Drude Model Research Articles

Single phase metamaterial behavior in [formula omitted] and [formula omitted] doped cobalt ferrites

This paper reports the characteristic properties of CoFe2O4(CFO), Co0.98Ag0.02Fe2O4(CAFO), and Co0.98Ti0.02Fe2O4(CTFO) spinel ferrites of Fd3‾m space group and grain size in the range of 160 – 170 nm. Fourier transform infrared spectra of these samples have revealed the metal-oxygen bands in the range of 448– 542 cm−1. Raman spectra have shown six distinct peaks corresponding to the mixed spinel structure, which have been used to calculate the cation distribution of the samples. The magnetic measurement at room temperature shows that after the doping of Ti4+ ions, the saturation magnetization increases from 47.70 to 66.68 emu/g, and coercivity decreases from 1.84 to 1.61 kOe, making the sample magnetically softer. The law of approach to saturation magnetization has been used to estimate the value of magneto crystalline anisotropy constant. The dielectric behavior of the samples has been thoroughly studied in this paper. The dielectric constant is positive below 300 °C; its value is comparable for CFO and CAFO samples but higher for CTFO. Above this temperature, the samples show an uncommon behavior of negative dielectric constant corresponding to the single phase metamaterial state and its value increases as temperature rises. This behavior can be interpreted with the help of Drude model of plasmonic resonance. The Nyquist plots change their properties from RC to RL type in this region. Such single phase metamaterials with negative dielectric constant could be useful for high temperature microwave applications.

Effect of thermal annealing on the surface plasmon properties of gold and silver nanodisk structures fabricated by electron beam lithography

This study investigates the effect of thermal annealing on the surface plasmon resonance properties of gold and silver nanodisk structures fabricated by electron beam lithography. Despite no significant size change due to a nickel adhesion layer, thermal annealing at 500 °C notably altered surface plasmon resonance properties, especially in gold nanodisks, which showed peak blue-shifts and narrowing, indicating improved crystallinity. We fitted the peak shift by using an electromagnetic field analysis and discussed the changes in the dielectric function. The dielectric function of the simple Drude model was adopted, which was fitted to the values of the Lorentz Drude model in a limited wavelength region. While both silver and gold exhibited increased oscillation strength, only gold nanodisk structures showed a decrease in damping frequency. Increased oscillation strength indicated that these structures should be useful for selective enhancement of the light at specific wavelengths by a very simple heat treatment.

Modeling and FDTD discretization of stochastic Maxwell's equations with Drude dispersion

We develop the stochastic Maxwell's equations with Drude model under both additive and multiplicative noises. The additive noises characterize the random fluctuations in the electric current and magnetic current densities in Maxwell's equations, while the multiplicative noise describes the external fluctuation of electric field in the Drude dispersion equation of motion. For the stochastic models with Drude dispersion, we derive the averaged global energy law considering both types of noises. The CN-FDTD and Yee-FDTD discretization schemes are developed for solving the stochastic system over staggered grids. We establish the discrete averaged global energy laws for the CN-FDTD and Yee-FDTD schemes. Numerical experiments show the discrete averaged global energy evolutions and the convergence rates of the schemes for the stochastic Maxwell's equations with Drude model. We numerically simulate and analyze the stochastic electromagnetic propagation within Drude materials under various sinusoidal sources, initial wave conditions and additive and multiplicative noises.

Rectified Lorentz Force from Thermal Current Fluctuations

In a conducting medium held at finite temperature, free carriers perform Brownian motion and generate fluctuating electromagnetic fields. In this paper, an averaged Lorentz force density is computed that turns out to be nonzero in a thin subsurface layer, pointing towards the surface, while it vanishes in the bulk. This is an elementary example of rectified fluctuations, similar to the Casimir force or radiative heat transport. The results obtained also provide an experimental way to distinguish between the Drude and so-called plasma models.

Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator

Miller’s rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller’s rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller’s rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller’s rule, and we illustrate this point by means of a numerical example.

