Drude-like Model Research Articles

Analytical study of linear optical properties of metal nanoparticle trimers: the impact of dipole-dipole interaction on different modes of configuration

In this study, we theoretically investigate the linear properties of a metal nanoparticle (MNP) trimer. Three identical spherical nanoparticles (NPs) whose centers are equidistantly oriented on a same straight line are considered. Using the solid core approximation for NPs and considering interaction between particles through induced electric dipoles, the motion equation of each NP conduction electrons is analytically solved. Some appropriately approximated expressions are derived for the permittivity of each NP based on a Drude-like model, allowing the clear observation of the contribution of inter-particle interaction. Depending on the orientation of the trimer axis and incident laser beam geometry (i.e., orientation of electromagnetic (EM) fields and wave vector of laser beam), three different configurations or modes are considered. The extinction efficiency of each NP as a function of wavelength is plotted, revealing that when the laser electric field is perpendicular to the symmetry axis of the trimer, it increases compared to the case of non-interactional single NP, and its plasmon resonance peak experiences a red shift. For other cases where the electric field of the laser beam is parallel to the trimer axis, the extinction efficiency of each NP decreases, and its peak shifts to the blue. In all cases, the effect of interaction on the optical properties of the middle NP is greater than on the other NPs.

DFT studies of the borophene basic optoelectronic properties doped with aluminum and gallium substitutional atoms

Currently, two-dimensional materials are widely studied from both theoretical and experimental points of view. Among a large list of systems, one finds a two-dimensional boron allotrope (borophene), which has attracted considerable attention due to its promising electronic and optical properties. Understanding and modifying these properties are crucial for implementation of borophene in high-technological applications, but for this to be possible we need to know its very basic physical properties. Therefore, in this work we study borophene that belongs to the P-mmm phase group via first principles to examine the variation of the optoelectronic properties of a pristine borophene monolayer, and the one with Al and Ga substitutional impurities. We report the band structure with the correspondingly density of the states for the pristine system as well as for the doped borophene one. We do reproduce the optical conductivity for the pristine borophene obtained from the complex dielectric function considering several values of the scattering time parameter (τ) of Drude-like model. In addition, here we report the effect of the impurities on the optical conductivity, with the same set of τ parameters, as well as the absorption coefficient with x- and y-polarized incident light. We have found that impurities significantly modify the optical conductivity, but, most importantly, this also enhances the absorption coefficient in the visible region of the electromagnetic spectrum.

Thermal conductance of the water-gold interface: The impact of the treatment of surface polarization in non-equilibrium molecular simulations.

Interfacial thermal conductance (ITC) quantifies heat transport across material-fluid interfaces. It is a property of crucial importance to study heat transfer processes at both macro- and nanoscales. Therefore, it is essential to accurately model the specific interactions between solids and liquids. Here, we investigate the thermal conductance of gold-water interfaces using polarizable and non-polarizable models. Both models have been fitted to reproduce the interfacial tension of the gold-water interface, but they predict significantly different ITCs. We demonstrate that the treatment of polarization using Drude-like models, widely employed in molecular simulations, leads to a coupling of the solid and liquid vibrational modes that give rise to a significant overestimation of the ITCs. We analyze the dependence of the vibrational coupling with the mass of the Drude particle and propose a solution to the artificial enhancement of the ITC, preserving at the same time the polarization response of the solid. Based on our calculations, we estimate ITCs of 200 MW/(m2 K) for the water-gold interface. This magnitude is comparable to that reported recently for gold-water interfaces [279 ± 16 MW/(m2 K)] using atomic fluctuating charges to account for the polarization contribution.

Linear optical properties of 2d assembly of interacting gold nanoparticles: analytical approach in dipole approximation

Using a Drude-like model for the conduction electrons of Metal Nanoparticles (MNPs) assembled in a periodic two-dimensional (2D) array, considering dipole-dipole interactions of adjacent particles, an analytical expression is achieved for the MNP permittivity where the functionality of interaction term on the different geometric and physical parameters is evident. A numerical analysis is carried out for a gold NP array for two different sizes of NPs and two different host media of water and glass. It is shown that, interaction of NPs leads to a substantial increase in the extinction cross section, the red-shift of the Surface Plasmon Resonance (SPR) wavelength and decrease in the full width at half maximum (FWHM) of cross section. The absolute values of the real and imaginary parts of complex permittivity of each MNP decrease in comparison with the single particle case.

