Electrostatic Approximation Research Articles

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular region Ωin into an annular region Ωout with a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using molecular dynamics (MD) simulations to find the system’s positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particles q 1 and q 2 on the layers Ωin and Ωout respectively with no background density. The second one corresponds to a finite Surface Electrode (SE) composed of planar metallic layers displayed on the regions Ωin , Ωout at constant voltages Vin , Vout considering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a 1/r —electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratio ξ=q1/q2 once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer’s geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractive ξ=−1 and repulsive layers ξ = 1.

Enhanced magneto-optical properties of Fe3O4@Au nanoparticles and its reverse core-shell nanostructure embedded in host matrix SiO2

We studied the effect of electric and magnetic polarizability of Fe3O4@Au and the reverse structure Au@Fe3O4 core-shell spherical nanostructures embedded in SiO2. Employing electrostatic approximation and Maxwell-Garnett effective medium theory, we evaluate the electric and magnetic polarizability, the refractive index and absorbance as a function of radiation energy. The modified Drude-Lorentz form and Lorentz model used to evaluate ϵ(ω) and μ(ω), respectively. For fixefd r2 = 30 nm, β = 0.875, εh = 3.9 and f = 0.001 maximum absorbance obtained at E = 2.742 eV for Au@Fe3O4 core-shell and at E = 2.937 eV for the reverse structure with β = 0.578. The ratio of the maximum absorbance peak of Au@Fe3O4 core-shell to Fe3O4@Au core-shell gives 3.5. Both graphs of n2 and absorbance possess three sets of peaks. All sets of resonance peaks of Fe3O4@Au found in the visible region. For the revers structure the first two sets of resonance peaks found in the visible region and the third set of resonance peaks in UV region. The peaks arise due to the coupling between the surface plasmon of the gold metal with Fe3O4∕SiO2 interfaces and the interaction of incident radiation with magnetic dipole moment of the magnetic semiconducting nanoparticles. The findings may be used in applications that require the combined plasmonic and magnetic effects such as drug delivery.

Theoretical Modeling of Plasmon Resonance Induced by Hollow Nanoshell Spheres Assisted with a Graphene Shell for Use as an Efficient Narrowband Absorber

We present theoretical modeling of the local surface plasmon resonance (LSPR) induced by hollow nanoshell spheres assisted with a graphene shell, aiming to examine their potential for use as efficient narrowband absorbers in the infrared wavelength region. We investigate two designs of hollow nanoparticles; namely, a hollow graphene nanosphere with a single graphene shell, and a hollow nanosphere with double shells comprising a graphene shell wrapped around a silver shell. The electric field in each region of the nanoshell is determined by solving the Laplace equation of the potential within the electrostatic approximation (the nanoshell radius [Formula: see text]50[Formula: see text]nm). Using the calculated polarizability of nanoshells, we derive analytical expressions for the absorption and scattering cross-sections. We show that in both proposed nanocomposite models, the graphene shell affords an ultra-narrow LSPR with an absorption efficiency significantly higher than the scattering efficiency. In addition, the graphene-assisted LSPR can be tuned through the visible and infrared regions by changing the Fermi energy and thickness of the graphene layer. Another exciting finding is that the use of a silver shell in the hollow bi-shell nanoparticles provides another LSPR peak besides that induced by the graphene shell. Both LSPRs of graphene and silver shells can be overlapped by changing the optical properties of graphene and/or the geometrical parameters of the silver shell. The resulting LSPR is characterized by a dominant absorption cross-section and a significant narrowband. In both proposed nanoshell designs, the properties of LSPRs are promising for use in various optical imaging and phototherapy applications.

Assessing Quantum Calculation Methods for the Account of Ligand Field in Lanthanide Compounds

We obtained thorough insight into the capabilities of various computational methods to account for the ligand field (LF) regime in lanthanide compounds, namely, a weakly perturbed ionic body and quasidegenerate orbital multiplets. The LF version of the angular overlap model (AOM) was considered. We intentionally took very simple idealized systems, the hypothetical [TbF]2+, [TbF2]+ and [Tb(O2NO)]2+, in order to explore the details overlooked in applications on complex realistic systems. We examined the 4f and 5d orbital functions in connection to f–f and f–d transitions in the frame of the two large classes of quantum chemical methods: wave function theory (WFT) and density functional theory (DFT). WFT methods are better suited to the LF paradigm. In lanthanide compounds, DFT faces intrinsic limitations because of the frequent occurrence of quasidegenerate ground states. Such difficulties can be partly encompassed by the nonstandard control of orbital occupation schemes. Surprisingly, we found that the simplest crystal field electrostatic approximation, reconsidered with modern basis sets, works well for LF parameters in ionic lanthanide systems. We debated the largely overlooked holohedrization effect that inserts artificial inversion symmetry into standard LF Hamiltonians.