A unified photo-excited GaAs model from ab initio simulation in terahertz regime

In this paper, we present a unified model for gallium arsenide (GaAs) based on ab initio simulations which characterizes its terahertz (THz) properties when excited by optical pump. We use density functional perturbation theory to calculate the dielectric properties of GaAs, and investigate the relaxation time of photo-excited GaAs through electron–phonon interactions. In light of the complexities arising from the mixed absorption mechanisms and the sensitivity of GaAs to laser parameters, we have developed a method that leverages time-dependent density functional theory and Boltzmann transport theory. This approach enables us to establish an accurate relationship between the pump laser intensity and the carrier concentration by introducing the percentage of excited electrons, facilitating the quantitative characterization of GaAs’s response under different optical pump intensities. Using the microscopic material parameters solved by first principles, we develop a unified Drude model to describe the macroscopic electromagnetic responses of photo-excited GaAs. We simulate several reported numerical examples of photo-excited GaAs, including a GaAs wafer and GaAs-based THz metamaterial modulators, to validate the proposed unified model as a reliable approach for predicting the THz properties of GaAs. The good agreement between the simulation and measurement results demonstrates that our model successfully captures the dynamic responses of photo-generated carriers and provides guidance for the design of optoelectronic devices based on GaAs. Furthermore, our modeling approach based on ab initio simulations is free from empirical parameters, providing a solid THz modeling method for other photo-excited semiconductor materials.

Generalized Drude–Lorentz Model Complying with the Singularity Expansion Method (Advanced Optical Materials 12/2024)

Generalized Drude–Lorentz Model Complying with the Singularity Expansion Method (Advanced Optical Materials 12/2024)

Optical and transport properties of plasma mixtures from ab initio molecular dynamics

Predicting the charged particle transport properties of warm dense matter/hot dense plasma mixtures is a challenge for analytical models. High accuracy ab initio methods are more computationally expensive, but can provide critical insight by explicitly simulating mixtures. In this work, we investigate the transport properties and optical response of warm dense carbon–hydrogen mixtures at varying concentrations under either conserved electronic pressure or mass density at a constant temperature. We compare options for mixing the calculated pure species properties to estimate the results of the mixtures. We find that a combination of the Drude model with the Matthiessen's rule works well for DC electron transport and low-frequency optical response. This breaks down at higher frequencies, where a volumetric mix of pure-species AC conductivities works better.

Kapok-derived carbon/fly ash ceramic metacomposites with tunable negative permittivity behavior

In this paper, kapok-derived carbon/fly ash (KDC/FA) ceramic metacomposites were fabricated by vacuum hot-press sintering with FA and kapok fiber as raw materials, and their conductivity, dielectric properties, and impedance response were researched. The composition and microstructure of the metacomposites had a significantly impact on the electrical characteristics. With the increase of KDC content, a 3D conductive network was formed inside the composite, accompanied by a shift in the conductive mechanism. The tunable plasma-type negative permittivity behavior was observed. The absolute value of negative permittivity and the plasma oscillation frequency became larger as the KDC contents increased, which were consistent with the analytical results of the Drude model. This study designed and prepared a new environmental metacomposite with adjustable negative permittivity using biomass materials (kapok fibers) and solid waste (FA), which had a great significance for development of metamaterials in the future.

The conductivity effect of the top coating on optical properties of thin Cu(Ag)-layered structures

