; Bolotin et al., ⋄ for −1 and ○ for 2.

Fig. 8
Fig. 8

Nickel: −1(ω) and 2(ω) vs frequency. The data from Ref. 14 are: Lynch et al., × for −1 and Δ for 2; Johnson and Christy, ⋄ for −1 and ○ for 2.

Fig. 9
Fig. 9

Palladium: −1(ω) and 2(ω) vs frequency. The data from Ref. 15 are: Weaver and Benbow, ⋄ for −1 and ○ for 2; Bolotin et al., + for −1 and □ for 2; Johnson and Christy, × for −1 and Δ for 2.

Fig. 10
Fig. 10

Platinum: −1(ω) and 2(ω) vs frequency. The data from Ref. 16 are Weaver et al., Δ for −1 and □ for 2.

Fig. 11
Fig. 11

Titanium: −1(ω) and 2(ω) vs frequency. The data from Ref. 17 are: Kirillova and Charikov, □ for both −1 and 2; Lynch et al., Δ for both; Johnson and Christy, ○ for both; Kirillova and Charikov, + for both; Bolotin et al., × for both.

Fig. 12
Fig. 12

Tungsten: −1(ω) and 2(ω) vs frequency. The solid line is the Drude model. The data from Ref. 18 are: Nomerovannaya et al., □ for both −1 and 2; Weaver et al., Δ for both.

Tables (40)

Tables Icon

TABLE 1 Al, ALUMINUME. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980)

Tables Icon

Table 2 H. E. Bennett and J. M. Bennett, Optical Properties and Electronics Structure of Metals and Alloys, ed. F. Abeles (North–Holland, 1966), p. 175.

Tables Icon

Table 3 L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954) and 362 (1954).

Tables Icon

TABLE 2 Cu, COPPERL. G. Schulz, J. Opt. Am. 44, 357 and 362 (1954).

Tables Icon

Table 5 A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966).

Tables Icon

Table 6 P. F. Robusto and Braunstein, Phys. Stat. Sol. (b) 107, 443 (1981).

Tables Icon

Table 7 H. J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

Tables Icon

Table 8 B. Dold and R. Mecke, Optik 22, 435 (1965).

Tables Icon

TABLE 3 Au, GOLDH. E. Bennett and J. M. Bennett, Optical Properties and Electronic Structure of Metals and Alloys edited by F. Abeles (North–Holland, Amsterdam, 1966), p. 175.

Tables Icon

Table 10 L. G. Schulz, J. Opt. Soc. Am. 44, 357 and 362 (1954).

Tables Icon

Table 11 G. P. Motulevich and A. A. Shubin, Soviet Phys. JETP 20, 560 (1965).

Tables Icon

Table 12 V. G. Padalka and I. N. Shklyarevskii, Opt. Spectr. U.S.S.R. 11, 285 (1961).

Tables Icon

Table 13 G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, and B. A. Charikov, Phys. Met. and Met. 13, 823 (1962).

Tables Icon

Table 14 G. Brandli and A. J. Sievers, Phy. Rev. B 5, 3550 (1972).

Tables Icon

Table 15 J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch (with C. G. Olson), Physics Data, Optical Properties of Metals, (Fach–Information Zentrum, Kalsrube, FOR, 1981).

Tables Icon

TABLE 4 Pb, LEADG. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972).

Tables Icon

Table 17 A. I. Golovashkin and G. P. Motulevich, Soviet Physics JETP 26, 881 (1968)

Tables Icon

TABLE 5 Ag, SILVERH. E. Bennett and J. M. Bennett in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abeles (North–Holland, Amsterdam, 1966), p. 175.

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Table 19 L. G. Schulz, J. Opt. Soc. Am. 44, p. 357 and 362 (1954).

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Table 20 H. J. Hageman, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

Tables Icon

TABLE 6 Co, COBALTM. M. Kirillova and B. A. Charikov, Opt. Spectry. 17, 134 (1964).

