Motion Of Free Electrons Research Articles

MXene Supported Surface Plasmon Polaritons for Optical Microfiber Ammonia Sensing.

The properties of surface plasmons are notoriously dependent on the supporting materials system. However, new capabilities cannot be obtained until the technique of surface plasmon enabled by advanced two-dimensional materials is well understood. Herein, we present the experimental demonstration of surface plasmon polaritons (SPPs) supported by single-layered MXene flakes (Ti3C2Tx) coating on an optical microfiber and its application as an ammonia gas sensor. Enabled by its high controllability of chemical composition, unique atomistically thin layered structure, and metallic-level conductivity, MXene is capable of supporting not only plasmon resonances across a wide range of wavelengths but also a selective sensing mechanism through frequency modulation. Theoretical modeling and optics experiments reveal that, upon adsorbing ammonia molecules, the free electron motion at the interface between the SiO2 microfiber and the MXene coating is modulated (i.e., the modulation of the SPPs under applied light), thus inducing a variation in the evanescent field. Consequently, a wavelength shift is produced, effectively realizing a selective and highly sensitive ammonia sensor with a 100 ppm detection limit. The MXene supported SPPs open a promising path for the application of advanced optical techniques toward gas and chemical analysis.

Optical LC-like resonances in high-index particles

Electric LC resonances, occurring in metallic circuits, govern the motion of free electrons or electric signals. In this paper, optical LC-like resonances in high-index particles (HIPs) or dielectric LC resonances have been studied, which involve bounded electrons and optical fields instead. The resonance effect is dominated by optical analogues of inductance and capacitance, which can be determined according to the electromagnetic energy bounded near the particle. The viewpoint of dielectric optical circuit with equivalent parameters facilitates the understanding of dielectric resonance effect. The result also provides a method for studying the optical properties of the HIPs.

Formation of probability and current waves at the scattering of a Gaussian wave packet by a double quantum well

Annotation. A numerical-analytical simulation of scattering by a three-barrier heterostructure of an electronic Gaussian wave packet, the spectral width of which is on the order of the distance between the levels of the doublet of quasi-stationary states, is carried out. This article proves that as a result of scattering, damped waves of electron charge and current densities are formed outside the double well, their characteristics are determined by the structure of the initial wave packet and the poles of the scattering amplitudes. The frequency of these waves is equal to the difference frequency of the doublet, the wavenumber is the difference between the wave numbers of free motion of electrons with resonant energies, and the speed of their propagation is the ratio of these quantities. The system can go into the regime of repetition or amplification of the emission of electron waves if a periodic resonant pumping of the doublet population is provided by scattering of a series of coherent wave packets.

A Potential‐Based Boundary Element Implementation for Modeling Multiple Scattering from Local and Nonlocal Plasmonic Nanowires

AbstractA novel boundary element implementation that models multiple scattering of plasmonic nanowires is presented. The modeling is based on potentials and the materials constituting the wires can be local (described by the local response model) or nonlocal (described by the nonlocal hydrodynamic model). The nonlocal hydrodynamic model (HDM) provides an important approximation describing nonclassical effects associated with the collective motion of free electrons in metals. The modeling is challenging as different interface conditions are needed at a boundary which separates 1) a local medium from a local medium; 2) a local (nonlocal) medium from a nonlocal (local) medium; and 3) a nonlocal medium from a nonlocal medium. The algorithm can address constructs of arbitrary geometry and material composition within the HDM; thus, it becomes a complete numerical tool for exploration of nonlocal nanowires. Fictitious sources are imposed at the boundaries, linking the scattered fields to the imposed sources, and matching the interface conditions at the boundaries. This procedure yields a set of Boundary Integral Equations (BIEs). Then, the BIEs are numerically solved utilizing the Boundary Element Method (BEM). The results from the BEM solver are verified quantitatively and qualitatively showing good agreement in both the near‐ and the far‐field regimes.