This study examines the optical properties of thin Cu (Ag)-layered structures covered with protective layers based on graphene, titanium (TiO2), or aluminium (Al2O3) oxides. The objective is to investigate the impact of these coatings on the optical behaviors of underlying metallic layers, specifically in the spectral range of excitation of surface plasmon resonances. Combining the methods of spectroreflectometry and spectro-ellipsometry was used to analyze the optical characteristics of the hybrid metal-oxide-graphene films. The study shows that graphene, due to its exceptional electrical conductivity and unique optoelectronic properties, significantly modifies the optical behavior of investigated structures. It includes notable changes in refractive and absorption indices, and optical conductivity indicating potential for enhancing light-matter interactions in plasmonic-graphene layered structures with the aim to apply as biosensor. It is important that addition of TiO2 and Al2O3 layers has also strong effects on the optical properties, which are relevant to their respective applications in the fields of optoelectronics and microelectronics. Employing the effective medium approximation and the Tauc–Lorentz model promotes deeper understanding the interplay between interband and intraband electronic transitions at the nanoscale level. It was revealed that the layer thickness of constituted materials and their individual dielectric functions together with addition of a graphene monolayer commit the significance for altering the optical properties of hybrid layered structures. The obtained results are important for the fields of plasmonics and nanotechnology, providing insights for designing sensors and devices with improved optical characteristics.

Investigated of the optical properties for SiO2 by using Lorentz model

Abstract In this work, the optical characteristics of SiO2 (refractive index [ n n ], dielectric constant [ ε r {\varepsilon }_{{\rm{r}}} ], reflectivity [R], transmissivity [T], absorptivity [A], and absorption coefficient [α]) were studied using the Lorentz model. A comparison was made with the practical results of previous studies and showed a good agreement.

Investigation of negative permittivity in BaTiO3/TiN metacomposites at the radio frequency region

The intriguing and unexpected properties of metacomposites have attracted significant attention, especially in terms of tuning their negative permittivity. In this study, we fabricated percolative BaTiO3/TiN (BTN) metacomposites employing mesoporous BaTiO3 nanoparticles synthesized via a novel solvothermal method as the matrix, combined with varying concentrations of TiN as the filler. Dielectric properties investigated in the frequency range of 100 Hz to 100 kHz unveiled a transition in the permittivity, shifting from positive to negative as the TiN content increased (primarily noticeable at frequencies above 10 kHz). The initial permittivity shifting is associated with an enhanced interfacial polarization, commonly recognized as Maxwell-Wagner-Sillars effect observed below the percolation threshold. Further, Lorentz model is attributed to induce dielectric resonance in the BaTiO3 matrix triggered by the Ti4+ ions in Ti–O octahedral sites leading to negative permittivity in conjunction with increase in TiN particles above the percolation threshold. Interestingly, AC conductivity exhibited an increase with increasing frequency when TiN content was lower. However, intriguingly, this frequency-dependence in the conductivity of BTN metacomposites did not hold as TiN content increased. Moreover, the investigation of reactance revealed the inductive character derived from the conductive network, a conclusion further confirmed through equivalent circuit analysis. The findings presented in this study are poised to unlock new possibilities in the design and development of metacomposites, ultimately facilitating practical applications of epsilon-negative materials in electromagnetic devices.

Phase transformation and plasmonic damping study for semi-solid ionic polymeric hydrogel system at higher temperature and low radio frequency

This article represents the findings regarding the phase transitions exhibited by a polymeric hydrogel material composed of sodium polyphosphate-polyethylene glycol. These transitions play a crucial role in the generation of ionic plasmons and the manifestation of surface plasmon resonance (SPR) with dielectric permittivity damping within the polymer electrolyte system of the hydrogel. Usually, SPR has been observed in electron-conducting systems within an optical frequency range. However, here SPR is observed in an ionic system within a lower radio frequency range of 104-10 (Parwati et al., 2024) 77 Hz for temperatures exceeding 80 °C. The mechanism responsible for permittivity damping can be elucidated by considering the accumulation of ionic charges at the interface between the electrode and the electrolyte, coupled with a high degree of charge absorption following the Drude model. A power law has been used to describe the resonance that occurs between the applied DC frequency and the motion of charge carrier ions, thus confirming the presence of free ionic motion within the hydrogel matrix. tan δ shows significant energy absorption further substantiating permittivity damping, which transitions from positive to negative values.

