Drude model parameters to fit the dielectric function of free electron metals including plasma frequencies and damping constants for Ag, Al, Au, Cu, K, Na, Pt

The region (where the real part of experimental dielectric constant is between approximately -10 and zero) is rather narrow region with a relatively little weight in an overall Drude fit, which stretches down to the values of the real part of dielectric constant below of -10**4. A Drude fit is, by its very definition, optimized for frequencies (wavelengths) lower (larger) than a plasma frequency (wavelength) and thus not so much concerned in the region where the real part of dielectric constant is in the proximity of zero. Consequently the latter can be significantly shifted compared to the real material data. By that I mean more than hundreds of nanometers!

Do you want an example? Whereas a Drude fit to the silver data employs a plasma frequency of 9.6 eV (wavelength 129 nm), the experimental material data exhibits zero of the real part of silver dielectric function at approximately 328 nm, what makes a difference by a factor higher than 2.5!

Unfortunately, the region where the real part of dielectric constant is between approximately -10 and zero is the most interesting region from the view of plasmonics and various plasmonic applications. You may try to replace the plasma frequency (wavelength) in that region by the frequency (wavelength) which corresponds to zero of the experimental real part of dielectric function, as I did in in Ref. [11]. But then you face the problem that a Drude fit yields typically much smaller slope of the real part of the dielectric function compared to experimental data.

A spectacular example has been provided in Ref. [12], where photonic band structure of two-dimensional metallic and metallo-dielectric photonic crystals was calculated. It has been demonstrated there that on using a Drude fit to silver data, an optimal lattice structure with the largest complete photonic band gap (CPBG) was a square lattice, whereas on using experimental silver data, an optimal lattice structure with the largest CPBG turned out to be a triangular lattice. (An additional information can be found here.) The reason behind the above behavior was that CPBG width turned out to be sensitive to the slope of the dielectric constant in the proximity of zero. One can verify that a Drude fit yields typically much smaller slope of the real part of the dielectric function compared to the true experimental data in the proximity of zero of the real part.

REFERENCES

1. M. G. Blaber, M. D. Arnold, and M. J. Ford, Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver, J. Phys. Chem. C 113(8), 3041-3045 (2009) (see compilation from different sources in Table 1 therein).

2. N. K. Grady, N. J. Halas, and P. Nordlander, Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles, Chem. Phys. Lett. 399(1-3), 167-171 (2004)

3. M. H. Hider and P. T. Leung, Nonlocal electrodynamic modeling of fluorescence characteristics for molecules in a spherical cavity, Phys. Rev. B 66, 195106 (2002).

4. I. R. Hooper and J. R. Sambles, Dispersion of surface plasmon polaritons on short-pitch metal gratings, Phys. Rev. B 65, 165432 (2002).

5. M. Kreiter, S. Mittler, W. Knoll, and J.R. Sambles, Surface plasmon-related resonances on deep and asymmetric gold gratings, Phys. Rev. B 65, 125415 (2002).

6. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr., L. L. Long, and 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) (see compilation from different sources in Table 1 therein).

7. E. J. Zeman and G. C. Schatz, An accurate electromagnetic theory study of surface enhancement factors for silver, gold, copper, lithium, sodium, aluminum, gallium, indium, zinc, and cadmium, J. Phys. Chem. 91(3), 634-643 (1987) (see compilation from different sources in Table 1 therein).

8. A. D. Rakic, A. B. Djuric, J. M. Elazar, and M. L. Majewski, Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic Devices, Appl. Opt. 37(22), 5271-5283 (1998).
   (They presented models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). The values for the respective plasma frequencies are summarized in Table 1 therein; the remaining Lorentz-Drude model parameters are summarized in Table 2 therein.)

9. K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, Plasmonic Films Can Easily Be Better: Rules and Recipes, ACS Photonics 2(3), 326-333 (2015).
10. M. Bruna and S. Borini, Optical constants of graphene layers in the visible range Appl. Phys. Lett. 94(3), 031901 (2009).
11. A. Moroz, Three-dimensional complete photonic bandgap structures in the visible, Phys. Rev. Lett. 83, 5274-5277 (1999).
    [Demonstrated for the first time the possiblity of a complete photonic bandgap (i.e. common for both polarizations and for all propagation directions) in a 3D fcc lattice of metallic spheres embedded in a dielectric matrix.]
12. H. van der Lem and A. Moroz, Towards two-dimensional complete photonic-bandgap structures below infrared wavelengths, J. Opt. A: Pure Appl. Opt. 2, 395-399 (2000) [pdf].
13. A. Moroz, Electron mean-free path in a spherical shell geometry, J. Phys. Chem. C 112(29), 10641-10652 (2008).
    (The article has been supplemented with a detailed Electronic Supporting Information. See also an accompanying F77 code fsc.f to calculate the mean-free path for various model cases discussed in the article.)

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Alexander Moroz August 16, 2009 (last updated on April 15, 2019)