Tables Icon

Table 22 P. B. Johnson and R. W. Christy, Phys. B 9, 5056 (1974).

Tables Icon

Table 23 J. H. Weaver, E. Colavita, D. W. Lynch and R. Rosei, Phys. Rev. B 19, 3850 (1979).

Tables Icon

TABLE 7 Fe, IronJ. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys. Rev. B 19, 3850 (1979).

Tables Icon

Table 25 G. A. Bolotin, M. M. Kirillova, and V. M. Mayevskiy, Phys. Met. Metall, 27(2) 31 (1969).

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TABLE 8 Ni, NICKELD. W. Lynch, R. Rosei and J. H. Weaver, Solid State Commun. 9, 2195 (1971).

Tables Icon

Table 27 B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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TABLE 9 Pd, PalladiumJ. H. Weaver and R. L. Bendow, Phys. Rev. B 12, 3509 (1975).

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Table 29 G. A. Bolotin, M. M. Kirilova, L. V. Nomerovannaya, and M. M. Noskov, Fiz. Metal. Metalloved 23, 463 (1967).

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Table 30 P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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TABLE 10 Pt, PlatinumJ. H. Weaver, Phys. Rev. B 11, 1416 (1975).

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Table 32 J. H. Weaver, D. W. Lynch, and C. G. Olson, Phys. Rev. B 10, 501 (1974).

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TABLE 11 Ti, TITANIUMM. M. Kirillova and B. A. Charikov, Opt. Spectry 17, 134 (1964).

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Table 34 D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev. B 11, 3617 (1975).

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Table 35 P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

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Table 36 M. M. Kirillova and B. A. Charikov, Phys. Met. 15, 138 (1963).

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Table 37 G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, and B. A. Charikov, Phys. Met. and Met. 13, 823 (1962).

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TABLE 12 W, TUNGSTENL. V. Nomerovannaya, M. M. Kirillova, and M. M. Noskov, Opt. Spectry. 17, 134 (1964).

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Table 39 J. H. Weaver, D. W. Lynch and C. G. Olson, Phys. Rev. B 12, 1293 (1975).

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Table 13 Optical Parameters Found using a Drude Model Fit of the Experimental Dielectric Functions for Six Metals for which the Dielectric Functions could be Fit; here ωf is the Frequency at which the Fit is Forced, and −1(0) is −1(ω) at dc; the Crossover Frequency Applies to −12.

Equations (14)

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c 1 + i 2 n c 2 ( n + i k ) 2 .
c = ω p 2 ω 2 + i ω ω τ ,
1 = ω p 2 ω 2 + ω τ 2 ,
2 = ω p 2 ω τ ω 3 + ω ω τ 2 .
ω p ( cm 1 ) = 1 2 π c ( 4 π N e 2 m * ) 1 / 2 ,
ω τ ( cm 1 ) = 1 2 π c τ ,
1 ( 0 ) ( ω p ω τ ) 2 .
σ 0 = ω p 2 / ( 4 π ω τ )
σ 0 ( cm 1 ) = 1 / [ 2 π c ρ o ( s ) ] = ( 9 × 10 11 ) / [ 2 π c ρ 0 ( Ω cm ) ] .
Z ( ω ) R ( ω ) + i X ( ω ) = 4 π c ( 1 + i ) ( ω ω τ 2 ω p 2 ) 1 / 2 ( 1 + i ω ω τ ) 1 / 2 .
R ( ω ) = 4 π c ( ω ω τ 2 ω p 2 ) 1 / 2 [ ω ω τ + ( 1 + ω 2 ω τ 2 ) 1 / 2 ] 1 / 2 .
ω τ = ω 2 ( 1 1 ) .
ω p 2 = ( 1 1 ) ( ω 2 + ω τ 2 ) .
R ( ω ) Z 0 = ( ω ω τ 2 ω p 2 ) 1 / 2 .

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