Energy transport and relaxation of phonon polaritons in two-dimensional polar crystals

Energy transport and relaxation of phonon polaritons (PhPs) are studied, based on a macroscopic phonon model, for atomic layers of hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDs). The velocity of the energy flow (energy velocity) is derived from the energy flow and density; it equals the group velocity, similar to the results of bulk and surface PhPs. In electrostatic approximation, valid once the frequency is slightly above ω0 (e.g., ω>1.002ω0∼224cm−1 for pentalayer MoTe2; ω0 is the zone-center optical-phonon frequency), simple formulas are obtained for the energy velocity and relaxation rate (ERR). While the energy velocity increases proportionally with the number of layers N, the ERR is independent of N. The ERR equals the phonon damping rate in freestanding layers, but it is slightly decreased in SiO2-supported layers and has a non-monotonic frequency dependence (the decrease is smaller than 5.4% for hBN layers and negligible for TMD layers). The energy velocity decreases significantly with frequency in both freestanding and supported layers. Near ω0, however, the PhP properties should be calculated rigorously, and they all depend on N as well as the dielectric environment. High-frequency screening should be included to study the energy transport. The energy velocity can be engineered by varying N and the dielectric environment; it also can be tuned together with the propagation quality factor by the incident light frequency. The MoTe2 layers should be exploited for a far-infrared PhP material (wavelengths 43–45 μm); this is just an example of application of the proposed model to the considered materials.

Electromagnetic Scattering by Bianisotropic Spheres

Electromagnetic fields in bulk bianisotropic media contain plane waves whose k-vectors can be found using the method of the index of refraction’s operator and belong to the Fresnel wave surfaces that fall into one of the five hyperbolic classes of the Durach et al. taxonomy of bianisotropic media. Linear combinations of vector spherical harmonics can be used as a set of solutions of vector Helmholtz equations in gyrotropic media to develop Mie’s theory of scattering by anisotropic spheres as accomplished by Lin et al. and Li et al. In this study, we introduced electromagnetic orbitals for bianisotropic media as linear combinations of vector spherical harmonics, which represent solutions of Maxwell’s equations in bianisotropic media. Using these bianisotropic orbitals, we developed a theory of the scattering of electromagnetic radiation by bianisotropic spheres with arbitrary effective material parameters and sizes. As a by-product, we obtained a simple expression for the expansion of a vector plane wave over vector spherical harmonics in a more compact form than the frequently used by Sarkar et al. We obtained the polarizability expressions in the Rayleigh limit in agreement with the results of the electrostatic approximation of Lakhtahia and Sihvola.

Measurements of the Atmospheric Electric Current Density by a Passive Horizontal Ring Antenna in the Surface Layer: Electrostatic Approximation

Measurements of the Atmospheric Electric Current Density by a Passive Horizontal Ring Antenna in the Surface Layer: Electrostatic Approximation

Development of an ensemble Monte Carlo simulator for high-power semiconductor devices with self-consistent electromagnetism and GPU implementation

The ensemble Monte Carlo (EMC) method is a powerful and widely used technique for modeling carrier transport in semiconductors in which one can easily take into account band structure and a variety of scattering mechanisms. In the usual implementations of EMC, the semiclassical electron dynamics is coupled self-consistently to the electrostatic field and this suffices for most devices. However, for high power, high current semiconductor device applications the electrostatic approximation is often not adequate and the full electromagnetic (EM) equations must be solved in fully-coupled fashion. We report on the development of a fully self-consistent, time-domain, EM-EMC simulator for two- and three-dimensional device simulations in which we also address a well known drawback of these methods, their computational intensiveness, by producing a GPU implementation.

Optical Response of Periodic Arrays of Graphene Nanodisks

Doped graphene nanostructures are a promising platform for photonics due to their exceptionally strong and tunable plasmonic resonances. When placed in a periodic array configuration, the plasmons supported by the individual nanostructures interact with each other and, under the appropriate conditions, can give rise to a collective mode known as a lattice resonance. Here, we perform a comprehensive analysis of the response of periodic arrays of graphene nanodisks and identify the conditions under which the system is able to support lattice resonances. We find that the ratio between the period of the array and the wavelength of the plasmon completely determines the behavior of the system. As a consequence, strong lattice resonances are achieved for micron-size nanodisks in the terahertz regime. We develop a theoretical model valid beyond the electrostatic approximation and use it to derive closed analytical expressions for the strength, the wavelength, and the width of the optical resonance of the arrays. The theoretical framework developed in this work paves the way for facile design and discovery of emerging properties of periodic arrays of graphene nanostructures that could enable applications in photonics and plasmonics.

