Nonlocal Dielectric Function Research Articles

Effect of material spatial dispersion in the degree of polarization of thermal radiation emitted by a spherical source

The influence of material spatial dispersion in the degree of polarization emitted by a metallic sphere is studied by means of fluctuational electrodynamics. The corresponding cross-spectral correlation functions of the electric field are calculated on a basis of a non-local scattering T-matrix for a spherical scatterer and for non-local dielectric functions for the metal such as those provided by the hydrodynamic model and the Lindhard theory. It is shown that the main effect of the material spatial dispersion is a blue shift of the spectra of the degree of polarization which, however, diminishes as the sphere size increases. Also, at the bulk plasma frequency, a local maximum of the degree of polarization emerges as a result of the excitation of bulk plasmons which is not evident when a local dielectric function is assumed.

Fluorescence quenching by a metal nanoparticle in the extreme near-field regime

We study the spontaneous decay rate of a dipole emitter close to a metallic nanoparticle in the extreme near-field regime. The metal is modeled using a nonlocal dielectric function that accounts for the microscopic length scales of the free electron gas. We describe quantitatively the crossover between the macroscopic and microscopic regimes and the enhanced nonradiative decay due to microscopic interactions. Our theory is in agreement with results previously established in the asymptotic near- and far-field regimes.

Finite-difference frequency-domain method for the extraction of effective parameters of metamaterials

Here, we report a numerical implementation of the nonlocal homogenization approach recently proposed in [M. Silveirinha, Phys. Rev. B 75, 115104 (2007)], using the finite difference frequency-domain method to discretize the Maxwell-Equations. We apply the developed formalism to characterize the nonlocal dielectric function of several structured materials formed by dielectric and metallic particles, and in particular, we extract the local permittivity, permeability and magnetoelectric coupling parameters when these are meaningful. It is shown that the finite differences frequency domain implementation of the homogenization method is stable and robust, yielding very accurate results.

A single molecule as a dielectric medium

For three molecules with weak or negligible charge overlap, we prove that the three-body interaction energy obtained from quantum perturbation theory (to leading order) fits a dielectric model with a nonlocal electronic screening function. The electronic charge cloud of each molecule acts as a dielectric medium for the interaction of the remaining two with the nonlocal dielectric function epsilon(r,r') obtained by O. S. Jenkins and K. L. C. Hunt [J. Chem. Phys. 119, 8250 (2003)], by considering the charge redistribution induced in a single molecule by an external perturbation. The dielectric function depends parametrically on the coordinates of the nuclei, within the Born-Oppenheimer approximation. We also prove that the force on each nucleus in molecule A depends on intramolecular dielectric screening within A. The potential from the charge distribution of B, screened by C acting as a dielectric medium, is further screened linearly within A; and similarly, with the roles of B and C reversed. In addition, the potential due to the unperturbed charge distribution of B and the potential due to the unperturbed charge distribution of C, acting simultaneously, are screened nonlinearly within A. The results show that nonlocal dielectric theory holds on the molecular level, provided that the overlap of the electronic charge distributions is weak.

Plasmonic excitations in tight-binding nanostructures

We explore the collective electromagnetic response in atomic clusters of various sizes and geometries. Our aim is to understand, and hence to control, their dielectric response, based on a fully quantum-mechanical description which captures accurately their relevant collective modes. The electronic energy levels and wave functions, calculated within the tight-binding model, are used to determine the non-local dielectric response function. It is found that the system shape, the electron filling and the driving frequency of the external electric field strongly control the resonance properties of the collective excitations in the frequency and spatial domains. Furthermore, it is shown that one can design spatially localized collective excitations by properly tailoring the nanostructure geometry.

Exciton Polaritons in One-Dimensional Metal-Semiconductor Photonic Crystals

We investigate theoretically the coupling of exciton with light in a one-dimensional photonic crystal. The unit cell of the crystal consists of two alternating layers, namely a metallic layer and a semiconductor one. The frequency-dependent dielectric function of the metal is described by the Drude model, whereas for the semiconductor we use a nonlocal excitonic dielectric function. The polariton dispersion for s-polarized modes in the metal-semiconductor photonic crystal is compared with that for a dielectric-semiconductor photonic crystal. Because of the metal layers, a low-frequency gap appears in the photonic band structure. The presence of the semiconductor gives rise to photonic bands associated with the coupling of light with size-quantized excitón states. At frequencies above the longitudinal exciton frequency, the photonic band structure exhibits anticrossing phenomena produced by the upper exciton-polariton mode and size-quantized excitons. It is found that the anticrossing phenomena in the metal-semiconductor photonic crystal occur at higher frequencies in comparison with the dielectric-semiconductor case.

