Fractional Derivative Modification of a Drude Model

TL;DR

This paper introduces a fractional derivative-based modification to the Drude model, providing a more flexible and accurate description of wave propagation in dispersive media with analytical and numerical validation.

Contribution

It presents a novel fractional derivative modification of the Drude model, enhancing flexibility and numerical implementation compared to existing models.

Findings

Dielectric susceptibility matches theoretical and numerical results.

Absorption coefficient and wave vector follow a power law in frequency.

The model's parameters improve adaptability for real-world applications.

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.