Drude Model Research Articles

Innovative active terahertz modulator based on dynamic graphene-silicon arrays

This paper presents an innovative active terahertz (THz) modulator that utilizes dynamic graphene-silicon arrays (DGSAs) to overcome the challenges of dynamically manipulating THz waves. The DGSA combines the exceptional electrical properties of graphene with the enhanced optical absorption capabilities of silicon arrays, enabling dual-mode active control through optical pumping and electrical biasing. An 808 nm laser is used to photoexcite carriers in the silicon arrays for optical pumping while a bias voltage modulates the Fermi level of graphene, subsequently varying Si conductivity and influencing the transmission properties of THz waves. Simulations have demonstrated modulation depths of up to 94% at 2.5 THz in the transmission mode and 89% at 1 THz in the reflection mode. Furthermore, this study delves into a theoretical analysis and numerical simulations, exploring the modulation mechanisms, including the role of graphene’s Drude model and PN junction effects. These insights provide a robust theoretical framework for understanding the DGSA’s operation and lay a solid foundation for the design and optimization of high-performance THz modulation devices.

Dissipative split-charge formalism: Ohm's law, Nyquist noise, and non-contact friction.

The split-charge equilibration method is extended to describe dissipative charge transfer similarly as the Drude model, whereby the complex-valued frequency-dependent dielectric permittivities or conductivities of dielectrics and metals can be mimicked at non-zero frequencies. To demonstrate its feasibility, a resistor-capacitor circuit is simulated using an all-atom representation for the resistor and capacitor. The dynamics reproduce the expected charging process and Nyquist noise, the latter resulting from the thermal voltages acting on individual split charges. The method bears promise to model friction caused by the motion of charged particles past metallic or highly polarizable media.

Diffusion, long-time tails, and localization in classical and quantum Lorentz models: A unifying hydrodynamic approach

Diffusion, long-time tails, and localization in classical and quantum Lorentz models: A unifying hydrodynamic approach

Enhanced plasmonic performance of TiO2 derived TiN films via gas nitridation

This study demonstrates a cost-effective method for planar titanium nitride plasmonic film by nitriding spin-coated TiO2 in ammonia atmosphere. The effect of nitridation temperature on the structural, morphological, electrical and optical characteristics of the coated films were investigated. The films exhibited high carrier concentration of 1022/cc with significant reduction in resistivity of more than three order of magnitude, indicating the conversion to the nitride phase. Negative permittivity, crucial for plasmonic applications in the visible wavelength region, was verified for wavelengths > 463 nm using Drude-Lorentz model. A three-layer model was employed to verify the material’s plasmonic behaviour. The straightforward fabrication route, which combines spin-coating and ammonia nitridation at 950 °C, offers a new approach for titanium nitride films for plasmonic based gas and biosensing device applications in the visible region. In addition, for fabricating titanium nitride coatings for applications that require abrasion resistance, electrical conductivity, chemical stability, and biocompatibility.

Exciton dynamics in CsPbBr3 single crystal: LT splitting energy, exciton-polariton dispersion, and biexciton binding energy.

Metal halide perovskite materials (MHPs) are promising for several applications due to their exceptional properties. Understanding excitonic properties is essential for exploiting these materials. For this purpose, we focus on CsPbBr3 single crystals, which have higher crystal quality, are more stable, and have no Rashba effect at low temperatures compared to other 3D MHPs. We have estimated exciton energy positions, longitudinal-transverse splitting energy, and damping energy using low-temperature reflection spectra. Under high excitation intensity, two biexciton emissions (M-emission) and exciton-exciton scattering emission (P-emission) were observed. We assign the two M-emissions to the emission to the states of longitudinal and transverse excitons, i.e., ML and MT emissions. From the energy position of the MT emission, the biexciton binding energy has been estimated to be ∼2meV. By analyzing P-emission obtained from the back side of the sample, we have estimated the exciton binding energy to be 17.8-23.7meV. This estimation minimizes the influence of the wavenumber distribution in the scattering process. In addition, time-resolved transmittance measurements using pulsed white light have revealed the group velocity dispersion. Comparing experimental results with theoretical calculations using the Lorentz model clarifies that exciton dynamics in CsPbBr3 can be described with a simple Lorentz model. These insights enhance the understanding of exciton behavior and support the development of exciton-based devices using MHPs.