Non-local optical response of two-dimensional arrays of metallic nanoparticles

The optical absorption spectra of two-dimensional (2D) arrays of spatially dispersivemetallic nanoparticles is examined. The corresponding non-local dielectric functionof the spheres is provided by (a) the hydrodynamic approximation and (b) theLindhard theory. More specifically, it is shown that the adoption of either types ofnon-local dielectric functions (hydrodynamic or Lindhard-type) for dilute 2Darrays of spheres does not alter the structure of the optical absorption spectrumbut leads to a blue-shift of all its distinct features. This effect becomes moreprominent as the radius of the nanoparticles decreases. However, for a close-packedarrangement of spheres, a non-local dielectric function provides a significantlydifferent optical spectrum than the local one, due to the dominant role of near-fieldeffects, which strongly depend on the choice of the dielectric function of the metal.

Nanostructure van der Waals interaction between a quantum well and a quantum dot atom

We examine the van der Waals interaction between mobile plasma electrons in a narrow quantum well nanostructure and a quantum dot atom. This formulation of the van der Waals interaction exhibits it to second order as the correlation energy (self-energy) of the dot-atom electrons mediated by the image potential arising from the dynamic, nonlocal and spatially inhomogeneous polarization of the quantum well plasma electrons. This image potential of the quantum-well plasma is, in turn, determined by the dynamic, nonlocal, inhomogeneous screening function of the quantum well, which involves the space-time matrix inversion of its spatially inhomogeneous, nonlocal and time-dependent dielectric function. The latter matrix inversion is carried out exactly, in closed form, and the van der Waals energy is evaluated in the electrostatic limit to dipole-dipole terms.

Nonlocal thin films in calculations of the Casimir force

The Casimir force is calculated between plates with thin metallic coating. Thin films are described with spatially dispersive (nonlocal) dielectric functions. For thin films the nonlocal effects are more relevant than for half-spaces. However, it is shown that even for film thickness smaller than the mean free path for electrons, the difference between local and nonlocal calculations of the Casimir force is of the order of a few tenths of a percent. Thus the local description of thin metallic films is adequate within the current experimental precision and range of separations.

A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere

Fast and numerically stable transfer-matrix solution is presented for the classical electromagnetics problem of a dipole radiating inside and outside a stratified sphere consisting of concentric spherical shells. There is no limitation on the dipole position, the number of the concentric shells, the shell medium, or on the sphere radius. Electromagnetic fields are determined anywhere in the space, the time-averaged angular distribution of the radiated power, the total radiated power, Ohmic losses due to an absorbing shell, and Green’s function are calculated. An absorbing, optically active, and ultrathin (≲10nm) metallic shell (core), characterized by a nonlocal dielectric function, are all allowed. The classical results are then applied to inelastic light scattering (fluorescence and Raman), the radiative and nonradiative normalized decay rates, and frequency shift. Using correspondence principle, the radiative decay rate is calculated from the Poynting vector, whereas the nonradiative decay rate is calculated from the Ohmic losses inside a sphere absorptive shell. Numerical stability of our method and limitations of classical description of decay rates are addressed. The importance of grouping various radiative and nonradiative decay mechanisms into local and nonlocal decay rates is emphasized. Further possible extensions of the theory presented here to the case of an arbitrary multilayered (axially symmetric) particle and to the classical problem of a radiating quadrupole in the presence of a multilayered particle are briefly outlined. Various applications for chemical speciation, LIDAR, fluorescent microscopy, engineering of decay rates, identification of biological particles, and monitoring specific cell functions are envisaged. Computer program is freely available at http://www.wave-scattering.com.

