Effective Dielectric Functions Research Articles

Reference-free self-calibrating tip-based scattering-type THz near-field microscopy

In this work, we present a quantitative analysis model based on reference-free self-calibration to analyze scattered fields and approach curves on a dielectric substrate for terahertz scattering-type scanning near-field optical microscopy. The results of our model are compared with experimentally measured data and a fully numerical analysis based on a line dipole image method and a quasi-electrostatic approximation. The model is used to extract the effective radius of the tip and the relative permittivity of the silicon substrate to the near-field scattering signal. The measured approach curves on Au and silicon substrates show good agreement with the calculated approach curves, and the refractive index for silicon is precisely determined to be 3.42. For a tip-based THz scattering-type scanning near-field optical microscope, the proposed analysis model allows for the extraction of the effective probe radius and dielectric functions, thereby enabling conclusive measurements of geometric parameters and optical constants.

Nonreciprocal optical properties of magneto-optical film doped with metal particles based on the effective medium theory

In search of next-generation optical information functional materials, magneto-optical microstructures have attracted great attention since they can break Kirchhoff’s law and produce higher photoelectric conversion efficiency. Theoretical studies using finite-difference time-domain and transfer matrix methods have been performed to investigate the optical properties of magneto-optical microstructures. However, these methods are computationally intensive and require periodic conditions, which may not be satisfied with most fabricated samples. The equivalent medium algorithm is improved to make it suitable for the equivalent of magneto-optical materials. Based on the improved equivalent medium theory (EMT), a magneto-optical InSb film structure doped with Au particles (D-InSb) is designed. The effective dielectric functions of the D-InSb layer for transfer matrix waves are obtained from the Bruggeman approximation. Thin-film optics formulas incorporating the anisotropic wave propagation in uniaxial media are employed to calculate the nonreciprocal absorptance of the D-InSb film. The effect of geometric parameters, such as filling ratio and number of layers, is investigated. In addition to modeling the directional radiative properties at various angles of incidence, the hemispherical properties are also calculated to understand the light absorption. The results of our study can provide methods and ideas for the design of solar cells, infrared absorbers, and optical isolators.

Effective Optical Properties of Laterally Coalescing Monolayer MoS2.

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) exhibit compelling dimension-dependent exciton-dominated optical behavior influenced by thickness and lateral quantum confinement effects. Thickness quantum confinement effects have been observed; however, experimental optical property assessment of nanoscale lateral dimension monolayer TMDCs is lacking. Here, we employ ex situ spectroscopic ellipsometry to evaluate laterally coalescing monolayer metalorganic chemical vapor deposited MoS2. A multisample analysis is used to constrain Bruggeman and Maxwell-Garnett effective medium approximations and the effective dielectric functions are derived for laterally coalesced and uncoalesced MoS2 films (∼10-94% surface coverage for ∼10-140 nm lateral grain sizes). This analysis demonstrates the ability to probe MoS2 optical exciton behavior at growth-relevant grain sizes in relation to chemical vapor nucleation density, ripening, and lateral growth conditions. Our analysis is pertinent toward expected in situ epitaxial 2D TMDC film growth metrology to enable the facile development of monolayer films with targeted process-dependent optical properties.

Influence of the Microstructure and Optical Constants on Plasmonic Properties of Copper Nanolayers.

Copper layers with thicknesses of 12, 25, and 35 nm were thermally evaporated on silicon substrates (Si) with two different deposition rates 0.5 and 5.0 Å/s. The microstructure of produced coatings was studied using atomic force microscopy (AFM) and powder X-ray diffractometer (XRD). Ellipsometric measurements were used to determine the effective dielectric functions <> as well as the quality indicators of the localized surface plasmon (LSP) and the surface plasmon polariton (SPP). The composition and purity of the produced films were analysed using X-ray photoelectron spectroscopy (XPS).