Thermophysical Properties of Vanadium Melts and Discussion of Thermal Diffusivity in Mott’s Theory

The temperature dependence of density, normal spectral emissivity, heat capacity at constant pressure, and thermal conductivity of the V melt were measured with high accuracy using electromagnetic levitation in a static magnetic field. Surface vibration, translational motion, and convection of the electromagnetically levitated droplet sample were suppressed by the magnetic field. In the measurement of thermal conductivity, convection in the V-melt was sufficiently suppressed by the application of a field of 7 T or higher. In this study, the measured emissivity and thermal conductivity are compared with those evaluated using the free-electron models (Drude model and Wiedemann–Franz rule). Correlations between the density of states and thermal diffusivity at the Fermi energy of transition metals in the liquid state are investigated and the applicability of Mott's s–d scattering model is discussed.

Comparison of the Casimir force between SiC plates with different permittivity models: Lorentz model and Palik data

Accurate calculation of Casimir forces is essential for the development of micro- and nanoelectromechanical systems. Silicon carbide (SiC) is an excellent material for fabricating microsensors due to its high durability, high stiffness, and low thermal expansion. The permittivity of the SiC could be characterized by the Lorentz model or the Palik data. However, the influence of the two models of calculating permittivity on the Casimir force has not been discussed. In this work, we calculate the Casimir force between SiC plates by the Lorentz model and the Palik data, respectively. The Casimir force calculated by the Lorentz model could be 4 times greater than the Palik data for SiC at a gap distance of 10 nm. The difference of the permittivity in the ultraviolet lead to different Casimir forces. This work demonstrates the difference between the two models of permittivity for calculating the SiC-based Casimir force, and provides a reliable base for more accurate Casimir force calculations.

Generalized Drude–Lorentz Model Complying with the Singularity Expansion Method

AbstractDeriving analytical expressions of dielectric permittivities is required for numerical and physical modeling of optical systems and the soar of non‐Hermitian photonics motivates their prolongation in the complex plane. Analytical models are based on the association of microscopic models to describe macroscopic effects. However, the question is to know whether the resulting Debye–Drude–Lorentz models are not too restrictive. Here, it is shown that the permittivity must be treated as a meromorphic transfer function that complies with the requirements of complex analysis. This function can be naturally expanded on a set of complex singularities. This singularity expansion of the dielectric permittivity allows to derive a generalized expression of the Debye–Drude–Lorentz model that complies with the requirements of complex analysis and the constraints of physical systems. It is shown that the complex singularities and other parameters of this generalized expression can be retrieved from experimental data acquired along the real frequency axis. The accuracy of this expression is assessed for a wide range of materials including metals, 2D materials and dielectrics, and it is shown how the distribution of the retrieved poles helps in characterizing the materials.

Design Optimization of Silicon-Based Optically Excited Terahertz Wave Modulation

The modulation of a terahertz (THz) wave on amplitude, phase and polarization is important for the application of THz technology, especially in the field of imaging, and is one of the current research hotspots. Silicon-based, optically excited THz modulator is a wavefront modulation technique with a simple, compact and reconfigurable optical path. It can realize the dynamic modulation of THz wavefronts by only changing the projected two-dimensional pattern, but it still suffers from the problems of lower modulation efficiency and slower modulation rates. In this article, the Drude model in combination with the multiple thin layers structure model and Fresnel matrix method is used to compare the modulation efficiencies of three modulation modes and more factors. The method is more accurate than the popular proposed method, especially when the thickness of the excited photoconductive layers reaches a few hundred microns. In comparing the three modes, namely transmission, ordinary reflection and total internal reflection, it is found the total internal reflection modulation mode has the best modulation efficiency. Further, under this mode, the effects of three factors, including the lifetime of photo-excited carriers, the wavelength of pump light and the frequency of THz wave, on the performance of THz modulator are analyzed. The simulation results show that the realization of total internal reflection using silicon prisms is a simple and effective method to improve the modulation efficiency of a silicon-based optically excited THz modulator, which provides references for the design of a photo-induced THz modulator.