Linear optical properties of a linear chain of interacting gold nanoparticles

In a Drude-like model for the conduction electrons of metal nanoparticles (MNPs) in a periodic linear chain, considering dipole-dipole interactions of adjacent particles, an analytical expression is derived for each particle permittivity for two different polarizations of incident light: parallel with and perpendicular to the chain line. A numerical analysis is carried out for a chain including 10 identical gold nanoparticles (NPs) for two different sizes of NPs and two different host media: air and glass. It is shown that in the parallel case of polarization, interaction of NPs leads to a substantial increase in the extinction cross section and the redshift of the surface plasmon resonance (SPR) wavelength. In comparison with the linear properties of a single NP, the second and penultimate particles have the most increase in the extinction cross section and SPR wavelength displacement while the first and last particles experience the least variations due to the mutual interactions. For the perpendicular polarization, inversely, the dipolar coupling causes a decrease in extinction cross section of all particles and the blue-shift of SPR wavelength. For the parallel polarization, the absolute values of the real and imaginary parts of complex permittivity of each MNP decrease in comparison with the single particle case while they increase for the perpendicular state of polarization.

Analytical Approach to the Surface Plasmon Resonance Characteristic of Metal Nanoparticle Dimer in Dipole-Dipole Approximation

This theoretical study deals with the effect of bi-particle interaction on the surface plasmon resonance (SPR) in a dimer which includes two identical metal nanoparticles (NPs). Considering the dipole-dipole interaction in a Drude-like model, an appropriate equation is derived for the permittivity of each NP. The restoration force related to the classical confinement originating from the finite size of NPs is considered, and an appropriate adjustment coefficient is considered for this term through analyzing experimental data. Two different polarizations are considered for the laser beam electric field, and it is shown that the orientation of the electric field has an essential role in the linear optical properties of a dimer. Numerical investigation is accomplished for a dimer of gold NPs with two different diameters of 4 nm and 20 nm. For the parallel polarization, dipole-dipole interaction leads to the redshift of SPR wavelength and increase in its peak value, while for the perpendicular polarization, the absolute opposite results are derived. For all cases, it is shown that SPR wavelength functionality with respect to the geometric factor a/d (NP radius to the separation) can be presented by a cubic equation that fits better than an exponential one suggested by the earlier studies which demonstrates the dipole-dipole characteristic of the interaction. Qualitatively, our results are in good agreement with the other experimental studies.

Modified Drude model for small gold nanoparticles surface plasmon resonance based on the role of classical confinement

In this paper, we study the effect of restoration force caused by the limited size of a small metallic nanoparticle (MNP) on its linear response to the electric field of incident light. In a semi-classical phenomenological Drude-like model for small MNP, we consider restoration force caused by the displacement of conduction electrons with respect to the ionic positive background taking into account a free coefficient as a function of diameter of nanoparticle (NP) in the force term obtained by the idealistic Thomson model in order to adjust the classical approach. All important mechanisms of the energy dissipation such as electron-electron, electron-phonon and electron-NP surface scatterings and radiation are included in the model. In addition a correction term added to the damping factor of mentioned mechanisms in order to rectify the deficiencies of theoretical approaches. For determining the free parameters of model, the experimental data of extinction cross section of gold NPs with different sizes doped in the glass host medium are used and a good agreement between experimental data and results of our model is observed. It is shown that by decreasing the diameter of NP, the restoration force becomes larger and classical confinement effect becomes more dominant in the interaction. According to experimental data, the best fitted parameter for the coefficient of restoration force is a third order negative powers function of diameter. The fitted function for the correction damping factor is proportional to the inverse squared wavelength and third order power series of NP diameter. Based on the model parameters, the real and imaginary parts of permittivity for different sizes of gold NPs are presented and it is seen that the imaginary part is more sensitive to the diameter variations. Increase in the NP diameter causes increase in the real part of permittivity (which is negative) and decrease in the imaginary part.

Mean squared displacement in a generalized Lévy walk model.