Tunable negative permittivity behavior and excellent electromagnetic shielding performance of pyrolytic carbon‐glass fiber felt/epoxy resin metacomposites

AbstractEffective and accurate adjustment of negative permittivity behavior is worthy of further investigation. Herein, pyrolytic carbon‐glass fiber felt/epoxy resin (PyC‐GFF/ER) metacomposites with tunable negative permittivity were prepared using an impregnation‐calcination method. The permittivity, electrical conductivity, and electromagnetic shielding performance of the polymer metacomposites were investigated. Due to the inherent three‐dimensional structural network of GFF, the PyC adhering to the surface of glass fiber easily formed a conductive network in the composites. As the PyC content increased in the ER composites, the conductivity mechanism changed from hopping conduction to metal‐like conduction. The ER composites with high PyC contents showed negative permittivity behavior and the epsilon‐near‐zero response owing to the low frequency plasma state of free electrons in the PyC‐conduction network. By controlling the PyC content, the negative permittivity behavior of ER composites could be effectively tuned. With the increase in PyC content, the values of negative permittivity increased, and the epsilon‐near‐zero frequency shifted to a higher frequency. Moreover, the ER composites with high PyC contents showed excellent electromagnetic shielding properties (29.4 dB) at X‐band. This work not only provided a feasible method to realize the tunable negative permittivity of polymer metacomposites, but also promoted its application in the microwave field.Highlights The pyrolytic carbon‐glass fiber felt/epoxy resin composites were fabricated. The negative permittivity was first reported in the PyC‐GFF/ER composites. Tunable negative permittivity could be well explained by Drude model. The polymer composites had excellent electromagnetic shielding property.

Enhanced Terahertz Characterization of Multilayer Graphene on Guided‐Mode Resonance Filter: Boosting Sensitivity and Precision in Electrical and Optical Characteristics

AbstractIn this study, terahertz time‐domain spectroscopy (THz‐TDS) is employed for the first time to explore the characteristics of mono‐, bi‐, and tri‐layer graphene coated on guided‐mode resonance filters (GMRFs). Owing to high quality‐factor (Q‐factor) resonances of GMRF, the proposed method significantly enhances the resonance depth variation by up to 9.3, 5.1, and 4.2 times at 0.58 THz in TE mode for mono‐, bi‐, and tri‐layer graphene, respectively, in contrast to conventional THz‐TDS methods relying on amplitude variation at 0.50 THz in TE mode. Excellent agreement is observed between experimental results and theoretical simulations using the Kubo formula and Drude model, even accounting for variations in sidelobes at an incident angle of 0.6 degrees. Through meticulous fitting process between measurements and simulations for the resonances formed by the GMRF and graphene, the study accurately determines the electrical and optical properties of mono‐, bi‐, and tri‐layer graphene, including frequency‐dependent sheet conductivity (σs(ω)), mobility (μ), carrier density (N), and Fermi velocity (vF). Furthermore, in the THz high‐frequency region, the observation reveals that as the number of graphene layers increases, the decrease in σs(ω) occurs more rapidly than in single‐layer graphene, attributed to the screening effect arising from electronic interactions between each graphene layer.

One-Dimensional Photonic Crystals Comprising Two Different Types of Metamaterials for the Simple Detection of Fat Concentrations in Milk Samples.

In this study, we demonstrate the reflectance spectrum of one-dimensional photonic crystals comprising two different types of metamaterials. In this regard, the designed structure can act as a simple and efficient detector for fat concentrations in milk samples. Here, the hyperbolic and gyroidal metamaterials represent the two types of metamaterials that are stacked together to construct the candidate structure; meanwhile, the designed 1D PCs can be simply configured as [G(ED)m]S. Here, G refers to the gyroidal metamaterial layers in which Ag is designed in a gyroidal configuration form inside a hosting medium of TiO2. In contrast, (ED) defines a single unit cell of the hyperbolic metamaterials in which two layers of porous SiC (E) and Ag (D) are combined together. It is worth noting that our theoretical and simulation methodology is essentially based on the effective medium theory, characteristic matrix method, Drude model, Bruggeman's approximation, and Sellmeier formula. Accordingly, the numerical findings demonstrate the emergence of three resonant peaks at a specified wavelength between 0.8 μm and 3.5 μm. In this context, the first peak located at 1.025 μm represents the optimal one regarding the detection of fat concentrations in milk samples due to its low reflectivity and narrow full bandwidth. Accordingly, the candidate detector could provide a relatively high sensitivity of 3864 nm/RIU based on the optimal values of the different parameters. Finally, we believe that the proposed sensor may be more efficient compared to other counterparts in monitoring different concentrations of liquid, similar to fats in milk.

Properties and Factors of CsxWO3 Slurry for Building Glass with High Visible Light Transmission and Outstanding Near-Infrared Insulation.

