Nonlocal Dielectric Response Research Articles

Surface enhanced Raman scattering from metallic nanoshells with nonlocal dielectric response

The Gersten–Nitzan model is applied to study the surface enhanced Raman scattering from a molecule adsorbed on a spherical metallic nanoshell. The nonlocal dielectric response from the nanoshell has been accounted for by using a phenomenological model. For a fixed outer radius of the shell, the enhancement ratio is calculated over a large range of scattering frequency and inner radius of the shell, including the case of a solid metallic particle. The effect due to different core materials is also studied. It is concluded that the nonlocal effects can be significant for very close molecule–shell distances, and for shells with very small sizes and/or thickness, leading to smaller enhancement in general. This can affect the plasmon resonances as well as the optimal shell thickness for the shell acting as a Raman enhancer.

Nonlocal dielectric response of an N‐quantum‐well superlattice embedded in bulk and semi‐infinite plasmas in magnetic field

AbstractWe derive explicit analytic results for the dynamic, nonlocal and inhomogeneous screening functions of a finite superlattice array of N equally spaced 2D quantum well plasmas embedded in infinite and semiinfinite host bulk‐plasma‐like media. The closed‐form results presented here for the screening functions, which are space‐time matrix inverses of the spatially inhomogeneous dielectric functions, are valid for any number of wells, and can accomodate nonlocality in both the 2D and host plasmas, as well as an ambient normal magnetic field. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electromagnetic field correlations near a surface with a nonlocal optical response

The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field's degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its $1/z^3$ divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to the Thomas-Fermi length. The electron mean free path, however, sets a larger scale where significant deviations from the local description are visible.

Non-local constitutive relations and the quasi-homogeneous approximation

The scattering from bodies exhibiting a non-local dielectric response is investigated within the weak scattering limit. A quasi-homogeneous approximation is introduced and investigated. A qualitative change in the scattering pattern of scattered radiation is seen to emerge with the onset of a non-local response.

Interaction of quantum well excitons with evanescent plane electromagnetic waves

A formalism based on non-local dielectric response theory and Green function techniqueshas been developed to describe the interaction of quantum well excitons with an evanescentoptical wave of a planar waveguide. Reflection spectra of a system in which aquantum well placed behind a dielectric interface at which light experiences totalinternal reflection have been calculated. It is shown that the spectral featurecorresponding to the exciton resonance becomes much more pronounced if the angle ofincidence is close to the critical angle of total internal reflection. The concept of ageneralized Snell law has been applied to provide simplification of the formalism.

Exact surface impedance formulation of the Casimir force: Application to spatially dispersive metals

We show that exact results are obtained for the calculation of Casimir forces between arbitrary materials using the concept of surface impedances, obtaining in a trivial way the force in the limit of perfect conductors and also Lifshitz formula in the limit of semi-infinite media. As an example we present a full and rigorous calculation of the Casimir force between two metallic half-spaces described by a hydrodynamic nonlocal dielectric response.

Semiconductor microcavities: towards polariton lasers

In this review paper we address one of the most rapidly developing new domains of semiconductor optics: light-matter coupling in semiconductor microcavities. Using the non-local dielectric response theory and transfer matrix technique, we show how two-dimensional confinement of a photonic mode coupled to an exciton resonance results in the appearance of two branches of exciton-polaritons, quasi-particles combining properties of photons and excitons. We obtain the dispersion relations of polaritons in microcavities and derive a condition for strong-weak coupling threshold. We show that being bosons, exciton-polaritons are subject to Bose-condensation which might result in emission of a coherent and monochromatic light in the strong coupling regime. A source of such coherent light is referred to as a polariton laser. We show that polariton lasers have theoretically no threshold and require essentially new basic physics as compared to conventional lasers described by Einstein theory. We give examples of model polariton laser structures expected to work at room temperature and overview the main difficulties on the way to producing these new opto-electronic devices.

Electromagnetic theory of the coupling of zero-dimensional exciton and photon states: A quantum dot in a spherical microcavity

Exciton-light coupling in spherical microcavities containing quantum dots has been treated by means of classical electrodynamics within the nonlocal dielectric response model. Typical anticrossing behavior of zero-dimensional exciton-polariton modes has been obtained, as well as the weak-coupling-strong-coupling threshold. The influence of the cavity Q factor on the optical response of the structure has been analyzed.

