Anomalous carrier transport model for broadband infrared absorption in metals

Abstract

We derive a model for accurately reproducing the broadband infrared optical response of common engineering metals. Here we use ``broadband infrared'' to refer to wavelengths beginning at $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ and extending to approximately $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ or more. The model generalizes the Drude theory to account for sources of anomalous intraband absorption. This is accomplished by modeling these sources as elements of disorder that introduce diffusive perturbations into the local field. In the stationary setting, the memory kernel description of the field relaxation leads to a fractional derivative with an order that corresponds to the memory decay strength. We demonstrate that this model is fully consistent with the Drude theory and that the semiclassical theory is recovered under requisite assumptions on the field relaxation or radiative wavelength. The anomalous model component is shown to reproduce empirically observed anomalous absorption that has been traditionally corrected by models possessing empirical components that have not been formally derived. Results are presented for several common metals for which the proposed model accurately reproduces the data over the entire modeled bandwidth. A comparative analysis confirms that the proposed model represents a robust, high fidelity alternative to previously proposed models that do not capture the observed physical response over the extended infrared range.