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 μm and extending to approximately 100 μm 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.

Temperature-dependent carrier transport: Low-complexity model for the infrared optical and radiative properties of nickel

“…This functionality of the modelthat is, to estimate phase information from real-valued measurements-provides a suitable alternative to other such methods for doing the same (e.g., Kramers-Kronig analysis). Furthermore, since the template formalism from which the thermophysical model was derived has been previously shown to adhere to the Kramers-Kronig relations, 12 we are assured that the same is true for estimates produced by the proposed model at any tempera-ture in the prescribed range.…”

“…The temperature-dependent model expands upon our previous study for the description of anomalous carrier dynamics over broad infrared bandwidths. 12 Here the term "anomalous" refers to intraband dynamics that systematically depart from the ideal free electron profile. The anomalous model interprets such departures as the addition of a structured component to the otherwise random perturbations in (1):…”

“…The energy partitioning property of nonlocal operators in a stationary frequency domain setting has been rigorously investigated in our recent study. 29 Decomposing the proposed model (12) into its real and imaginary components χ φ = χ φ + i χ φ and appealing to the relation ε = 1 + χ = 1 + χ φ + χ β , 30 where the χ β are the contributions from bound states, one has for the temperature-dependent relative permittivity…”

“…Though, even the properties of materials that are expected to represent "good" free-electron metals (e.g., the monovalent noble metals) have been shown to deviate from the Drude model results at very long wavelengths. 10,12 The matter of modeling these materials is further complicated when one seeks to accurately describe thermophysical property variations. Since not all wavelength-dependent dynamics are also temperaturedependent, a practically useful thermophysical model must be capable of reproducing the independent effects of these contributions.…”

Beyond Fresnel: absorption of fibre laser radiation on rough stainless steel surfaces

“…The applicability of these values is therefore questionable. Second, the Drude model only performs well in the intermediate infrared region while it struggles for short wavelengths [9] due to the anomalous absorption from surface imperfections. Third, the usage of Fresnel's formulas can have an influence on the accuracy of the estimates.…”