Electrodynamics of conductive oxides: Intensity-dependent anisotropy, reconstruction of the effective dielectric constant, and harmonic generation

We study electromagnetic pulse propagation in an indium tin oxide nanolayer in the linear and nonlinear regimes. We use the constitutive relations to reconstruct the effective dielectric constant of the medium, and show that nonlocal effects induce additional absorption resonances and anisotropic dielectric response: longitudinal and transverse effective dielectric functions are modulated differently along the propagation direction, and display different epsilon-near-zero crossing points with a discrepancy that increases with increasing intensity. We predict that hot carriers induce a dynamic redshift of the plasma frequency and a corresponding translation of the effective nonlinear dispersion curves that can be used to predict and quantify nonlinear refractive index changes as a function of incident laser peak power density. Our results suggest that large, nonlinear refractive index changes can occur without the need for epsilon-near-zero modes to couple with plasmonic resonators. At sufficiently large laser pulse intensities, we predict the onset of optical bistability, while the presence of additional pump absorption resonances that arise from longitudinal oscillations of the free electron gas give way to corresponding resonances in the second and third harmonic spectra. A realistic propagation model is key to unraveling the basic physical mechanisms that play a fundamental role in the dynamics.

Structural and Optoelectronic Properties of the α-, β-, and γ-Glycine Polymorphs and the Glycine Dihydrate Crystal: A DFT Study

Density functional calculations were performed to study the properties of the three main glycine solid-state polymorphs α, β, and γ and the glycine dihydrate (GDH) crystal. Optimized unit cell geometries, Kohn–Sham electron energy bands, electron densities of states, population charges, carrier effective masses, optical absorption, and complex dielectric functions were obtained for each glycine system using a GGA functional plus the TS dispersion correction, leading to lattice parameters very close to the experimental values. The theoretical fundamental gaps of all glycine crystals are indirect and near 5 eV. The carrier effective masses are anisotropic and especially heavy (∼26 free electron masses at most) for holes in the case of the GDH crystal. The optical absorption and the dielectric function are very sensitive to the polarization of light in all glycine-based crystals.

Semiconductor Hyperbolic Metamaterials at the Quantum Limit

We study semiconductor hyperbolic metamaterials (SHMs) at the quantum limit experimentally using spectroscopic ellipsometry as well as theoretically using a new microscopic theory. The theory is a combination of microscopic density matrix approach for the material response and Green’s function approach for the propagating electric field. Our approach predicts absorptivity of the full multilayer system and for the first time allows the prediction of in-plane and out-of-plane dielectric functions for every individual layer constructing the SHM as well as effective dielectric functions that can be used to describe a homogenized SHM.

Morphology and effective dielectric functions of ultra-thin gold films

In the present study, a new method for analyzing the dielectric functions in dependence with the thickness of ultra-thin gold films is proposed. The reliability of the method is carefully verified through the correlation of optical properties and structural morphology of gold films at thicknesses around the percolation threshold (from 2 to 20 nm). The optical characterization of deposited films is performed in visible and NIR regions (300-1500 nm) by a spectroscopic ellipsometry along with transmission spectra measurements at normal incidence. Fitting of the ellipsometric data allows one to calculate the effective complex dielectric function of cluster-like and continuous films of different mass-equivalent thickness. Surface morphology of the films is analysed by scanning electron microscopy.

Engineering Low‐Frequency Dielectric Function with Metamaterial Plasmonic Structures

Metamaterial plasmonic composites offer remarkable flexibility in controlling effective dielectric properties of matter. These composites rely on trapped plasmonic resonances in metallic micro‐ or nano‐structures. Such composites can have very large and/or small effective dielectric functions at various frequencies, depending on the composite design. In the electronics industry, there is a need for so‐called high‐k materials, which have large (and largely real, to minimize losses) low frequency dielectric function. In this Letter, metamaterial plasmonic composites with inductive elements are demonstrated to function as effective high‐k materials, without heavy metal loading, confirming an earlier theoretical study. Moreover, embedding the high‐k structures in dielectric or semiconducting matrices can address the parallel need for low leakage current devices.