Kinetic investigation of the planar multipole resonance probe under arbitrary pressure

A new plasma diagnostic tool called planar multipole resonance probe (pMRP) has been proposed in the past decade. It has a minimally invasive structure and allows simultaneous measurement of electron density, temperature, and collision frequency. Previous work has investigated the behavior of the pRMP by the Drude model, which misses kinetic effects, and the collisionless kinetic model, which misses collisional damping. To further study the pMRP at arbitrary pressure, a collisional kinetic model is proposed in this paper. The electron dynamics is described by the kinetic equation, which considers the electron-neutral elastic collision. Under the electrostatic approximation, the kinetic equation is coupled to the Poisson equation. The real part of the general complex admittance is calculated to describe the spectral response of the probe–plasma system. The calculated spectra of the idealized pMRP demonstrate that this collisional kinetic model can capture both collisionless kinetic damping and collisional damping. This model overcomes the limitations of the Drude model and the collisionless kinetic model and allows discussion of the validity of simpler models.

The effect of surface plasmonic resonances on magneto-plasmonic spherical core-shell nanocomposites

In this study, the effect of plasmon resonance on magneto-plasmonic spherical core-shell nanocomposite enclosed in a dielectric host medium is theoretically investigated by applying electrostatic approximation (esa) and Maxwell-Garnet effective medium theories to obtain magneto-optical parameters such as; effective electric permittivity and magnetic permeability as well as the corresponding extinction cross-sections. Likewise, for a fixed size of QDs (of radius nm) numerical analysis was performed to determine the plasmonic resonance effect by varying the parameters such as the metal fraction (β) and the dielectrics (εh) of the host medium on the magneto-plasmonic nanostructures (nss). The results depict that graphs of absorption, scattering, and extinction cross-sections as a function of wavelength have two positions of resonance peaks. The first set of peaks are in the ultraviolet (uv) and the second located in visible regions. These peaks originated from the strong coupling between a regular periodic vibrations of surface plasmons of silver (Ag) with the excitonic state of the dielectric/semiconductor at the internal ( ) and external (Ag/host) interfaces. As β increases, the absorption and scattering cross-sections are blue-shifted in the first peak and red shifted the second set of peaks. Similarly, as εh increases or as β decreases, the sets of resonance peaks for extinction cross-section gets enhanced; while keeping one of these parametric quantities fixed at once. The resulting surface plasmon resonance effect might be utilized in a variety of applications that combines both the plasmonic and magnetic core-shell nanostructures ranging from UV to Visible spectral regions.

The initial radius of lightning return stroke channel and its relation with discharge intensity

The initial radius of the return stroke is one of the important parameters reflecting lightning discharge intensity. Based on spectral diagnosis and electrostatic approximation of the vertically descending leader model, the lightning channel temperature, line charge density, and electrostatic energy of seven dart leader–return stroke sequences were estimated. Finally, the initial radii of the return strokes were obtained. We analyzed the relationship between the initial radii and the corresponding discharge parameters. The initial radius is found to have a good linear correlation with each of the following quantities: the line charge density of the dart leader, the total intensity of ionic lines in the spectra, and the optical radius. It is also inversely proportional to the leader duration. These correlations confirm that the initial radius is closely related to discharge intensity, and that the charge stored in the leader channel directly determines the initial radius and discharge intensity of the return stroke.

Two-dimensional phonon polaritons in multilayers of hexagonal boron nitride from a macroscopic phonon model

Phonon polaritons (PHPs) in freestanding and supported multilayers of hexagonal boron nitride are systematically studied using a macroscopic optical-phonon model. The PHP properties such as confinement, group velocity, propagation quality factor (PQF), and wavelength scaling are studied. Owing to high-frequency screening, there is an upper frequency limit making the two-dimensional (2D) PHPs have a frequency band and also a maximum PQF occurs near the center frequency. The substrate’s dielectric response should be included to accurately calculate the PHP properties. While the simple electrostatic approximation (ESA) is valid for PHPs with frequencies ω above ω0 (e.g., ω>1.03ω0 for the 30-layers; ω0 is the Γ point optical-phonon frequency), it fails to describe the PHP properties near ω0 and the effect of retardation should be included for a proper description. The PHP wavelength vs layer thickness near ω0 deviates significantly from a linear scaling law given by the ESA due to strong coupling of photons and longitudinal optical phonons. The calculated PHP dispersion and scaling are compared with experimental data of a number of spectroscopic studies and found to be in good agreement for most of the results. While the frequency of incident light should be near the center frequency to maximize the PQF, the PHP wavelength, confinement, and propagation length can be engineered by varying the multilayer thickness and its dielectric environment.

