Fractional Derivative Modification of a Drude Model

Abstract

A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and numerical results. The absorption coefficient and wave vector -- key parameters describing the propagation of waves in such a medium -- are shown to follow a power law in the frequency domain, which is a common phenomenon in many real life applications. The introduction of two separate parameters provides a more flexible model than some other approaches found in literature and is well suited for numerical implementation.