Bulk Dielectric Function Research Articles

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions.

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

On Damping of Plasmons and Plasmon-Polaritons in Metallic Nanostructures and Its Influence onto Numerical Simulations

AbstractWe show that the damping of plasmons in metallic nanoparticles highly exceeds that caused by scattering of electrons on defects, phonons, and other electrons and on boundaries of particles. The radiation losses in far-field zone due to the Lorentz friction is especially high at nanometre scale of metal confinement (e.g. attains the maximum at ca. 100 nm diameter of particle, Au in vacuum). This causes a different e-m response of such size structures in comparison to conventional solution of Maxwell-Fresnel equations using the bulk dielectric function for metal. The strong discrepancy occurs also if plasmons are coupled in near-field zone to nearby-located absorbing medium, e.g. semiconductor substrate. This coupling cannot be accounted for by classical electrodynamic treatment (e.g. by numerical solution of Maxwell equations by finite element method for differential equation solution) and needs the application of quantum Fermi golden rule to estimate plasmon damping and related modifications of dielectric functions both of metallic nanoparticles and of absorbing medium. Similarly, the perfect cancellation of radiative losses of plasmon-polaritons in metallic nano-chains is beyond classical Maxwell equation modelling, as it reveals the perfect vanishing of Lorentz friction losses in chain segments by radiative contribution from other segments in near-, medium- and far-field zones. This demonstrates that nano-plasmonic effects cannot be reliably numerically modelled using material parameters from conventional packets referred to optical constants measured in bulk.

Optical modeling of single and multilayer two-dimensional materials and heterostructures

Bidimensional materials are ideally viewed as having no thickness, as their name suggests. Their optical response have been previously modelled by a purely bidimensional surface current or by a very thin film with some contradictory results. The advent of multilayer stacks of bidimensional materials and combinations of different materials in vertical van der Waals heterostructures highlights, however, that these materials have a finite thickness. In this article, we propose a new model that reconciles both approaches and we show how volume properties of stacked bidimensional layers can be calculated from the bidimensional response of each individual layer, and conversely. In our approach, each bidimensional layers is surrounded by vacuum and described as a kind of transfer matrix with intrinsic parameters that do not depend on the external medium. This provides a link between continuous thin films and discrete layers. We show how to model heterostructures of bidimensional materials and identify the parameters of the current sheet that represents the bidimensional material in the zero-thickness limit, namely the in-plane surface susceptibility and the out-of-plane displacement susceptibility. We show that our unified model is perfectly compatible with existing ellipsometric data with the same reliability as the existing interface model but with different values of the surface susceptibility or bulk dielectric function. We discuss in detail the origin of the discrepancies and show that our approach allows to determine intrinsic properties of the bidimensional materials with the advantage that multilayer and monolayer systems are described in a same framework.

Bulk contributions to the Casimir interaction of Dirac materials

Exploiting methods of Quantum Field Theory we compute the bulk polarization tensor and bulk dielectric functions for Dirac materials in the presence of a mass gap, chemical potential, and finite temperature. Using these results (and neglecting eventual boundary effects), we study the Casimir interaction of Dirac materials. We describe in detail the characteristic features of the dielectric functions and their influence on the Casimir pressure.

Radiative Contributions Dominate Plasmon Broadening for Post-Transition Metals in the Ultraviolet

We use classical electrodynamics calculations to investigate the plasmonic properties of the post-transition metals Al, Bi, Ga, In, and Sn, which are active in the ultraviolet, focusing in particular on the material- and resonance-dependent origins of plasmon broadening. Analytic Mie theory, the modified-long wavelength approximation, and the quasistatic dipole approximation together show that radiative processes dominate plasmon dephasing and damping in small (5–25 nm radius) Al, Bi, Ga, In, and Sn spheres. For Al, Ga, In, and Sn, the radiative contribution (∼0.5–2 eV) to the plasmon linewidth is more than 100-fold greater than the nonradiative contribution (0.001–0.02 eV) derived from the bulk dielectric function. This is significantly different than what is observed for Ag spheres, where nonradiative contributions (∼0.1 eV) are the primary source of broadening up to a radius of 25 nm. Overall, these data suggest that the plasmonic properties, dephasing, and lifetimes for Al, Ga, In, and Sn—and to a lesser extent Bi—spheres are qualitatively similar. To develop a more general understanding of the relationship between plasmon energy and linewidth, we use a model for ideal free-electron Drude metals. It is seen that the linewidth increases at higher energies even for lossless Drude metals, suggesting that the increased broadening observed in UV-active metals is a generalizable observation. These data have important implications for the use of these metals for ultraviolet plasmonics. The increased importance of radiative damping for post-transition metals could influence the ability to harvest photons, generate hot carriers, and enhance spectroscopy in the ultraviolet while providing new opportunities for manipulating high-energy photons.