This study is dedicated to the development of a new type of cesium tungsten bronze energy-saving laminated glass and explores its application in insulating glass combinations, offering innovative ideas and practical solutions for advancing energy-saving glass technology. Experimental results show that both CsxWO3 (CWO) dispersions exhibit good visible light transmittance and near-infrared shielding properties, with CWO1 demonstrating superior shielding in the 650-950 nm range, attributed to differences in shape and size distribution and verified by simulations using the Drude-Lorentz model and the finite element method.

Annealing effect of Ca3TaGa3Si2O14 catangasite crystals on their optical activity

The spectral dependences of transmission and absorption in the wavelength range of 200–2500 nm were measured for Ca3TaGa3Si2O14 crystals cut perpendicular to the optical axis in the initial state (without annealing) and after isothermal annealing in vacuum and in air. It was found that annealing in vacuum leads to a decrease, and annealing in air leads to an increase in the intensity of absorption bands. A spectrophotometric method for measuring and calculating the specific rotation angle ρ of the plane of polarization of light in gyrotropic crystals from the transmission coefficient spectra at different angles between the polarizer and the analyzer is considered. The transmission spectra were normalized in order to eliminate shifts in the spectra associated with measurement features. Spectral dependences of the values of ρ for all three samples, which are approximated by the extended Drude formula, are obtained; the influence of the annealing atmosphere on the values of the coefficients of this formula is established.

Ultrabroadband Optical Properties of 2D Titanium Carbide MXene.

MXenes have rapidly ascended as a prominent class of two-dimensional (2D) materials, renowned for their distinctive optical and electrical properties. Despite extensive exploration of MXenes' optical properties, existing studies predominantly focus on the near-infrared (NIR) to the ultraviolet spectral range, leaving the mid-infrared (mid-IR) range relatively uncharted. In this study, we conducted a comprehensive characterization of the intrinsic optical properties of Ti3C2Tx MXene across an ultrabroadband spectral range, spanning from mid-IR (28 meV) to vacuum ultraviolet (VUV, 6.4 eV). For this purpose, Ti3C2Tx MXene films of varying thicknesses were coated on quartz substrates, resulting in two distinct categories: thin film samples with thicknesses below 50 nm and bulk-like samples with thicknesses exceeding 500 nm. Using spectroscopic ellipsometry, we analyzed the optical properties of films of various thicknesses and extracted detailed information on their dielectric functions. Our findings reveal resonances in the mid-IR to VUV range. Employing the Lorentz-Drude model to examine these resonances has uncovered the optical resistivity of MXene films and led to the identification of multiple plasmonic modes active in the visible to NIR range, as well as broad band-to-band transition-like resonances in the mid-IR range. This ultrabroadband optical versatility of Ti3C2Tx MXene is anticipated to bring about a wide range of thermal and optical applications.

Investigating the optical bistability of pure spheroidal nanoinclusions in passive and active host matrices

The study examined the effects of the depolarization factor (L) and the real and imaginary parts of the dielectric function of the host matrix (εh ) on the local field enhancement factor and optical bistability of pure spheroidal nanoinclusions with both passive and active host matrices. By solving the Laplace equation in the quasi-static limit, we derived expressions for the electric potentials of the pure spheroidal nanoinclusions. We then incorporated L and the Lorentz-Drude model into these expressions to derive the equation for the enhancement factor in the core of the spheroidal nanoinclusions. The results show that, regardless of whether L varies or remains constant, the pure spheroidal nanoinclusions exhibit only one set of enhancement factor peaks, independent of whether the host matrix is passive or active. However, for the same increase in ε h , the enhancement factor intensities of the pure metal spheroidal nanoinclusions are higher when the host matrix is active compared to when it is passive. The number and intensities of the enhancement factor peaks, as well as the optical bistability of the pure spheroidal nanoinclusions, vary significantly depending on whether the core is made of a passive or active dielectric material. Furthermore, by adjusting parameters such as L and the real and imaginary parts of the host matrices, we were able to achieve tunable enhancement factors and optical bistability, which could be useful for applications in optical sensing, nonlinear optics, and quantum optics.