OpenSANS: A Semi-Analytical solver for Nonlocal plasmonicS

Prompted by the renewed interest the past decade in the hydrodynamic model for the description of nanoplasmonic systems, we present OpenSANS, a MATLAB toolbox for the simulation of canonical (that is, standalone spherical and cylindrical) nanoparticles and planar stratified structures whose critical dimensions are of mere nanometres. The method comprises of a generalisation of Mie theory to properly address the hydrodynamic motion of free electrons in metals and a compact S matrix formulation for the efficient treatment of multiple layers. The toolbox is built in a modular manner; each part (routine) has its own important functionality and can be used independently from the others. Our primary goal is the presentation of a highly efficient and accessible solver for the nanoplasmonics community. This is achieved by the very semi-analyticity of the chosen method and by powerful vectorisation techniques optimised in a very popular environment, MATLAB. Program summaryProgram Title: OpenSANSCPC Library link to program files:https://doi.org/10.17632/hmk224xngb.1Code Ocean capsule:https://codeocean.com/capsule/2246190Licensing provisions: GPLv3Programming language: MATLAB R2018b and newer.Supplementary material: See Appendix A.Nature of problem: Solve the scattering problem from multilayered, dielectric, local or nonlocal metallic nanoparticles, excited by a plane wave and placed in a local (dielectric or metallic) background.Solution method: Mie theory, appropriately extended to incorporate nonlocal effects (longitudinal waves) as predicted by the Hard Wall-Hydrodynamic Model, combined with S matrix theory for efficient handling of the multilayered structure.

A Boundary Integral Equation Formalism for Modeling Multiple Scattering of Light from 3D Nanoparticles Incorporating Nonlocal Effects

AbstractA novel computational scheme that models the scattering of light at interfaces in a deep‐nanometric (deep‐nm) plasmonic system is presented. The nonclassical effects associated with the collective motion of free electrons in metals of the system are investigated by a nonlocal hydrodynamic (HD) model. Due to the HD model, three types of interfaces, that is, the dielectric–dielectric interface, the dielectric–metal interface, and the metal–metal interface, are distinguished. The scattering of light at these interfaces is described by Boundary Integral Equations (BIEs), which are constructed by using the surface equivalence principle, the concept of the Green' function and the interface conditions. The BIEs are numerically solved by the boundary element method (BEM) for 3D nanoparticles of arbitrary shapes. To validate, the computed results are first quantitatively contrasted with analytical solutions from the Mie theory for spherical core–shell structures, with good agreements being demonstrated in both the near field and the far field. Then, a qualitative study is performed for dimers consisting of spheres with various gap sizes for both the classical local response model and the nonlocal HD model. The observed trends agree well with the results reported in previous works.

Band geometry from position-momentum duality at topological band crossings

We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under gauge field. This identifies the trace of quantum metric as the dual energy in momentum space. The band crossings with Berry defects thus induce the dual energy quantization in the trace of quantum metric. For the $\mathbb{Z}$ nodal-point and nodal-surface semimetals in three dimensions, the dual Landau level quantization occurs owing to the Berry charges. Meanwhile, the two-dimensional (2D) Dirac points exhibit the Berry vortices, leading to the quantized dual axial rotational energies. Such a quantization naturally generalizes to the three-dimensional (3D) nodal-loop semimetals, where the nodal loops host the Berry vortex lines. The ${\mathbb{Z}}_{2}$ monopoles bring about additional dual axial rotational energies, which originate from the links with additional nodal lines. Nontrivial band geometry generically induces finite spread in the Wannier functions. While the spread manifest quantized lower bounds from the Berry charges, logarithmic divergences occur from the Berry vortices. The band geometry at the band crossings may be probed experimentally by a periodic-drive measurement.

Classical electronic and molecular dynamics simulation for optical response of metal system.