A nonlocal electrostatics model for ions in concentrated primitive electrolyte solutions

In this paper, a nonlocal electrostatics model is developed for ions in primitive electrolyte solutions. When a charge renormalization process is applied to the Ornstein-Zernike(OZ) equation of an electrolyte mixture, an exact Debye-Hückel-like equation with the exclude volume effect is derived. Further assuming that linear response approximation applies to the solution, the electric potential ϕ(r) of an ion in the solution is further approximated by an extended Debye-Hückel equation ∇2ϕ(r)=κ2ϕ(r)+∫H(|r−r′|)∇2ϕ(r′)dr′, with H(r)=∑lMle−Λlr4πr the kernel function. The parameters, say κ, {Λl} and {Ml}, are determined in a self-consistent way to reproduce the bulk dielectric response function. The theory can reproduce the well known multi-Yukawa electric potentials in concentrated electrolyte solutions. Analytical expressions for induced charge densities, electric potentials and electrostatic energies are derived for spherical ions. The theory is applied to ions in concentrated electrolyte solutions, where the good agreement with hyper-netted-chain(HNC) theory demonstrates its validity.

Electron spill-out effects in plasmon excitations by fast electrons

A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.

Surface plasmons at the interface of metamaterial and topological insulator

We investigate the propagation of surface plasmon polaritons (SPPs) at the boundary of metamaterial and topological insulators. Instances of Bi2Se3, Bi2Te3 and metamaterial boundaries are investigated. The topological insulators under consideration are three dimensional topological insulators of the second generation. Dispersion relations, absorption characteristics and propagation lengths of SPPs are calculated. The variation of bulk dielectric functions of topological insulators and metamaterial is considered by means of the Drude model and effective medium approximation theory. The key parameters making a dramatic impact on propagation lengths are acknowledged and mechanisms for engineering dispersion properties are suggested.

Collective electronic excitations in Ti and Zr and their dihydrides

Electron excitation spectra in Ti and Zr transition metals are calculated in the framework of time-dependent density functional theory. Several peaks found in the obtained loss functions are interpreted as collective excitations. The energy positions of the dominating bulk plasmons are in close agreement with the energy loss experiments. We investigated how the absorption of hydrogen modifies the dielectric properties of these materials. It is shown that the main plasmon energy blueshifts in a such process, again in agreement with experimental observations. On base of the calculated bulk dielectric functions of all these systems, we performed analysis of the excitation spectra at surfaces and nanoparticles. Several plasmon peaks in these systems with rather short lifetimes are found at reduced energies. It is shown how the nanoparticle excitation spectra are modified in the ultraviolet-frequency range upon hydrogen absorption.

Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness

Surface plasmon polariton (SPP) resonance spectra for noble metals (Au, Ag, and Cu) were comprehensively studied in the Kretschmann attenuated total reflection (ATR) geometry, in the wavelength (λ) range from 300 to 1000 nm with the angle of incidence (θ) ranging from 45 to 60° and the film thickness (d) ranging from 41 to 76 nm. The experimental plasmon resonance spectra were reproduced by a calculation that included the broadening effects as follows: (1) the imaginary part of the bulk dielectric constant, (2) the thickness-dependent radiative coupling of the SPP at the metal–air interface to the prism, (3) the lack of conservation of the wavevector parallel to the interface kx(k||) caused by the surface roughness, (4) scanning λ at a fixed θ (changing both energy and kx at the same time) over the SPP dispersion relation. For Au and Ag, the experimental results were in good agreement with the calculated results using the bulk dielectric constants, showing no film thickness dependence of the plasmon resonance energy. A method to extract the true width of the plasmon resonance from raw ATR spectra is proposed and the results are rigorously compared with those expected from the bulk dielectric function given in the literature. For Au and Ag, the width increases with energy, in agreement with that expected from the relaxation of bulk free electrons including the electron–electron interaction, but there is clear evidence of extra broadening, which is more significant for thinner films, possibly due to relaxation pathways intrinsic to plasmons near the interface. For Cu, the visibility of the plasmon resonance critically depends on the evaporation conditions, and low pressures and fast deposition rates are required. Otherwise, scattering from the surface roughness causes considerable broadening of the plasmon resonance, resulting in an apparently fixed resonance energy without clear incident angle dependence. For Cu, the observed plasmon dispersion agrees well with that expected from the bulk dielectric function even with nominal oxidation of the surface, but the widths at long wavelengths are much larger than those theoretically expected.

A molecular Debye-Hückel theory of solvation in polar fluids: An extension of the Born model.

A dielectric response theory of solvation beyond the conventional Born model for polar fluids is presented. The dielectric response of a polar fluid is described by a Born response mode and a linear combination of Debye-Hückel-like response modes that capture the nonlocal response of polar fluids. The Born mode is characterized by a bulk dielectric constant, while a Debye-Hückel mode is characterized by its corresponding Debye screening length. Both the bulk dielectric constant and the Debye screening lengths are determined from the bulk dielectric function of the polar fluid. The linear combination coefficients of the response modes are evaluated in a self-consistent way and can be used to evaluate the electrostatic contribution to the thermodynamic properties of a polar fluid. Our theory is applied to a dipolar hard sphere fluid as well as interaction site models of polar fluids such as water, where the electrostatic contribution to their thermodynamic properties can be obtained accurately.

Nanoscale Dielectric Function of Fe, Pt, Ti, Ta, Al, and V: Application to Characterization of Al Nanoparticles Synthesized by Fs Laser Ablation

Development and applications of new nanomaterials and nanocomposites that include metal nanoparticles have received much attention in the last years. However, there are relatively few studies concerning basic physical characteristics of the dielectric function at the nanoscale, which is needed for predicting their optical and plasmonic response. The size-dependent complex dielectric function of metal Fe, Pt, Ti, Ta, Al, and V nanoparticles (NPs) is calculated for the first time for an extended wavelength range from UV to FIR, based on experimental bulk complex refractive index measurements in the mentioned range at room temperature. Calculation is based on a “top-down” approach, based on a stepwise modification of the Drude model. Bulk plasma frequency (ω p) and damping constant (γ free) in this model are determined using a method that improves the relative uncertainties in their values and provide an insight about the wavelength range over which the metal may be considered Drude like. Validation of ω p and γ free values is demonstrated by the improved accuracy with which the experimental bulk dielectric function is reproduced. For nanometric and subnanometric scales, dielectric function is made size dependent considering size-corrective terms for free and bound electron contributions to the bulk dielectric function. These results are applied to analyze the synthesis of Al NP suspensions using a 120-fs pulse laser to ablate an Al solid target in n-heptane and water. The presence of Al, Al-Al2O3, and air-Al core-shell structures is also reported for the first time in these type of colloids. Analysis of the structure, configuration, sizing, and relative abundance was carried out using optical extinction spectroscopy (OES). Sizing results are compared with those provided by atomic force microscopy (AFM) studies.

Optical interaction between small plasmonic nanowires: a perspective from induced forces and torques

This paper addresses a new numerical study of the near electromagnetic coupling between two small, metallic nanowires under plane-wave illumination. The forces and torques induced give a different point of view of the interaction. The analysis of these near-field, mechanical observables is based entirely on the plasmon hybridization model, with the help of an adequate correlation with far fields. Although several studies of the opto-mechanical inductions have been done, unexpected features of the movement are obtained. ‘Coordinated’ spin for the wires are found, in addition to binding or repulsion forces between the wires and scattering forces. For heterodimers, also orbital torques are obtained. The binding and rotation of the nanowires as well as orbital torques are strongly dependent on the plasmonic excitations of the system. They identify uniquely the surface plasmons. In particular, dark modes can be optically detected without using evanescent fields. The optical forces and torques are calculated exactly by Maxwell stress tensor. ‘Realistic’ infinite nanowires of silver and gold are simulated by a size correction in bulk dielectric function. Thus, the importance of this correction on the mechanical results is also studied. The results can contribute to the design of devices for real observation/detection of surface plasmons. The spectra of forces, and specially of torques, show more resolved resonances because overlapping effects are not as present as in far-field calculations. The spinning of wires found and the analysis made could open new directions of studies and applications of dimers.

