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Communication

Fractional Derivative Modification of Drude Model

Institute of Mathematics and Physics, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland
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Author to whom correspondence should be addressed.
Academic Editors: Venkat R. Bhethanabotla and Sanchari Chowdhury
Sensors 2021, 21(15), 4974; https://doi.org/10.3390/s21154974
Received: 25 June 2021 / Revised: 15 July 2021 / Accepted: 21 July 2021 / Published: 22 July 2021
(This article belongs to the Special Issue Plasmonic Biosensors)
A novel, two-parameter modification of a Drude model, based on fractional time derivatives, is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing good agreement between theoretical description and numerical results. The absorption coefficient and wave vector are shown to follow a power law in the frequency domain, which is a common phenomenon in electromagnetic and acoustic wave propagation in complex media such as biological tissues. The main novelty of the proposal is the introduction of two separate parameters that provide a more flexible model than most other approaches found in the literature. Moreover, an efficient numerical implementation of the model is presented and its accuracy and stability are examined. Finally, the model is applied to an exemplary soft tissue, confirming its flexibility and usefulness in the context of medical biosensors. View Full-Text
Keywords: digital filters; electrodynamics; electromagnetic propagation; finite difference methods; optical surface waves; physics computing; propagation digital filters; electrodynamics; electromagnetic propagation; finite difference methods; optical surface waves; physics computing; propagation
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MDPI and ACS Style

Karpiński, K.; Zielińska-Raczyńska, S.; Ziemkiewicz, D. Fractional Derivative Modification of Drude Model. Sensors 2021, 21, 4974. https://doi.org/10.3390/s21154974

AMA Style

Karpiński K, Zielińska-Raczyńska S, Ziemkiewicz D. Fractional Derivative Modification of Drude Model. Sensors. 2021; 21(15):4974. https://doi.org/10.3390/s21154974

Chicago/Turabian Style

Karpiński, Karol, Sylwia Zielińska-Raczyńska, and David Ziemkiewicz. 2021. "Fractional Derivative Modification of Drude Model" Sensors 21, no. 15: 4974. https://doi.org/10.3390/s21154974

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