Surface roughness effects on aluminium-based ultraviolet plasmonic nanolasers

We systematically investigate the effects of surface roughness on the characteristics of ultraviolet zinc oxide plasmonic nanolasers fabricated on aluminium films with two different degrees of surface roughness. We demonstrate that the effective dielectric functions of aluminium interfaces with distinct roughness can be analysed from reflectivity measurements. By considering the scattering losses, including Rayleigh scattering, electron scattering, and grain boundary scattering, we adopt the modified Drude-Lorentz model to describe the scattering effect caused by surface roughness and obtain the effective dielectric functions of different Al samples. The sample with higher surface roughness induces more electron scattering and light scattering for SPP modes, leading to a higher threshold gain for the plasmonic nanolaser. By considering the pumping efficiency, our theoretical analysis shows that diminishing the detrimental optical losses caused by the roughness of the metallic interface could effectively lower (~33.1%) the pumping threshold of the plasmonic nanolasers, which is consistent with the experimental results.

Broadband dielectric spectroscopy of standard and core-shell BaTiO3-NiO ceramic composites compared to the BaTiO3 ceramics

ABSTRACTUsing spark plasma sintering we have processed and studied two ceramic composites of 70 vol% BaTiO3 (BTO) and 30 vol% NiO with different topologies: standard and core-shell composites. The materials were characterized by X-ray diffraction and scanning electron microscopy and studied by quantitative broadband dielectric spectroscopy up to the infrared range using four different spectroscopic techniques in the 10-450 K temperature range. The spectra, which differed quite appreciably from each other, were fitted with the factorized dielectric function of generalized damped oscillators in the infrared-terahertz range and by a set of Cole-Cole relaxations at lower frequencies below the polar phonon frequency range. All three ferroelectric phase transitions were indicated by the maxima in the temperature dependent low-frequency permittivity, with no temperature shift compared to BTO. Using the dielectric functions of the BTO ceramics and NiO crystal, we modelled the effective dielectric functions of the composite using three models based on the effective medium approximation: Bruggeman, Lichtenecker and generalized brick model (coated spheres). The models were discussed on the basis of the degree of BTO-grain percolation through the composite, which strongly affects the effective BTO soft-mode behaviour. Qualitative agreement between the experimental and modelled effective dielectric functions was obtained, but small discrepancies indicate some interdiffusion between the BTO grains and NiO shells, which also affected the rather complex dielectric dispersion and conductivity spectra below the phonon frequency range.

Self-Consistent Approach to Calculation of the Optical Response and Absorption Profiles of Thin Nanocomposite Films

The absorption profiles for different nanocomposite thin films are calculated in the frame of approach based on a local-field method for calculations of optical properties of nanocomposite thin films having a matrix topology. The electrodynamic interactions between the inclusions as well as inclusions-matrix interactions are explicitly taken into account. It is shown that the absorption spectra are strongly dependent both on inclusions concentration and on materials the nanocomposite is made of. The dependences of the effective dielectric functions of different nanocomposites on type of inclusions, and their volume fraction are analyzed. The optical properties of thin nanocomposite films with different distributions of identical spherical inclusions along the film thickness are studied.

Percolation in the dielectric function of Pb(Zr, Ti)O3 – Pb2Ru2O6.5 ferroelectric – metal composites

A set of composite PbZr0.53Ti0.47O3 − xPb2Ru2O6.5 (PZT 53/47 − xPRO) and pure PbZr0.53Ti0.47O3 (PZT 53/47), PbZr0.38Ti0.62O3 (PZT 38/62) and PbZr0.36Ti0.64O3 (PZT 36/64) thick films (thicknesses 20–30 µm, porosity 25–50%) prepared by screen printing on (0001) single-crystal sapphire substrates, were studied using Fourier-transform infrared (FTIR) reflectivity and time-domain terahertz transmission spectroscopy. The compositions studied with 10, 15, 20 and 25 vol% PRO were around the electrical percolation threshold in the bulk ceramic composites (~17 vol%), known from impedance spectroscopy by Bobnar et al (2008 Appl. Phys. Lett. 92 182911). To obtain the effective dielectric functions of the films, we accounted for their porosity by using the Lichtenecker model. Using the dielectric functions of bulk pure PZT 53/47 ceramics and PRO single crystals from the literature available, effective dielectric functions were compared with those obtained using the generalized effective medium model by McLachlan with percolation threshold and critical percolation exponents, which fit the low-frequency data by Bobnar et al. The effective dynamic response in all the samples was dominated by an overdamped THz conductivity peak (central mode), as in pure PZT. The percolation threshold was not particularly apparent in the polar-phonon frequency range as it characterized the localized response. Unlike the low-frequency permittivity, which diverged at the percolation threshold, the effective microwave–terahertz permittivity increased above it.