Exchange effects in the screening of a phonon mode in a semiconductor quantum well

We study the screening of the first two polar optical phonon modes in a QW using the rigid wall case. The screened potential was calculated by employing nonlocal dielectric functions obtained in multisubband extensions of (a) the RPA and (b) the Hubbard (H) approximations. The purpose of the calculations is to study the influence of the design parameters, such as the well width and the change in carrier population, in the above mentioned different approximations. The QW is modelled by an infinite potential well and also by the selfconsistent Hartree approximation to consider the modulation doped QW. The main design parameter is found to be the carrier population. Furthermore, it is found that the selfconsistent re-shaping of the electronic potential well—and hence the carrier distribution—affects the resulting screened potential significantly.

Nonlocal dielectric functions on the nanoscale: Screened forces from unscreened potentials

In this work, we prove that an intramolecular dielectric model yields accurate results for the forces between nonoverlapping molecules, at first order in the intermolecular interaction. The analysis is valid within the Born–Oppenheimer approximation. Within any perturbed molecule, a nonlocal dielectric function εv−1(r,r′) describes the screening of external potentials due to the induced redistribution of electronic charge, i.e., this function acts as the integral kernel that determines the effective potential at point r (within linear response), when an external potential φex(r′) acts on the molecule, at other points r′. The dielectric function εv−1(r,r′) depends on the nonlocal charge-density susceptibility, which can be calculated ab initio or by density functional techniques. From quantum mechanical perturbation theory, at first order the interaction energy of two molecules is determined by the unscreened Coulomb interaction energy of the unperturbed molecular charge distributions. Yet the first-order forces on the nuclei include dielectric screening effects, due to the redistribution of the electronic charge density of each molecule in the presence of the other. This counterintuitive result follows from a relation between the charge-density susceptibility and the derivatives of the electronic charge density with respect to nuclear coordinates. The derivation provides a quantum mechanical validation for dielectric screening models on the nanoscale, when the dielectric function for electronic response is nonlocal.

The analytical expression for the static nonlocal dielectric function of a polar liquid with due account of the overscreening effect

The extension of model Hamiltonian of Kornyshev et al. [Electrochim. Acta 42 (1997) 849] is suggested, and a modified analytical expression for the static nonlocal dielectric function ε( k) of a polar liquid with due account of the ovescreening effect is obtained. The goal is to correct the too small values of some of the fitted correlation lengths presented in the former work. The extension consists in the introduction of a nonlocality into the coupling of one of the polarization modes of a liquid to the scalar field and results in the appearance of a new fitting parameter. The new analytical expression for ε( k) almost retains the form suggested by Kornyshev et al. However, it is shown that the new expression permits to bring the values of fitted parameters into a range where they can be interpreted more realistically. Using the results of computer simulations for ε( k), a number of parameterizations of ε( k) for water, acetonitrile, and dimethyl is obtained and presented.

Non-local dielectric functions on the nanoscale: electronic polarization and fluctuations

In this work, we use a non-local dielectric theory to describe the electronic polarization induced by perturbing fields, and to characterize spontaneous, quantum mechanical fluctuations in the polarization. The theory holds on the intramolecular length scale, within the Born-Oppenheimer approximation. A non-local dielectric function ε d ( r , r ′) acts as an integral kernel that gives the dielectric displacement D( r) at point r within a molecule, in terms of the electric field E( r′) acting at other points r ′. Due to the inhomogeneity of the intramolecular environment, ε d ( r , r ′) differs from the non-local dielectric function ε v ( r , r ′) that characterizes the screening of applied potentials; however, the longitudinal component of the spatial Fourier transform ε d ( k , k ′) is completely determined by k, k′, and ε v ( k , k ′). For a molecule in equilibrium with a radiation bath at a fixed temperature, the fluctuation-dissipation theorem relates correlations of the spontaneous polarization fluctuations to the imaginary part of the non-local polarizability density. From this result, we derive a relation between the correlations of the fluctuating electronic polarization and the dielectric function ε d ( r , r ′;iω).