An extended molecular dynamics simulation that incorporates classical free electron dynamics in the framework of the force-field model has been developed to enable us to describe the optical response of metal materials under the visible light electric field. In the simulation, dynamical atomic pointcharges follow equations of motion of classical free electrons that include Coulomb interactions with the oscillating field and surrounding atomic sites and collision effects from nearby electrons and ions. This scheme allows us to simulate an interacting system of metals with molecules using an ordinary polarizable force-field and preserves energy conservation in the case without applying an external electric field. As the first applications, we show that the presented simulation accurately reproduces (i) the classical image potential in a metal-charge interaction system and (ii) the dielectric function of bulk metal. We also demonstrate (iii) calculations of absorption spectra of metal nano-particles with and without a water solvent at room temperature, showing reasonable red-shift by the solvent effect, and (iv) plasmon resonant excitation of the metal nano-particle in solution under the visible light pulse and succeeding energy relaxation of the absorbed light energy from electrons to atoms on the metal and to the water solvent. Our attempt thus opens the possibility to expand the force-field based molecular dynamics simulation to an alternative tool for optical-related fields.

Van Hove Singularities and Trap States in Two-Dimensional CdSe Nanoplatelets.

Semiconductor nanoplatelets, which offer a compelling combination of the flatness of two-dimensional semiconductors and the inherent richness brought about by colloidal nanostructure synthesis, form an ideal and general testbed to investigate fundamental physical effects related to the dimensionality of semiconductors. With low temperature scanning tunnelling spectroscopy and tight binding calculations, we investigate the conduction band density of states of individual CdSe nanoplatelets. We find an occurrence of peaks instead of the typical steplike function associated with a quantum well, that rule out a free in-plane electron motion, in agreement with the theoretical density of states. This finding, along with the detection of deep trap states located on the edge facets, which also restrict the electron motion, provides a detailed picture of the actual lateral confinement in quantum wells with finite length and width.

On energy accommodation coefficient of gas molecules on metal surface at high temperatures

The electron-relating energy transfer on the interface between a gas and metal and its contribution to the energy accommodation coefficient (EAC) is discussed. The semi-empirical approach is utilized to highlight effects that are responsible for the EAC. The Coulomb blockage of a free electron motion due to the particle charging by the thermionic emission is suggested as a mechanism, which leads to the EAC drop at high temperatures. The numerical estimate shows that the EAC decrease by a couple of orders of magnitude is possible.

Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of p - and n -domains

The conductivity of a two-dimensional HgTe quantum well with a width $\sim$6.3~nm, close to the transition from ordinary to topological insulating phases, is studied. The Fermi level is supposed to get to the overall energy gap. The consideration is based on the percolation theory. We have found that the width fluctuations convert the system to a random mixture of domains with positive and negative energy gaps with internal edge states formed near zero gap lines. In the case with no potential fluctuations, the conductance of a finite sample is provided by a random edge states network. The zero-temperature conductivity of an infinite sample is determined by the free motion of electrons along the zero-gap lines and tunneling between them. The conductance of a single $p$-$n$ junction, which is crossed by the edge state, is found. The result is applied to the situation when potential fluctuations transform the system to a mixture of $p$- and $n$-domains. It is stated that the tunneling across $p$-$n$ junctions forbids the low-temperature conductivity of a random system, but the latter is restored due to the random edge states crossing the junctions.

Solar photosphere magnetization

Context.A recent review shows that observations performed with different telescopes, spectral lines, and interpretation methods all agree about a vertical magnetic field gradient in solar active regions on the order of 3 G km−1, when a horizontal magnetic field gradient of only 0.3 G km−1is found. This represents an inexplicable discrepancy with respect to the divB = 0 law.Aims.The objective of this paper is to explain these observations through the lawB = μ0(H+M) in magnetized media.Methods.Magnetization is due to plasma diamagnetism, which results from the spiral motion of free electrons or charges about the magnetic field. Their usual photospheric densities lead to very weak magnetizationM, four orders of magnitude lower thanH. It is then assumed that electrons escape from the solar interior, where their thermal velocity is much higher than the escape velocity, in spite of the effect of protons. They escape from lower layers in a quasi-static spreading, and accumulate in the photosphere. By evaluating the magnetic energy of an elementary atom embedded in the magnetized medium obeying the macroscopic lawB = μ0(H+M), it is shown that the Zeeman Hamiltonian is due to the effect ofH. Thus, what is measured isH.Results.The decrease in density with height is responsible for non-zero divergence ofM, which is compensated for by the divergence ofH, in order to ensure div B = 0. The behavior of the observed quantities is recovered.Conclusions.The problem of the divergence of the observed magnetic field in solar active regions finally reveals evidence of electron accumulation in the solar photosphere. This is not the case of the heavier protons, which remain in lower layers. An electric field would thus be present in the solar interior, but as the total charge remains negligible, no electric field or effect would result outside the star.

