Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method

We propose an accurate description for the dispersion of gold in the range of 1.24–2.48 eV. We implement this improved model in an FDTD algorithm and evaluate its efficiency by comparison with an analytical method. Extinction spectra of gold nanoparticle arrays are then calculated.

Figure 1

Real part of the permittivity of gold as published in Ref. 12, calculated with the single Drude model and calculated with the Drude-Lorentz model.

Figure 2

Imaginary part of the permittivity of gold as published in Ref. 12, calculated with the single Drude model and calculated with the Drude-Lorentz model.

Figure 3

Coefficient of transmission through a layer of 20 nm of gold, respectively, calculated analytically, with the simple Drude model and with the Drude-Lorentz model. The relative error on $\mid t\mid$ by comparison with the analytical result is also depicted.

Figure 4

Coefficient of transmission through a layer of 50 nm of gold, respectively, calculated analytically, with the simple Drude model and with the Drude-Lorentz model. The relative error on $\mid t\mid$ by comparison with the analytical result is also depicted.

Figure 5

Intensity transmitted above a gold cylinder of radius 15 nm, respectively, calculated analytically (Mie theory), with the simple Drude model and with the Drude-Lorentz model. The relative error by comparison with the analytical result is also depicted.

Figure 6

Geometry of the structure studied for the calculation of the extinction spectrum.

Figure 7

Extinction spectra calculated for gold cylinders with an elliptical basis: the height is 60 nm, the grating constant is 300 nm, and the major and minor axes are, respectively, 100 nm and 100 nm (structure A), 125 nm and 100 nm (structure B), and 150 nm and 100 nm (structure C). Calculations performed with the Drude-Lorentz model are depicted with a thick line. Calculations performed with the Drude model are depicted with a thin line. Peak positions for structures A, B, and C are, respectively, $\lambda =637\mathrm{nm}$, $\lambda =680\mathrm{nm}$, and $\lambda =712\mathrm{nm}$ with the Drude-Lorentz model, and $\lambda =637\mathrm{nm}$, $\lambda =683\mathrm{nm}$, and $\lambda =715\mathrm{nm}$ for the Drude model.

Figure 8

Extinction spectra calculated for gold cylinders: the height is 60 nm, the diameter is 100 nm, and grating contants are, respectively, 200 nm (structure A), 250 nm (structure B), and 300 nm (structure C). Calculations performed with the Drude-Lorentz model are depicted with a thick line. Calculations performed with the Drude model are depicted with a thin line. Peak positions for structures A, B, and C are, respectively, $\lambda =625\mathrm{nm}$, $\lambda =630\mathrm{nm}$, and $\lambda =638\mathrm{nm}$ with the Drude-Lorentz model, and $\lambda =628\mathrm{nm}$, $\lambda =630\mathrm{nm}$, and $\lambda =638\mathrm{nm}$ for the Drude model.