Surface plasmon polaritons in topological insulator nano-films and superlattices.

We investigate the propagation of surface plasmon polaritons (SPPs) in thin films of topological insulators. Cases of single films and multilayered stacks are analyzed. The materials considered are second generation three dimensional topological insulators Bi2Se3, Bi2Te3, and Sb2Te3. Dispersion relations and propagation lengths of SPPs are estimated numerically, taking into account the variation of bulk dielectric functions of topological insulators, as well as substrate, using the Drude-Lorentz model. The key factors affecting propagation length are identified and experimental modifications for tuning the dispersion relations are proposed. The apparent discrepancy between the experimental data and previously considered theory is resolved.

Size-dependent complex dielectric function of Ni, Mo, W, Pb, Zn and Na nanoparticles. Application to sizing

This work determines the size dependent metal nanoparticle (NP) dielectric function from a ‘top-down’ approach using the bulk experimental refractive index as a starting point. Free-electron damping constant () and plasma frequency () parameters in the Drude model are calculated for nickel (Ni), molybdenum (Mo), tungsten (W), lead (Pb), zinc (Zn) and sodium (Na) using a method developed in our group. Determined and parameters allow to develop an expression that improves the precision in reproducing the discrete metal bulk dielectric function in a wide wavelength range (UV-FIR). The bulk dielectric function is modified for describing the nanometric case by adding size corrective terms for free and bound electrons contributions. As an application of this study we characterize Ni spherical NPs synthesized by ultrafast laser ablation of a solid target in water. Using Mie theory together with the size-dependent dielectric function, we theoretically reproduce its experimental extinction spectrum. From this fitting, composition and size distribution of the particles in the colloidal suspension may be derived. Transmission electron microscopy (TEM) results agree with the sizes and structure derived from optical extinction spectroscopy (OES).

Far infrared and Raman response in tetragonal PZT ceramic films

PbZr0.38Ti0.62O3 and PbZr0.36Ti0.64O3 thick films deposited by screen printing on (0001) single crystal sapphire substrates and prepared at two different sintering temperatures, were studied by Fourier-transform infrared reflectivity, time-domain THz transmission spectroscopy and micro-Raman spectroscopy. The dielectric response is discussed using the Lichtenecker model to account for the porosity of the films and to obtain the dense bulk dielectric functions. Results are compared with bulk tetragonal PZT 42/58 ceramics. The dynamic response in the films is dominated by an overdamped lead-based vibration in the THz range, as known in PZT, but its evaluated dielectric contribution is affected by the porosity and roughness of the surface.

Determination of plasma frequency, damping constant, and size distribution from the complex dielectric function of noble metal nanoparticles

This paper develops a novel method for simultaneously determining the plasma frequency ωP and the damping constant γfree in the bulk damped oscillator Drude model, based on experimentally measured real and imaginary parts of the metal refractive index in the IR wavelength range, lifting the usual approximation that restricts frequency values to the UV-deep UV region. Our method was applied to gold, silver, and copper, improving the relative uncertainties in the final values for ωp (0.5%–1.6%) and for γfree (3%–8%), which are smaller than those reported in the literature. These small uncertainties in ωp and γfree determination yield a much better fit of the experimental complex dielectric function. For the case of nanoparticles (Nps), a series expansion of the Drude expression (which includes ωp and γfree determined using our method) enables size-dependent dielectric function to be written as the sum of three terms: the experimental bulk dielectric function plus two size corrective terms, one for free electron, and the other for bound-electron contributions. Finally, size distribution of nanometric and subnanometric gold Nps in colloidal suspension was determined through fitting its experimental optical extinction spectrum using Mie theory based on the previously determined dielectric function. Results are compared with size histogram obtained from Transmission Electron Microscopy (TEM).