Prediction of metallo-dielectric transmission filter performance based on underlying dispersion relations

The dispersion relation for electromagnetic/optical wave propagation based on the Helmholtz equation for an infinite one-dimensional metallo-dielectric structure is derived using the Bloch theorem and heuristically modified to include material dispersion. We investigate the connection between the dispersion relation of an infinite metallo-dielectric structure with the transmittance characteristics of finite metallo-dielectric structures. The dispersion relation is used to determine the center wavelength and bandwidth as a function of the material properties and the thicknesses of the metal and dielectric layers. These estimates are found to be in excellent agreement with the values obtained from numerically calculated transmittance spectra using the transfer matrix method for finite metallo-dielectric structures with the same building units. The dispersion relation calculations and simulations for the transmittance are done for an ideal case where the real part for the refractive index of the metal and imaginary part for the refractive index of the dielectric are zero, and also with actual values of the real and imaginary parts of the refractive index for the metal and dielectric obtained from literature, instead of using the canonical Drude model for the metal. It is shown that the real part of the dispersion relation for the actual case is almost identical to the ideal case in the visible and NIR range, implying that essential information on the center wavelength and bandwidth can be obtained from the ideal dispersion relation. It is also found that an ideal metal and dielectric give near-unity transmittance in the passband. It is predominantly the presence of a finite real part of the refractive index of the metal that introduces attenuation. The effective refractive index of the structure can also be determined. Oscillations present in the transmittance spectrum can be explained as a Fabry–Perot effect. Approximate simple estimates of the center wavelength and bandwidth can be useful in initiating intelligent designs of finite metallo-dielectric filter structures for fabrication and characterization.

Promising way for enhancing light absorption in silicon via silver nanoparticles: experimental and numerical study

Silver nanoparticles (Ag-Nps) were grown on the surface of a p-type crystalline silicon (C-Si) substrate using electroless metal deposition. It was found that the Ag-Nps distribution on C-Si was controlled by the silver nitrate (AgNO3) concentrations. Atomic force microscopy observations revealed the formation of a continuous layer at high concentration. In contrast, a distribution of Ag-Nps with a spherical shape was obtained at lower concentration. The samples were also examined by optical microscopy under dark field illumination. The light reflected from Ag-Nps was obtained with different colors. This difference indicates a slight change in particle size. It is demonstrated that a silicon substrate with deposited Ag-Nps shows a significant decrease in reflectance and an increase of the absorption in the region from 200 to 800 nm. Moreover, the behavior of small Ag-Nps while interacting with light (absorbed or scattered light) is theoretically described using the Mie theory based on the Drude model. The introduction of silver nanoparticles on silicon surface is used to improve the efficiency of solar cells by reducing reflection and increasing the light absorption.

Dendritic Ag@c-Si structure for influenza A virus detection by SERS and machine learning

The combination of Surface-enhanced Raman Scattering (SERS) method and machine learning algorithms has been successfully demonstrated for the detection and differentiation of influenza A virus in buffer medium. Dendritic Ag nanostructures on single-crystal Si wafer have been proposed as SERS-active substrates, which are fabricated using a low-cost and reproducible AgNO3 reduction method. Depending on the time of Ag deposition, structures of different morphologies were obtained. These structures were studied by spectroscopic ellipsometry (SE). To analyze the spectra obtained by SE, we used the Bruggeman effective medium approximation to determine the volume fraction and height of the metal, the Drude model to describe free electrons, the Tauc-Lorentz model to describe the influence of interband transitions, as well as Lorentz model and Gauss model to describe localized surface plasmon resonance (LSPR). SERS was achieved through LSPR excitation and the presence of “hot spots” in the regions around the tips and in the spaces between close-packed dendritic Ag nanostructures. The sample with the most developed surface is the most promising for SERS, since the spectral position of the LSPR is at 658 nm, which is close to the excitation wavelength of the He–Ne laser. The SERS spectra of influenza A virus in buffer medium are difficult to distinguish, so a machine learning algorithms (principal component analysis and support vector machine) were used to directly classify them. For the sample with the most developed morphology, the detection accuracy of influenza A virus was 76.6 ± 4.2 % at a total protein concentration in the test analyte of 300 μg/ml (according to the Lowry method).