Effect of Overscreening on the Localization of Hydrated Electrons

The problem of the ground state of hydrated electron is revisited with a focus on the effects due to nonlocal dielectric response of water. The standard variational analysis is performed. It takes into account – in addition to nonlocal polarization of nuclear modes – the electron repulsion from the closed shells of water molecules, a possibility to form a cavity around the electron and the interaction of the hydrated electron with the high frequency electronic degrees of freedom of water. The classical dielectric continuum limit, shown for a reference, gives the ground state hydration energy that is 2.5 times smaller than the experimental value. The situation alters dramatically if one accounts for the nonlocal dielectric response of water. If one takes literally the existing MD simulation data for the static wave-vector dependent dielectric response function (with an "over-screening" resonance at

Exciton polaritons in quantum-dot photonic crystals

We present a theory of the photonic band structure of three-dimensional arrays of quantum dots (QDs). A system of Maxwell’s and material equations is solved and the dispersion equation for exciton-polaritons is derived making allowance for a nonlocal dielectric response of quasi-zero-dimensional excitons confined in QDs. The reflection and transmission coefficients are calculated for a single plane, a pair of planes and a stack of equidistant planes of QDs. Two different approaches are proposed to perform a calculation. One of them is based on recurrent equations relating the reflection coefficients for N + 1 and N planes, while in the other approach the Bloch solutions for an infinite QD lattice are used.

Exciton polaritons in a cylindrical microcavity with an embedded quantum wire

Exciton-light coupling in cylindrical microcavities containing quantum wires has been treated by means of classical electrodynamics within the nonlocal dielectric response model. A typical anticrossing behavior of quasi-one-dimensional exciton-polariton modes has been obtained, as well as the weak-coupling--strong-coupling threshold. Effects of the nonradiative damping of the exciton resonance in the quantum wire on the optical response of the microcavity structure have been analyzed.

Electron energy loss in ordered arrays of polarizable spheres

We develop a theory for the energy loss of swift electrons traveling parallel to an ordered array of polarizable spheres. The energy loss is given in terms of a surface response function which is expressed as a spectral representation. The poles and weights in this representation are determined through the eigenvalues and eigenvectors of an interaction matrix. This matrix takes account of the quasistatic electromagnetic interaction between the polarized spheres to an arbitrary multipolar order. We use our theory to calculate the energy-loss spectra for cubic arrays of aluminum spheres with various numbers of layers and compare the results with those obtained using a dielectric continuum model. @S0163-1829~99!05843-9# Electron-energy-loss spectroscopy ~EELS! of inhomogeneous systems has been an active field of research during the last decades. Here, we will be interested in the calculation and analysis of EELS spectra of granular matter. The calculation of the energy loss of swift electrons passing through a system of nanometric inclusions embedded in an otherwise homogeneous matrix was stimulated by the recent experiments of Walsh. 1 The concept of an effective medium for the calculation of the energy-loss function in a granular composite has been very appealing because one might expect that this function could be written in terms of the effective dielectric function associated with the composite. The first attempts along these lines were done by using the effective dielectric functions which had proved to be successful in describing the optical properties of granular composites, 1 like the ones devised, for example, by Maxwell Garnett, 2 Bruggeman, 3 or Landau and Lifshitz. 4 The main problem encountered in using these types of effective dielectric functions was that the peaks in energy loss coming from the excitation of the bulk plasmons of the inclusions did not appear in the calculated spectra. The origin of this problem was the local nature of the effective dielectric response, that is, the effective dielectric response depended only on the frequency of the applied field and had no dependence on its wave vector. This actually means that the response is valid only in the limit as the wave vector tends to zero. Although this limit might be appropriate when the system interacts with light, this is certainly not true when the applied field is the field carried by a moving electron, as in the case of EELS. One would expect that an effective dielectric function that could describe properly the energy-loss process should be nonlocal, that is, should depend on the frequency and the wave vector of the applied field. This approach was taken by Barrera and Fuchs, 5 who find a nonlocal effective dielectric response that could be used to calculate the energy-loss spectra of fast electrons passing through a system of random spherical inclusions contained in a matrix. In their approach, it was assumed that both the spheres and the matrix were described by local dielectric responses but the interaction among the polarized spheres was taken to all multipolar orders within the mean-field approximation. The calculated spectra using this theory showed well-defined peaks coming from the excitation of the bulk plasmons of the inclusions and the matrix, as well as the ones coming from the excitation of interfacial modes, that is, modes in which the induced charge is located at the interface of the spheres and the matrix. These calculated spectra also agreed with the experimental spectra of Walsh. Further theoretical developments 6 also showed the merits and limitations of an ad hoc phenomenological theory 7 devised to explain the experimental results. These developments have also shown the possibility of defining an effective local dielectric response that could describe the energy-loss process. There is also interest in the calculation of energy-loss spectra for an experimental setup in which the electron trav

Optical spectroscopy study of the phase of the reflection coefficient of a single quantum well in the exciton resonance region

Using reflectivity and thermally detected optical absorption spectra of a (In,Ga)As/GaAs single quantum well (QW) sample we have restored the complex amplitude reflection coefficient of the QW in the vicinity of the exciton resonance region. Our method has allowed experimental determination of the phase of the reflection coefficient of a QW. Knowing this phase we were able to distinguish between inhomogeneous and homogeneous contributions to the exciton broadening. A model based on the nonlocal dielectric response theory and assuming the in-plane component of the wave vector of light to be conserved has provided an excellent agreement with the data. The time-resolved reflection spectra of a single QW have been obtained by the numerical Fourier transform of the complex reflection coefficient of the QW. They have shown pronounced oscillations caused by an inhomogeneous broadening of the single exciton resonance.