Radiative effects in plasmonic aluminum and silver nanospheres and nanorods

We explore localized surface plasmon resonances in small (5–30 nm radius) aluminum and silver nanoparticles using classical electrodynamics simulations, focusing on radiative (far-field scattering) effects and the unique characteristics of aluminum as a plasmonic material. In Al spheres, higher-order plasmon resonances (e.g. quadrupoles) are significant at smaller sizes (>15 nm) than in Ag spheres. Additionally, although the plasmon width is minimized at a radius of about 15 nm for both materials, the Al plasmon linewidth (~1.4 eV) for the dipole mode is much larger than that observed in Ag (~0.3 eV). The radiative contribution to damping dominates over non-radiative effects for small (5–20 nm) Al spheres (>95%) whereas for similar size Ag spheres damping is almost entirely attributed to the bulk dielectric function (non-radiative). For Al nanorods the linewidths can be narrowed by increasing aspect ratio such that for an aspect ratio of 4.5, the overall Al (0.75 eV) linewidth is reasonably close to that of the same size Ag rod (0.35 eV). This narrowing arises from frequency dispersion in the real part of the Al dielectric function, and is associated with a 65% (1.5 to 0.5 eV) decrease in the radiative contribution to the linewidth for Al. Concurrently, an increase in the non-radiative width occurs as the aspect ratio increases and the plasmon tunes to the red. This demonstrates that anisotropy can be used as a parameter for controlling Al plasmon dephasing where the composition of the plasmon linewidth (radiative or non-radiative) can be tailored with aspect ratio. Overall, these data suggest that localized surface plasmon resonance dephasing mechanisms in Al nanostructures are inherently different from those in the noble metals, which could allow for new applications of plasmonic materials, tunable plasmon lifetimes, and new physics to be observed.

Reflectance anisotropy of the anatase Tio2(0 0 1)-(4 × 1) surface

The dielectric functions of bulk anatase TiO2 and its (4 × 1) reconstructed (0 0 1) surface were calculated using a hybrid density functional theory method. The bulk dielectric function is compared to data obtained from synchrotron radiation reflectivity measurements in the energy range 0–20 eV and to dielectric functions from two Bethe–Salpeter calculations. There is agreement between predictions of the two theoretical methods, except at the absorption threshold, where there is some shift of spectral weight to lower energy in the Bethe–Salpeter calculations. All features observed in the dielectric function derived from synchrotron reflectivity data are reproduced in calculations. There are some differences in relative peak intensities for dielectric functions derived from experiment and theory. A dispersionless surface state is found which is localised on the topmost oxygen ion in the reconstructed surface. The reflectance anisotropy spectrum of the TiO2(0 0 1)-(4 × 1) surface shows strong features in the energy range to 12 eV but does not show any features caused by sub-bandgap surface state transitions.

Optical and Structural Properties of Ultra‐thin Gold Films

Realizing laterally continuous ultra‐thin gold films on transparent substrates is a challenge of significant technological importance. In the present work, formation of ultra‐thin gold films on fused silica is studied, demonstrating how suppression of island formation and reduction of plasmonic absorption can be achieved by treating substrates with (3‐mercaptopropyl) trimethoxysilane prior to deposition. Void‐free films with deposition thickness as low as 5.4 nm are realized and remain structurally stable at room temperature. Based on detailed structural analysis of the films by specular and diffuse X‐ray reflectivity measurements, it is shown that optical transmission properties of continuous ultra‐thin films can be accounted for using the bulk dielectric function of gold. However, it is important to take into account the non‐abrupt transition zone between the metal and the surrounding dielectrics, which extends through several lattice constants for the laterally continuous ultra‐thin films (film thickness below 10 nm). This results in a significant reduction of optical transmission, as compared to the case of abrupt interfaces. These findings imply that the atomic‐scale interface structure plays an important role when continuous ultra‐thin films are considered, e.g., as semi‐transparent electrical contacts, since optical transmission deviates significantly from the theoretical predictions for ideal films.