Fitting optical properties of metals by Drude-Lorentz and partial-fraction models in the [0.5;6] eV range

Abstract

Fitting optical properties of metals is of great interest for numerical methods in electromagnetism, especially finite difference time domain (FDTD). However, this is a tedious task given that theoretical models used usually fail to interlink perfectly with the experimental data. However, in this paper, we propose a method for fitting the relative permittivity of metals by a sum of Drude-Lorentz or a sum of partial-fraction models. We use the particle swarm optimization (PSO) hybridized either with Nelder-Mead downhill simplex, or with gradient method. The main electronic transitions in metals help to guide the fitting process toward the solution. The method is automatic and applied blindly to silver, gold, copper, aluminum, chromium, platinum, and titanium.

Performance of Surface Plasmon Resonance Sensors Using Copper/Copper Oxide Films: Influence of Thicknesses and Optical Properties

“…The wavelength of laser illumination is λ 0 = 632.8 nm. The photon energy of the excitation light (E = 1.96 eV) is close to that of the transition from d states (valence band) to th es-p conduction band [18] (2.1 eV, see the vertical black line in Figures A1, A7 and A11). Therefore, we expect a good quality of the plasmon resonance for adequate thickness of copper: a sharp dip and a small minimum.…”

“…In addition to its non-toxic nature, the oxide layer can be used to tune the position of the SPR resonance [9]. Indeed, the oxide layer could be used to adjust the resonance near the copper transition 2.1 eV that is characteristic of the inter-band transition from d states (valence band) to the 's-p' conduction band [18] (Figures A1, A7 and A11 where the vertical line shows the photon energy of illumination used in the SPR setup E = 1.96 eV). Let us note that cuprous copper oxide (Cu 2 O) and cupric copper oxide (CuO) are p-type semiconductors with a bandgap of approximately 2.2-2.9 and 1.2-2.1 eV, respectively.…”

“…We use the partial fraction model, also called the complex-conjugate pole-residue pair model [16], to describe the dispersion of materials [17,18]. In a recent paper, the partial fraction model of dispersion yielded more accurate results than a sum of Drude-Lorentz functions to fit the bulk copper [18]. The relative permittivity is a complex number that is the square of the refractive index n:…”

High-resolution impedance mapping using electrically activated quantitative phase imaging

“…Based on the Drude–Lorentz model 46 – 48 , one can derive the dependence of the components of the dielectric constant of the thin layer ε tl of the solid facing the electrolyte (with the thickness equal to the penetration depth of the quasi-static electromagnetic field) on the surface charge distribution, as well as the related variations due to an AC electric field 49 : where d tl is the penetration depth of the electric field (the Thomas–Fermi screening length) within the electrode at the electrode–liquid interface, ε tl ( ) is the free-electron contribution to the dielectric constant of the electrode, and n e is the free-electron density of the bulk solid. Corresponding to the same material, ε tl differs from ε el due to the biasing effect of the DC value of the electrode potential, which is additionally modulated by the local AC field.…”

“…Based on the Drude-Lorentz model [46][47][48] , one can derive the dependence of the components of the dielectric constant of the thin layer ε tl of the solid facing the electrolyte (with the thickness equal to the penetration depth of the quasi-static electromagnetic field) on the surface charge distribution, as well as the related variations due to an AC electric field 49 :…”