Numerical modeling of SNSPD absorption utilizing optical conductivity with quantum corrections

Superconducting nanowire single-photon detectors are widely used in various fields of physics and technology, due to their high efficiency and timing precision. Although, in principle, their detection mechanism offers broadband operation, their wavelength range has to be optimized by the optical cavity parameters for a specific task. We present a study of the optical absorption of a superconducting nanowire single photon detector with an optical cavity. The optical properties of the niobium nitride films, measured by spectroscopic ellipsometry, were modeled using the Drude–Lorentz model with quantum corrections. The numerical simulations of the optical response of the detectors show that the wavelength range of the detector is not solely determined by its geometry, but the optical conductivity of the disordered thin metallic films contributes considerably. This contribution can be conveniently expressed by the ratio of imaginary and real parts of the optical conductivity. This knowledge can be utilized in detector design.

Complex Permittivity Spectra of Granular Polymer Composites with Dispersed Ag-Coated Cu Flakes

AbstractConductive particle-containing granular composites with tuneable negative permittivity are being studied to improve the performance of electromagnetic devices, such as shielding materials. In this study, we investigated the relative complex permittivity and electrical conductivity of granular composites of polyphenylene sulfide (PPS) resin and Ag-coated Cu flakes in the radio- to microwave-frequency range and compared them with those of PPS/bare Cu flake composites. Electrical conductivity measurements revealed that the PPS/Ag-coated Cu flake composites have a lower percolation threshold (φc) than the PPS/bare Cu flake composites, whereas the electrical conductivity of the PPS/Ag-coated Cu flake composites in the percolated particle state was higher at the same particle volume fraction. At particle contents above φc, a low-frequency plasmonic state of conduction electrons was achieved in the percolated particle chains in both composites, and negative permittivity spectra were obtained. The percolated PPS/Ag-coated Cu flake composites had a negative permittivity up to a higher frequency than the percolated PPS/bare Cu flake composites. Furthermore, the Drude model was used to analyze the negative permittivity spectra of the composites in the percolated particle state. The plasma frequency of the composites with percolated Ag-coated Cu flakes was higher than that of the composites with percolated bare Cu flakes. Thus, coating Ag on Cu particles improved the conductivity of the composite, leading to negative permittivity up to higher frequencies. This study contributes to the enhancement of the negative permittivity achieved by granular composites, which is useful for microwave technology applications. Graphical Abstract

Near-Unity All-Optical Modulation of Third-Harmonic Generation with a Fano-Resonant Dielectric Metasurface.

We demonstrate all-optical modulation with a near-unity contrast of nonlinear light generation in a dielectric metasurface. We study third-harmonic generation from silicon Fano-resonant metasurfaces excited by femtosecond pulses at 1480 nm wavelength. We modulate the metasurface resonance by free carrier excitation induced by absorption of an 800 nm pump pulse, leading to up to 93% suppression of third-harmonic generation. Modulation and recovery occur on (sub)picosecond time scales. According to the Drude model, the pump-induced refractive index change blue-shifts the metasurface resonance away from the generation pulse, causing a strong modulation of third-harmonic conversion efficiency. The principle holds great promise for spatiotemporal programmability of nonlinear light generation.

Adaptive indefinite kernels in hyperbolic spaces

Learning embeddings in hyperbolic space has gained increasing interest in the community, due to its property of negative curvature, as a way of encoding data hierarchy. Recent works investigate the improvement of the representation power of hyperbolic embeddings through kernelization. However, existing developments focus on defining positive definite (pd) kernels, which may affect the intriguing property of hyperbolic spaces. This is due to the structures of hyperbolic spaces being modeled in indefinite spaces (e.g., Kreĭn space). This paper addresses this issue by developing adaptive indefinite kernels, which can better utilize the structures in the Kreĭn space. To this end, we first propose an adaptive embedding function in the Lorentz model and define indefinite Lorentz kernels (iLks) via the embedding function. Due to the isometric relationship between the Lorentz model and the Poincaré ball, these iLks are further extended to the Poincaré ball, resulting in the development of what are termed indefinite Poincaré kernels (iPKs). We evaluate the proposed indefinite kernels on a diversity of learning scenarios, including image classification, few-shot learning, zero-shot learning, person re-identification, knowledge distillation, etc. We show that the proposed indefinite kernels can bring significant performance gains over the baselines and enjoy better representation power from RKKSs than pd kernels.