Lévy walks represent a class of stochastic models (space-time-coupled continuous-time random walks) with applications ranging from the laser cooling to the description of animal motion. The initial model was intended for the description of turbulent dispersion as given by the Richardson law. The existence of this Richardson regime in the original model was recently challenged [T. Albers and G. Radons, Phys. Rev. Lett. 120, 104501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.104501]: The mean squared displacement (MSD) in this model diverges, i.e., does not exist, in the regime, where it presumably should reproduce the Richardson law. In the Supplemental Material to that work the authors present (but do not investigate in detail) a generalized model interpolating between the original one and the Drude-like models known to show no divergences. In the present work we give a detailed investigation of the ensemble MSD in this generalized model, show that the behavior of the MSD in this model is the same (up to prefactors) as in the original one in the domains where the MSD in the original model does exist, and investigate the conditions under which the MSD in the generalized model does exist or diverges. Both ordinary and aged situations are considered.

Beyond the Drude model in transport and optical properties of dense plasma of silver

We calculate optical and transport properties of dense silver plasma via quantum molecular dynamics together with the Kubo-Greenwood formalism and compare the results with ones obtained using a semi-analytical Drude-like model. The quantum molecular dynamics highlights an important contribution of d-electrons to the properties of silver, and thus the thermal conductivity is not described by the Drude model. At the same time, the imaginary part of dielectric function can be fitted by the Drude-like model with reasonable accuracy in the optical range of frequencies.

Magnetic Field Effect on Fresnel Coefficients of the Thin Slab of Graphite Nanocomposite

In this theoretical study, optical properties of a thin slab including graphite nanoparticles doped in a host medium such as silica and silicon have been investigated. A constant magnetic field is used for controlling Fresnel coefficients of the slab. Depending on the direction of the normal vector of the basal plane of the graphite structure with respect to the electric field of the incident electromagnetic wave (perpendicular or parallel), optical behavior of graphite is different. Electric permittivity of an individual magnetized graphite nanoparticle is calculated by a semi-empirical Drude-like model for both kinds of the normal vector of the basal plane orientation. By means of well-known Maxwell-Garnett theory, effective permittivity of the magnetized nanocomposite slab is obtained. It is shown that at the mid-IR frequency range, exerting a magnetic field of few hundred Tesla can lead to the substantial variations of Fresnel coefficients. Effect of the magnetic field on the optical properties of the slab is more evident when the population of the graphite nanoparticles with the parallel orientation of the basal plane is increased.

Time-Domain Green's Function for a Vertical Dipole Above a Graphene Sheet

The three-dimensional potential time-domain Green's function for a vertical electric dipole radiating in vacuum in the presence of a graphene sheet is derived in a semi-analytical form, by assuming a local Drude-like model for the graphene conductivity in the intraband regime, through a modified Cagniard-de Hoop approach. The derived expression is simple and requires only a straightforward evaluation of a finite smooth one-dimensional integral. Moreover, for the particular and practical case of source and observer along the same vertical axis, the result is provided in a closed form thus allowing for an extremely efficient calculation of the pulsed time-domain field. Numerical results are provided that validate the proposed formulation and assess its computational efficiency against a direct numerical inversion of the relevant spectral-domain potential.

Localized acoustic surface modes

We introduce the concept of localized acoustic surface modes. We demonstrate that they are induced on a two-dimensional cylindrical rigid surface with subwavelength corrugations under excitation by an incident acoustic plane wave. Our results show that the corrugated rigid surface is acoustically equivalent to a cylindrical scatterer with uniform mass density that can be represented using a Drude-like model. This, indeed, suggests that plasmonic-like acoustic materials can be engineered with potential applications in various areas including sensing, imaging, and cloaking.

Semi-Analytical Representation of the Two-Dimensional Time-Domain Green's Function of a Graphene Sheet in the Intraband Regime

The 2-D time-domain Green's function of a graphene sheet is here derived, by assuming a local Drude-like model for the graphene conductivity valid in the absence of biasing magnetic fields and when both spatial-dispersion effects and interband terms are negligible (i.e., up to the low terahertz range). The sought Green's function is derived in a semi-analytical form through a modified Cagniard-De Hoop approach. This allows for deriving simple semi-analytical expressions for the fields radiated by a pulsed line source in the presence of a graphene sheet, which can be computed in a fast and straightforward way. Theoretical and numerical validations are presented by obtaining the known results for nondispersive metallic sheets as limiting cases and through comparisons with results obtained numerically through an exact canonical double inverse Fourier transform.

Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell–Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model

This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [, ], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [–]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects.