Failure of local Mie theory: optical spectra of colloidal aggregates

Fully retarded calculations of the optical properties of aggregates of metallic nanoparticles have been performed. Within a local theory, the optical spectra of particles in contact with each other are dominated by a series of resonances below the Fröhlich resonance of isolated spheres. The resonances are shown to be related to surface plasmon polaritons of extremely short wavelength, which are localised at the points of contact of the particles, and are connected with strong field enhancements in the vicinity of the contact point. Standard local Mie theory of the optical properties of interacting spheres does not describe this excitation correctly at finite cut-off multipole orders ⩽30. Intensity distributions and spectra were therefore calculated by means of the semianalytical multiple multipole technique. For small particles, however, a nonlocal refinement of aggregate Mie theory predicts, that the localised surface excitations are strongly damped by the excitation of volume plasmons at the surface. Local Mie theory should therefore not be applied to colloidal aggregates of small metallic particles in contact with each other. The localised surface plasmon polaritons are important, on the other hand, for aggregates of somewhat larger particles, even if nonlocality is taken into account. Employing aggregate Mie theory with a nonlocal dielectric function, we show in addition, that, even for relatively small particles, retardation effects and high-order multipoles must be taken into account.

Coupling of 2D plasmons to nonlocal bulk plasmons

An explicit closed-form position-space expression for the highly inhomogeneous inverse dielectric response function of a quantum well (QW) of finite width (with a single bound subband state) embedded in a bulk medium having a continuum of extended states is derived here analytically. The resulting position-dependent nonlocal dynamic inverse dielectric function ε −1(z,z′; q ||, ω) , given in position representation for the z-direction across the well, depends on the in-plane wave vector q || and frequency ω as well as on the positional variables z, z′. Spatial inhomogeneity arises from the lack of translational invariance in the z-direction due to the presence of the QW. The frequency poles of ε −1(z,z′; q ||, ω) obtained here represent the coupling of nonlocal bulk plasmons with two-dimensional (2D) intrasubband plasmons of the QW. The dispersion relation of the coupled modes is examined. The bulk particle–hole modes damp the collective excitations of the coupled 2D and bulk systems and we estimate the damping rate.

Dynamical Response and Surface Excitations in Thin Films

The non-local dynamically screened Coulomb interaction propagator W(Q, z, z', ω) in the vicinity of thin metal film is calculated for points inside and outside of the film, taking both collective modes and single-particle excitations into account. This is achieved by calculating the non-local dielectric function ϵp(Q, z, z', ω) of the thin jellium film within the Random Phase Approximation (using Local Density Approximation wave-functions), from which we then derive W(Q, z, z', ω). The calculated dielectric function is also used to obtain excitation spectra, and specifically dispersion relations of the collective modes.

Nonlocal dielectric functions of molecular liquids from computer simulations

The longitudinal dielectric function, χ( k)=1−1/ ε L( k), of both polar and nonpolar liquid environments is a key ingredient to modern theories of solvent effects upon charge transfer reactions in solution and solvation dynamics processes in general. In this work, we present a molecular dynamics simulation study of the dielectric function of several molecular liquids ranging from associating (H 2O, CH 3OH) and nonassociating ((CH 3) 2SO, CH 3CN) polar liquids to nondipolar ones (C 6H 6, CCl 4 and CO 2) aiming to better understand the relationships between the structure of the χ( k) functions to the charge–charge spatial correlations in each liquid. We show that the characteristic main peak of χ( k), located at some wave vector k ∗ , whose value depends on the liquid, arises from spatial charge density fluctuations of wavelength 2 π/k ∗ for all liquids considered, with the exception of CO 2. Further details about the shape of the χ( k) functions for the simulated liquids are discussed in terms of intra and intermolecular charge–charge correlations.

Nonlocal dielectric function of water: How strong are the effects of intramolecular charge form factors?

Abstract We study the effect of continuous electronic charge distributions in molecular models on the nonlocal dielectric response function of water. We show that, without changing the atomic distribution, the inclusion of the continuous electronic charge distribution within each molecule changes significantly the results obtained so far with the use of site-site- or multiple-models.

Computer simulation of the non-local dielectric function of polar liquids: boundary conditions revisited

For the calculation of ϵ(k) via the correlation function of the bound charge density fluctuations or the ratio of the bound charge density to an external charge density, a generalized form of the fluctuation dissipation theorem is derived which accounts for different types of boundary conditions through a modified Green's function. It is demonstrated for the case of an interaction site model of water that it is possible to obtain consistent results for the non-local dielectric function with different types of boundary conditions. This is shown by calculating ϵ(k) both from the correlation function ⟨ρb(k)ρb(-k)⟩ and from the dielectric response to an external electric field.