Laterally Modulating Carrier Concentration by Ion Irradiation in CdO Thin Films for Mid‐IR Plasmonics

AbstractThis report demonstrates tunable carrier densities in CdO thin films through local ion irradiation, providing lateral control of mid‐IR optical properties. Ion‐solid interactions produce donor‐like defects that boost electron concentrations from the practical minimum of 2.5 × 1019 cm−3 to a maximum of 2.5 × 1020 cm−3 by metered ion exposure. This range is achieved using He, N, Ar, or Au ions at 1–2.8 MeV; when normalized by displacements per atom, all ion species produce comparable results. Since CdO is well‐described by the Drude model, irradiation‐tuned carrier densities directly alter the infrared dielectric function, and in turn, mid‐infrared optical properties. Further, it is demonstrated that by combining irradiation with traditional lithography, CdO films expose to ions in the presence of 3‐µm thick, patterned photoresist exhibit lateral carrier density profiles with ≈400‐nm resolution. Scanning near‐field optical microscopy reveals sharp optical interfaces with almost no companion contrast in surface morphology, microstructure, or crystallinity. Finally, CdO lateral homostructures supporting surface plasmon polaritons (SPPs) are demonstrated whose dispersion relation can be tuned through periodic patterning in a monolithic platform by simple nanofabrication. Numerical simulations show these polaritons result from strong coupling between excitations at CdO plasma frequencies and SPPs supported by the platinum substrate.

Characteristic frequencies of transverse electric modes in a double negative slab waveguide with Kerr-type nonlinearity

The evolution equation for guided transverse electrical modes in a slab waveguide having a double negative core is derived for the electrical field. Special solutions of the dispersion equation for the case with double positive symmetric cladding are searched for. Relevant eigenmodes are formulated in terms of characteristic frequencies as a new method, and these frequencies corresponding to the oscillating guided modes are found for different wave numbers and core widths assuming the lossless Drude model can be used for the core medium with a Kerr-type nonlinearity. Results show that normalized characteristic frequencies increase with increasing wave numbers and mode numbers.

Optical properties of 4H-SiC and 6H-SiC from infrared to vacuum ultraviolet spectral range ellipsometry (0.05–8.5 eV)

Complex dielectric function (ɛ = ɛ1 + iɛ2) spectra are obtained from reflection mode spectroscopic ellipsometry and unpolarized transmittance measurements for 4H and 6H stacking sequence silicon carbide (SiC) nitrogen-doped single crystals from the infrared (IR) to vacuum ultraviolet (VUV) spectral range. A single parametric model describing ɛ predominately for the ordinary directions is developed over the 0.05–8.5 eV spectral range from analysis of (0001)-oriented back side roughened 4H-SiC and 6H-SiC single crystals with some contribution from the extraordinary direction of 6H-SiC in the IR region. Indirect bandgaps for 4H-SiC and 6H-SiC are found to be 3.30 and 3.03 eV, respectively, and the corresponding direct optical gaps are at 4.46 and 4.42 eV. A model describing the optical response in the IR spectral range is created using a Drude expression and either transverse optical (TO) and longitudinal optical (LO) (TOLO) or Lorentz oscillator models. Free carrier concentration (N) is optically measured to be 3.7 × 1018 and 3.3 × 1018 cm−3 using TOLO and Lorentz oscillator models, respectively, and the corresponding carrier mobility (μ) is 34 and 39 cm2/V s for 4H-SiC. Under the same assumption for 6H-SiC, N is measured to 8 × 1018 cm−3 using either TOLO or Lorentz oscillator models and μ is 9 and 10 cm2/V s using the TOLO and Lorentz oscillator models, respectively, in the ordinary direction and 5 cm2/V s in the extraordinary direction using either model. For 4H-SiC, using the TOLO oscillator model, TO and LO phonon modes are measured at 797.7 and 992.1 cm−1, respectively, and corresponding modes are found at same locations using the Lorentz oscillator model. In 6H-SiC, using the TOLO model, TO modes in ordinary and extraordinary directions are found at 797.7 and 789.7 cm−1, and corresponding modes are at 796.9 and 788.9 cm−1 using the Lorentz oscillator model. The LO modes using the TOLO model are found at 992 and 984 cm−1 in the ordinary and extraordinary directions, respectively, and the same modes in the corresponding direction using the Lorentz oscillator model are located at 975.9 and 967.9 cm−1.

Non-Foster approach to broadband optical metamaterials based on Lorentzian gain materials

All passive metamaterials are inherently narrowband due to fundamental dispersion-energy constraints, and their dispersive properties are usually approximated by a Lorentz model. However, there are broadband active metamaterials in the radio frequency (RF) regime based on negative capacitors with non-Foster dispersion properties. Non-Foster dispersion is usually considered as an “electronic-engineering trick” that cannot be applied at optical frequencies. Here, we demonstrate that the dispersion relation of a RF non-Foster capacitor is similar to that of an optical gain material described by a Lorentz model. This insight paves the way to realize non-Foster optical metamaterial structures. As the simplest example, we develop a broadband non-Foster optical epsilon-near-zero slab with a 1:10 bandwidth.