Features of the formation of an electric field in a non-uniform conducting medium

The paper considers the influence of the electric field of the current on the behaviour of a gas bubble in an electrically conductive melt. We propose a model which makes it possible to predict a change in the size of gas bubbles in a metal, provided that its crystallization occurs in the presence of an electric current. The model takes into account the interaction of the charge induced on the surface of the gas bubble — metal-gas interface — with the electric field of the current. The force that deforms the gas bubble is introduced. The magnitude of the force is determined by the charges induced on the surface of the bubble due to the action of the electric field of the current. The surface density of the charges is proportional to the square of the current density and depends on the geometry of the object that is affected, as well as on the material parameters of the medium, such as electrical resistivity and magnetic permeability. Additional forces of electrical nature acting on the surface of the gas bubble contribute to its deformation in the electric field of the current. In the presence of such forces, the interfaces between the media — liquid metal and gaseous — can be deformed. Under the conditions of an orderly motion of free electrons and their collisions with ions of the crystal lattice, the size of the interfaces between the media can be changed. The gas bubble under the action of additional forces is deformed and can subsequently be fragmented.

Free electron relativistic correction factors to collisional excitation and ionisation rates in a plasma

This paper presents approximate correction factors to collisional excitation and ionisation rates which account for special relativity in the free electron motion as a function of free electron temperature and the threshold energy of the reaction. These are calculated by taking the ratio of collisional rates derived from simple empirical cross sections using relativistic and non-relativistic mechanics. These results are extended to de-excitation and three body recombination rates using detailed balance. It is found that the relativistic correction is significant in regimes potentially important to galactic intracluster media and diagnostic dopants in burning ICF plasmas.

A Boundary Integral Equation Scheme for Simulating the Nonlocal Hydrodynamic Response of Metallic Antennas at Deep-Nanometer Scales

Modeling the interaction between light and a plasmonic nanoantenna, whose critical dimension is of a few nanometers, is complex owing to the “hydrodynamic” motion of free electrons in a metal. Such a hydrodynamic effect inevitably leads to a nonlocal material response, which enables the propagation of longitudinal electromagnetic waves in the material. In this paper, within the framework of a boundary integral equation and a method of moments algorithm, a computational scheme is developed for predicting the interaction of light with 3-D nonlocal hydrodynamic metallic nanoparticles of arbitrary shape. The numerical implementation is first demonstrated for the test example of a canonical spherical structure. The calculated results are shown to be in the excellent agreement with the theoretical results obtained with the generalized Mie theory. In addition, the capability of treating 3-D structures of general shapes is demonstrated by ellipsoids and dimers.

Low-loss plasmon-assisted electro-optic modulator.

For nearly two decades, the field of plasmonics1 - which studies the coupling of electromagnetic waves to the motion of free electrons in a metal2 - has sought to realize subwavelength optical devices for information technology3–6, sensing7,8, nonlinear optics9,10, optical nanotweezers11 and biomedical applications12. Although the heat generated by ohmic losses is desired for some applications (e.g. photo-thermal therapy), plasmonic devices for sensing and information technology have largely suffered from these losses inherent to metals13. This has led to a widespread stereotype that plasmonics is simply too lossy to be practical. Here, we demonstrate that these losses can be bypassed by employing “resonant switching”. In the proposed approach, light is only coupled to the lossy surface plasmon polaritons in the device’s off-state (in resonance) where attenuation is desired to ensure large extinction ratios and facilitate sub-ps switching. In the on state (out of resonance), light is prevented from coupling to the lossy plasmonic section by destructive interference. To validate the approach, we fabricated a plasmonic electro-optic ring modulator. The experiments confirm that low on-chip optical losses (2.5 dB), high-speed operation (>>100 GHz), good energy efficiency (12 fJ/bit), low thermal drift (4‰ K-1), and a compact footprint (sub-λ radius of 1 μm) can be realized within a single device. Our result illustrates the potential of plasmonics to render fast and compact on-chip sensing and communications technologies.

