## Drude model in Meep

I tried to simulate metal with Drude-Lorentz model. However, the expression given in Meep docs for the Drude term is slightly different, check this page. In Meep the dispersion relation is given by

$\epsilon(\omega) = \epsilon_\infty + \frac{\omega_D^2 \sigma_D}{\omega_D^2-\omega^2-\imath \omega \gamma_D} + \frac{\Omega_L^2 \sigma_L}{\Omega_L^2-\omega^2-\imath \omega \Gamma_L}$

where as the usual Drude-Lorentz model is given by

$\epsilon(\omega) = \epsilon_\infty - \frac{\omega_D^2 }{\omega^2+\imath \omega \gamma_D} - \frac{\Omega_L^2 \sigma_L}{(\omega^2-\Omega_L^2)+\imath \omega \Gamma_L}$

The last term, Lorentz term, is of course the same. The drude term, however, is slightly different. In the Meep-discuss forum, the following suggestion was given.

• Use a very small value for $\omega_D$, in this way, the $\omega_D$ in the denominator of the Drude term can be ignored.
• The sigma value is computed to give the right resonance frequency for the Drude term.