Surface plasmon polariton model of high-spatial frequency laser-induced periodic surface structure generation in silicon

In recent years, high-spatial frequency laser-induced surfaces structures have been generated in a large variety of dielectrics. In silicon subwavelength ripples, some of which featured periodicities below 100 nm, were formed using ultrafast lasers. We demonstrate for Si(100) surfaces that generation of a dense electron-hole plasma in the focal spot of ultrashort-pulsed laser light followed by massive excitation of plasma waves provides an explanation for the formation of such high-spatial frequency surface structures. The applied Drude-like model includes carrier-carrier collisions and is in excellent agreement with the experimentally observed ripple period.

Negative Magnetoresistance Generated by Combination of Spin–Orbit Interaction and Applied Magnetic Field

We have theoretically studied a negative magnetoresistance (MR) the mechanism of which is completely different from conventional mechanisms, i.e., spin-related mobility-increased mechanisms and orbital-motion-related mechanisms including a quantum interference effect. Our proposed negative MR is caused by the interplay between a spin–orbit interaction (SOI) and the Lorentz force due to an externally applied magnetic field. We have phenomenologically approached this mechanism using the Drude-like model, in which the carrier scattering by SOI is considered as a transverse scattering term in addition to the longitudinal scattering term due to usual collisions and the Lorentz force term. Also, the possibility of observing our proposed negative MR was discussed by comparing our prediction with experimental results for Ni and Gd films, which were newly measured in this study.

Linear and Nonlinear Transmission of Surface Plasmon Polaritons in an Optical Nanowire

ABSTRACTPolymer-metal composites offer the possibility of strongly enhanced nonlinear optical properties, which can be used for ultrasmall photonic devices. In this paper, we investigate numerically, by means of the finite-difference time-domain (FDTD) method, the propagation characteristics of surface plasmon polariton (SPP) modes excited in an optical nanowire consisting of a chain of either metallic cylinders or metallic spheres embedded in dielectric shells made of polymers (or other material) with optical Kerr nonlinearity. Our FDTD calculations incorporate both the nonlinear optical response of the dielectrics as well as the frequency dispersion of the metals, which is considered to obey a Drude-like model. It is demonstrated that, in the linear limit, the nanowire supports two SPP modes, a transverse and a longitudinal one, separated by Δλ = 20 nm. Furthermore, the dependence of the transmission of these SPP modes, on both the pulse peak power and Kerr coefficient of the dielectric shell, is investigated. Nonlinear optical phenomena, such as power-dependent mode frequency, switching, or optical limiting, are observed.

Optical conductivity of oxides

Abstract Optical conductivity spectra of conducting oxides, cuprates, including high-Tc superconductors, nickelates, manganites, doped titanates, barium–lead–bismuth oxides, barium–potassium–bismuth–lead oxides, oxides showing metal–insulator phase transitions, and conducting polymers for the sake of comparison, are reviewed in the spectral range from the milli-electron-volt up to a few electron-volts. The optical conductivity profiles evolve from Drude-like to incoherent scattering and even pseudo-gap-like, depending on doping and temperature. When Drude or Drude-like models do not apply, the screening of phonons by charge carrier is generally incomplete and the polaron concept is considered. Spectra are fairly well modeled within a general approach compatible with the Drude framework and extended by factorizing over all complex poles and zeroes of the dielectric response, allowing discrimination of trapped and mobile polarons. Other models are reviewed: extended Drude with either frequency-dependent relaxation time or non-persistent electron velocity, marginal Fermi liquid, Luttinger liquid, localization, Anderson disordered metal, and those implying opening of gaps or pseudo-gaps in the conductivity. The signatures of stripes resulting from ordering of charges and spins—commensurate or incommensurate with the period of the crystal lattice—observed in certain nickelates, cuprates and manganites are discussed.

The Anomalous Optical Conductivity of Metallic La2−xSrxCuO4

The in-plane optical conductivity of three metallic La2−x Sr x CuO4 single crystals with 0.10 ≤ x ≤ 0.15 has been studied between 30 and 295 K. Strong peaks in the far-infrared are observed, which cannot be explained by Drude-like models. Their similarity with peaks reported in Cu–O “ladders” with one-dimensional charge-ordering, their extremely low frequency, and their behavior with temperature allows us to conclude that those anomalous features are excitations of charge stripes in the Cu–O planes.