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

In this work, we study the gapped surface electrode (SE), a planar system composed of two-conductor flat regions at different potentials with a gap between both sheets. The computation of the electric field and the surface charge density requires solving Laplace’s equation subjected to Dirichlet conditions (on the electrodes) and Neumann boundary conditions over the gap. In this document, the gapless surface electrode is modeled as a two-dimensional classical Coulomb gas having punctual charges +q and −q on the inner and outer electrodes, respectively, interacting with an inverse power law 1/r-potential. The coupling parameter Γ between particles inversely depends on temperature and is proportional to q 2. Precisely, the density charge arises from the equilibrium states via Monte Carlo (MC) simulations. We focus on the coupling and the gap geometry effect. Mainly on the distribution of particles in the circular and the harmonically-deformed gapped SE. MC simulations differ from electrostatics in the strong coupling regime. The electrostatic approximation and the MC simulations agree in the weak coupling regime where the system behaves as two interacting ionic fluids. That means that temperature is crucial in finite-size versions of the gapped SE where the density charge cannot be assumed fully continuous as the coupling among particles increases. Numerical comparisons are addressed against analytical descriptions based on an electric vector potential approach, finding good agreement.

Extinction and scattering of light by nonspherical plasmonic particles in absorbing media

Electromagnetic scattering by spheres embedded in an absorbing medium has attracted much attention and has been solved recently by an extension of conventional Lorenz-Mie (LM) theory. By contrast, no relevant studies have been published for nonspherical absorbing particles. To the best of our knowledge, we present the first T-matrix method (TMM) formalism and relevant computer simulations for nonspherical particles embedded in an absorbing host. We also derive analytical electrostatic and improved electrostatic approximations (EA and IEA) for small spheroids in an absorbing host. To exemplify the developed theory and computer codes, we consider randomly oriented prolate and oblate Au and Ag nanospheroids, cigar-like nanorods, and nanodisks embedded in a water-like absorbing medium with the complex refractive index 1.33+i(0-0.3), in a lossy poly(3-hexylthiophene) (P3HT) matrix, and the lossless poly(methyl methacrylate) (PMMA). We analyze two far-field optical observables inherent to the particles: the extinction cross section and the normalized 4 × 4 scattering matrix. Specifically, we discuss the spectral extinction, the phase function, and the depolarization ratio, which characterizes the cross-polarized intensity of scattered light. To normalize the phase function, we also calculated the effective far-field scattering cross section. For maximal size parameters less than 1, IEA and TMM cross section spectra agree perfectly, independently on the aspect ratio (1–10) and imaginary part of host absorption (0–0.3). Thus, IEA provides a simple, accurate, and user-friendly alternative to TMM codes when the maximal particle size is less than 200 nm, irrespective of the host absorption. The general effect of increasing host absorption is to decrease and broaden the plasmonic extinction and scattering peaks, independently of the particle shape, material (Au or Ag), and the size correction of optical constants. However, in the lossy P3HT matrix, the dominant plasmonic resonances (PRs) are red-shifted and narrowed compared to the corresponding peaks in PMMA. In particular, the absolute FWHM of 12–20 nm and the relative FWHM/PR values of 1.9–2.5% were found for prolate Au and oblate Ag particles embedded in P3HT. This unusual narrowing is explained by the extreme spectral dependence of P3HT absorption. The phase function of Au and Ag nanorods is symmetrical irrespective of the aspect ratio and the host absorption, but it does not follow the Rayleigh law. The host absorption decreases the spectral maxima of the depolarization ratio and shifts them slightly to the red.

Long time dynamics and upper semi-continuity of attractors for piezoelectric beams with nonlinear boundary feedback

A system of boundary-controlled piezoelectric beam equations, accounting for the interactions between mechanical vibrations and the fully-dynamic electromagnetic fields, is considered. Even though electrostatic and quasi-static electromagnetic field approximations of Maxwell’s equations are sufficient for most models of piezoelectric systems, where the magnetic permeability is completely discarded, the PDE model considered here retains the pronounced wave behavior of electromagnetic fields to accurately describe the dynamics for the most piezoelectric acoustic devices. It is also crucial to investigate whether the closed-loop dynamics of the fully-dynamic piezoelectric beam equations, with nonlinear state feedback and nonlinear external sources, is close to the one described by the electrostatic/quasi-static equations, when the magnetic permeability μ is small. Therefore, the asymptotic behavior is analyzed for the fully-dynamic model at first. The existence of global attractors with finite fractal dimension and the existence of exponential attractors are proved. Finally, the upper-semicontinuity of attractors with respect to magnetic permeability to the ones of the electrostatic/quasi-static beam equations is shown.

