Fractional Derivative Modification of Drude Model

Karpiński, Karol; Zielińska-Raczyńska, Sylwia; Ziemkiewicz, David

doi:10.3390/s21154974

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…Therefore, the attenuation of transmitted THz waves only comes from two aspects: Fresnel reflection loss and Drude attenuation, unaffected by processes such as interband absorption. When VO2 is in the insulating phase, its dielectric constant is e = 9. d For the metallic phase of vanadium dioxide, we employed the Drude [26] model to describe its relative conductivity, as follows:…”

Section: Transmission Characteristics and Principles With Absorbermentioning

confidence: 99%

Temperature-controlled tunable metamaterial absorber based on vanadium dioxide with ‘switch’ functionality

Zhu,

Pan,

Tang

2024

Phys. Scr.

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A THz wave modulator, utilizing temperature-controlled phase change materials, is proposed to address the limitation of absorbers' inability to adjust to external environments. This modulator enables the switch function of metamaterial absorbers, comprising a gold reflector layer, a silicon dioxide depletion layer, and a vanadium dioxide pattern layer. Simulations via finite element method reveal two nearly perfect absorption peaks, up to 99.99%. As temperature rises, absorption rates increase, stabilizing gradually after vanadium dioxide transitions from insulating to metallic phase. With a modulation depth of 98.49%, the absorber achieves adjustability. It enables polarization-independent absorption of electromagnetic waves, exhibiting strong absorption at incident angles from 0° to 50° for TE and TM waves. Leveraging vanadium dioxide's phase change characteristics, the absorber can switch between ON and OFF states based on temperature changes, promising potential applications in light modulation and THz absorbers.

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Section: Transmission Characteristics and Principles With Absorbermentioning

confidence: 99%

Temperature-controlled tunable metamaterial absorber based on vanadium dioxide with ‘switch’ functionality

Zhu,

Pan,

Tang

2024

Phys. Scr.

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“…It includes the empirical four-parameter dielectric model based on viscoelastic analysis techniques [67], the fractional model illustrated in [81] as well as the mixing Debye and Cole-Cole relationship proposed in [79]. It can be also adapted to include the complex conjugate residual pairs and the Drude critical-points dispersive relationships [82,83], the two-parameter variant of the Drude model presented in [84], as well as the modified Lorentz model [85]. Therefore, the use of ( 12) makes the modeling of permittivity functions composed of multiple Debye or Cole-Cole terms possible.…”

Section: Fractional Dielectric Response Modelsmentioning

confidence: 99%

FDTD-Based Electromagnetic Modeling of Dielectric Materials with Fractional Dispersive Response

Mescia

Bia²,

Caratelli

2022

Electronics

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The use of fractional derivatives and integrals has been steadily increasing thanks to their ability to capture effects and describe several natural phenomena in a better and systematic manner. Considering that the study of fractional calculus theory opens the mind to new branches of thought, in this paper, we illustrate that such concepts can be successfully implemented in electromagnetic theory, leading to the generalizations of the Maxwell’s equations. We give a brief review of the fractional vector calculus including the generalization of fractional gradient, divergence, curl, and Laplacian operators, as well as the Green, Stokes, Gauss, and Helmholtz theorems. Then, we review the physical and mathematical aspects of dielectric relaxation processes exhibiting non-exponential decay in time, focusing the attention on the time-harmonic relative permittivity function based on a general fractional polynomial series approximation. The different topics pertaining to the incorporation of the power-law dielectric response in the FDTD algorithm are explained, too. In particular, we discuss in detail a home-made fractional calculus-based FDTD scheme, also considering key issues concerning the bounding of the computational domain and the numerical stability. Finally, some examples involving different dispersive dielectrics are presented with the aim to demonstrate the usefulness and reliability of the developed FDTD scheme.

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“…As far as metals [11] are concerned, existing fractional models such as [12], although providing useful insights, are limited by a short range of wavelengths and do not focus on energy adsorption and scattering.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Model of Complex Permittivity of Conductor Media with Relaxation: Theory vs. Experiments

Ciancio

Ciancio²,

d’Onofrio

et al. 2022

Fractal Fract

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Moving from the study of plasmonic materials with relaxation, in this work we propose a fractional Abraham–Lorentz-like model of the complex permittivity of conductor media. This model extends the Ciancio–Kluitenberg, based on the Mazur–de Groot non-equilibrium thermodynamics theory (NET). The approach based on NET allows us to link the phenomenological function of internal variables and electrodynamics variables for a large range of frequencies. This allows us to closer reproduce experimental data for some key metals, such as Cu, Au and Ag. Particularly, our fitting significantly improves those obtained by Rakic and coworkers and we were able to operate in a larger range of energy values. Moreover, in this work we also provide a definition of a substantial fractional derivative, and we extend the fractional model proposed by Flora et al.

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Fractional Derivative Modification of Drude Model

Cited by 6 publications

References 29 publications

Temperature-controlled tunable metamaterial absorber based on vanadium dioxide with ‘switch’ functionality

Temperature-controlled tunable metamaterial absorber based on vanadium dioxide with ‘switch’ functionality

FDTD-Based Electromagnetic Modeling of Dielectric Materials with Fractional Dispersive Response

A Fractional Model of Complex Permittivity of Conductor Media with Relaxation: Theory vs. Experiments

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