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.

Inhomogeneous structure of the nonlocal dynamic dielectric response of a quantum-well bound state and a three-dimensional band of extended states

An explicit position-space inversion of the highly inhomogeneous dielectric function of a planar quantum well with a bound state embedded in a bulk medium having a three-dimensional (3D) band of extended states is carried out here in closed form. The resulting nonlocal dynamic inverse dielectric function ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ given in position representation for the z direction across the well depends upon lateral wave vector $\overline{q}$ and frequency $\ensuremath{\omega}$ as well as on positional variables ${z,z}^{\ensuremath{'}}.$ ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ is exact within the framework of the random-phase approximation with the assumption that the 3D band of extended states is approximately translationally invariant in the z direction. Spatial inhomogeneity arises from the lack of translational invariance in the z direction due to the presence of the planar quantum well. The frequency poles of ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ obtained here represent the coupling of nonlocal bulk plasmons with 2D intrasubband plasmons of the quantum well, and the residues at these poles provide the oscillator strengths of such coupled collective modes. The dispersion relation of the coupled modes is examined using the hydrodynamic model of 3D plasma nonlocality.

Dynamic dielectric response of an asymmetric double quantum well near the bounding surface of a semi-infinite dynamic plasmalike host medium

We have examined the dynamic, nonlocal dielectric response function of a pair of asymmetric quantum wells embedded in a semi-infinite dynamic (local) host plasmalike medium, near its bounding surface, by carrying out a closed form inversion of the dielectric function of this system explicitly. The resulting random-phase-approximation (RPA) inverse dielectric function ${K(z,z}^{\ensuremath{'}};\mathbf{q},\ensuremath{\omega}),$ which depends on lateral wave vector q and frequency \ensuremath{\omega}, is obtained analytically in position representation with ${z,z}^{\ensuremath{'}}$ describing distances into the medium from the bounding surface. In this, we neglect intersubband transitions in the two quantum wells (assumed to be thin) and ignore tunneling effects. The frequency poles of ${K(z,z}^{\ensuremath{'}};\mathbf{q},\ensuremath{\omega}),$ describe the collective modes resulting from the coupling of the double quantum well quasi-two-dimensional intrasubband plasmons with the bulk and surface plasmons of the host medium, and the residues at these poles provide the oscillator strengths of such coupled collective modes.

Nonlocal nonlinear static dielectric response of polar liquids

Abstract A linear, phenomenological theory of the nonlocal dielectric response is extended to the non-linear case. For small external electric fields, we give solutions within a perturbation approach. Results, obtained by molecular dynamics computer simulations for the non-linear response of water are in very good agreement with the theory predictions. The results are applied to the calculation of the electrostatic potential of ions in solution. For the electric field strengths, for which the perturbation theory is still applicable, there are only minor differences with respect to the linear case. A fitting procedure to the simulation data, which covers a wider range of electric fields shows, however, that at larger fields the non-linear effects may change the results considerably, relative to those obtained on the basis of the linear response approximation. We discuss a generalization of the nonlocal electrostatic approach to the calculation of solvation energies, which takes into account non-linear effects.

Excitons in the preionization electric field of a Schottky barrier

The low-temperature (T=80 K) exciton reflectance spectra of CdS crystals in the electric field of a Schottky barrier are investigated. An anomalous Stark shift of a hydrogenic exciton state is detected in the preionization limit. An analysis of the spectra within the theory of a nonlocal dielectric response in a spatially inhomogeneous medium reveals the character of the subbarrier electric field distribution.

The surface plasmon enhancement effect on adsorbed molecules at elevated temperatures

The surface plasmon enhancement effect on adsorbed molecules at elevated substrate temperatures is studied theoretically using surface enhanced Raman scattering (SERS) as an example. The surface structure is idealized to be a monodisperse spherical particle with its nonlocal dielectric response accounted for. The temperature effects are modeled using a temperature-dependent collision frequency in the Drude model. Numerical results show that only a small decrease in the SERS enhancement ratio occurs for temperatures up to the melting point of the substrate, even for scattering close to the surface plasmon resonance frequency of the metal. More definitive results are subjected to more realistic modeling as well as systematic experimental studies. The implication of this result to other surface photochemical processes is discussed.

Two dimensional exciton polaritons in microcavities with embedded quantum wires

Optical anisotropy of the periodical array of quantum wires embedded in a semiconductor microcavity is shown to result in polarization-dependent vacuum-field Rabi-splitting and a triple-anticrossing shape of the exciton–polariton dispersion curves. Both effects originate from the resonant diffraction of light at the grating of quantum wires. The calculation has been done within the nonlocal dielectric response theory and using the 4×4 transfer matrix technique.