2D electrostatic modeling of twisted pairs

PurposeThis paper aims to model a three-dimensional twisted geometry of a twisted pair studied in an electrostatic approximation using only two-dimensional (2D) finite elements.Design/methodology/approachThe proposed method is based on the reformulation of the weak formulation of the electrostatics problem to deal with twisted geometries only in 2D.FindingsThe method is based on a change of coordinates and enables a faster computational time as well as a high accuracy.Originality/valueThe effectiveness of the adopted approach is demonstrated by studying different configurations related to the IEC 60851-5 standard defined for the measurement of the electrical properties of the insulation of the winding wires used in electrical machines.

Self-thermophoresis of laser-heated spherical Janus particles

An analytic framework is presented for calculating the self-induced thermophoretic velocity of a laser-heated Janus metamaterial micro-particle, consisting of two conducting hemispheres of different thermal and electric conductivities. The spherical Janus is embedded in a quiescent fluid of infinite expanse and is exposed to a continuous light irradiation by a defocused laser beam. The analysis is carried under the electrostatic (Rayleigh) approximation (radius small compared to wavelength). The linear scheme for evaluating the temperature field in the three phases is based on employing a Fourier–Legendre approach, which renders rather simple semi-analytic expressions in terms of the relevant physical parameters of the titled symmetry-breaking problem. In addition to an explicit solution for the self-thermophoretic mobility of the heated Janus, we also provide analytic expressions for the slip-induced Joule heating streamlines and vorticity field in the surrounding fluid, for a non-uniform (surface dependent) Soret coefficient. For a ‘symmetric’ (homogeneous) spherical particle, the surface temperature gradient vanishes and thus there is no self-induced thermophoretic velocity field. The ‘inner’ temperature field in this case reduces to the well-known solution for a laser-heated spherical conducting colloid. In the case of a constant Soret phoretic mobility, the analysis is compared against numerical simulations, based on a tailored collocation method for some selected values of the physical parameters. Also presented are some typical temperature field contours and heat flux vectors prevailing in the two-phase Janus as well as light-induced velocity and vorticity fields in the ambient solute and a new practical estimate for the self-propelling velocity.Graphic abstract

Kinetic investigation of the planar multipole resonance probe in the low-pressure plasma

Active Plasma Resonance Spectroscopy (APRS) is a well-established plasma diagnostic method: a radio frequency signal is coupled into the plasma via a probe or antenna, excites it to oscillate, and the response is evaluated through a mathematical model. The majority of APRS probes are invasive and perturb the plasma by their physical presence. The planar multipole resonance probe (pMRP) solves this problem: it can be integrated into the chamber wall and minimize the perturbation. Previous work has studied the pMRP in the frame of the Drude model, but it misses important kinetic effects like collision-less damping. In this work, a collision-less kinetic model is developed to further investigate the behavior of the pMRP. This model consists of the Vlasov equation, which is coupled with the Poisson equation under electrostatic approximation. The spectral response of the probe–plasma system is found by calculating the complex admittance. This model covers the kinetic effects and overcomes the limitations of the Drude model.

Modeling of generation of characteristic x-ray radiation under vacuum heating of electrons of nanocylinders

A model is developed for the generation of hot electrons near the surfaces of ionized cylinders by a laser field of nonrelativistic intensity, which allows one to go beyond the electrostatic approximation and takes into account the absorption of the laser field energy by the generated electrons. A model of Kα x-ray generation in a copper substrate, when the cylinders are located on the substrate obliquely and parallel to each other, and the laser field propagates perpendicularly to the substrate, is also considered. It is revealed that the Kα radiation yield depends rather strongly on the angle of inclination of the cylinders. The optimal parameters, the cylinder radius multiplied by the laser wavenumber, the angle of inclination of the cylinders, and direction of the linearly polarized laser electric field, are determined at the laser field amplitude aL = 0.2. With these parameters, the yield of Kα radiation from a copper substrate covered with cylinders is 2.7 times higher than the maximum yield of Kα radiation from the substrate covered with ionized clusters under the same irradiation conditions and 4 times higher than the maximum yield of Kα radiation from a flat copper target irradiated by a p-polarized laser field of the same amplitude. An increase in the yield of Kα radiation from the substrate covered with nanocylinders as compared to the yield of Kα radiation from the substrate covered with ionized clusters is due to an increase in the number of accelerated electrons.