Constructing superconductors by graphene Chern–Simons wormholes

We propose a new model which simulates the motion of free electrons in graphene by the evolution of strings on manifolds. In this model, molecules which constitute sheets of graphene are polygonal point-like structures which build (N+1)-dimensional manifolds. By breaking the gravitational-analogue symmetry of graphene sheets, we show that two separated child sheets and a Chern–Simons bridge are produced giving rise to a wormhole. In this structure, free electrons are transmitted from one child sheet to the other producing superconductivity. An analogue between “effective gravitons” and “Cooper pairs” is found. In principle, this phenomenology provides the possibility to construct superconductor structures by using the analogue of cosmological models.

S-matrix approach to the problem of high-harmonic generation in the field of intense laser wave

A method using expansion of the wave function in the basis of photonic and free atomic eigenstates is proposed for calculating the emission spectrum of an atom in a laser field. The wave function is constructed using the Kramers−Henneberger transformation so that the expression for the transition S matrix explicitly includes the nonlinear interaction with the laser field. The expansion coefficients are determined by the residual interaction, which depends on the coordinates of the classical free electron motion in the laser field. Resonances at the atomic transition frequencies explicitly arise in the emission spectrum when the residual interaction is considered in the first order. The numerical solution of the timedependent Schro¨ dinger equation for the hydrogen atom within the semiclassical approach is used to obtain emission spectra for laser pulses of different intensities and durations.

Hyperbolic metamaterials: beyond the effective medium theory

Sub-wavelength layered metal/dielectric structures whose effective permittivities for different polarizations have different signs are known as hyperbolic metamaterials (HMMs). It is believed they are unique in their ability to support electromagnetic waves with very large wavevectors and, therefore, large densities of states, leading to a strong Purcell enhancement (PE) of spontaneous radiation. To verify this conventional wisdom, we use an analytic Kronig–Penney (KP) model and discover that hyperbolic isofrequency surfaces exist for all combinations of layer permittivities and thicknesses, and the strongest PE of radiation is achieved away from the nominally hyperbolic region. Furthermore, large wavevectors and PE are always combined with high loss, short propagation distances, and large impedances; hence, PE in HMMs is essentially a direct coupling of the energy into the free electron motion in the metal, or quenching of the radiative lifetime. PE in HMMs is not related to the hyperbolicity, per se, and is simply the consequence of strong dispersion of the permittivity in metals or polar dielectrics, as our conclusions are relevant also for the infrared HMMs that occur in nature. Moreover, detailed comparison of field distributions, dispersion curves, and Purcell factors between the HMM and surface plasmon polariton (SPP) guided modes in metal/dielectric waveguides demonstrates that HMMs are nothing but weakly coupled gap or slab SPP modes. Broadband PE is not specific to the HMMs and can be just as easily attained in single or double thin metallic layers. When it comes to enhancement of radiating processes and field concentrations, HMMs are in no way superior to far simpler plasmonic structures.

A NEW METHOD TO DETERMINE THE TEMPERATURE OF CMES USING A CORONAGRAPH FILTER SYSTEM

The coronagraph is an instrument that enables the investigation of faint features in the vicinity of the Sun, particularly coronal mass ejections (CMEs). So far coronagraphic observations have been mainly used to determine the geometric and kinematic parameters of CMEs. Here, we introduce a new method for the determination of CME temperature using a two filter (4025 Å and 3934 Å) coronagraph system. The thermal motion of free electrons in CMEs broadens the absorption lines in the optical spectra that are produced by the Thomson scattering of visible light originating in the photosphere, which affects the intensity ratio at two different wavelengths. Thus the CME temperature can be inferred from the intensity ratio measured by the two filter coronagraph system. We demonstrate the method by invoking the graduated cylindrical shell (GCS) model for the 3-dimensional CME density distribution and discuss its significance.