Characterisation of coloured TiOx/Ti/glass systems

This paper presents a study of the optical properties, microstructure and chemical composition of titanium oxide layers deposited on Ti film using gas injection magnetron sputtering (GIMS). The samples are examined by means of spectroscopic ellipsometry, atomic force microscopy and X-ray photoelectron spectroscopy. The investigation is complemented by colorimetric measurements. The influence of deposition time on the thickness of dielectric layers has been found. A comprehensive analysis of effective dielectric functions of titanium and titanium oxide films is presented. The thickness of titanium oxide film ranges from 13nm to 54nm and directly determines the colour of a sample from gold to blue, respectively.

Inelastic x-ray scattering from valence electrons near absorption edges of FeTe andTiSe2

We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to low-energy particle-hole excited states of metallic FeTe and semimetallic ${\mathrm{TiSe}}_{2}$ for photon incident energy tuned near the ${L}_{3}$ absorption edge of Fe and Ti, respectively. We show that the cross-section amplitudes are well described within a renormalization-group theory where the effect of the core electrons is captured by effective dielectric functions expressed in terms of the the atomic scattering parameters ${f}_{1}$ of Fe and Ti. This method can be used to extract the dynamical structure factor from experimental RIXS spectra in metallic systems.

Magnetized plasma photonic crystals band gap

In this paper, the effect of the magnetic field on one-dimensional plasma photonic crystal band gaps is studied. The one-dimensional fourfold plasma photonic crystal is applied that contains four periodic layers of different materials, namely plasma1–MgF2–plasma2–glass in one unit cell. Based on the principle of Kronig–Penney's model, dispersion relation for such a structure is obtained. The equations for effective dielectric functions of these two modes are theoretically deduced, and dispersion relations for transverse electric (TE) and transverse magnetic (TM) waves are calculated. At first, the main band gap width increases by applying the exterior magnetic field. Subsequently, the frequency region of this main band gap transfers completely toward higher frequencies. There is a particular upper limit for the magnitude of the magnetic field above which increasing the exterior magnetic field strength doesn't have any significant influence on the dispersion function behavior. (With an increase in incident angle up to θ1= 66°, the width of photonic band gap (PBG) changes for both TM/TE polarization.) With an increase in incident angle up to θ1= 66°, the width of PBG decreases for TM polarization and the width of PBG increases for TE polarization, but it increases with further increasing of the incident angle from θ1= 66° to 89° for both TE- and TM-polarizations. Also, it has been observed that the width of the photonic band gaps changes rapidly by relative difference of the two-plasma frequency. Results show the existence of several photonic band gaps that their frequency and dispersion magnitude can be controlled by the exterior magnetic field, incident angle, and two plasma frequencies. The result of this research would provide theoretical instructions for designing filters, microcavities, fibers, etc.

Resonant wavelength tuning of localized plasmons in silver-aluminum nanoparticles

We have succeeded in tuning the localized surface plasmon resonant wavelength in Ag-Al nanoparticles (NPs) by using the Al content. The plasmon resonant wavelength of the Ag-Al NP ensemble shifts toward a shorter wavelength from 590 to 510 nm (approximately 80 nm) with an increase in the Al content from 0 to 7.16 atomic percent (at.%). A theoretical interpretation and model for the experimental results are presented. The effective dielectric functions are modeled by taking into account the variations in both the bulk plasma frequency and the structural information on the Ag-Al NPs with the Al content.

Anisotropic Bruggeman effective medium approaches for slanted columnar thin films

Two different formalisms for the homogenization of composite materials containing ellipsoidal inclusions based on Bruggeman's original formula for spherical inclusions can be found in the literature. Both approximations determine the effective macroscopic permittivity of such an idealized composite assuming randomly distributed dielectric particles of equal shape and differ only in the definition of the depolarization factors. The two approaches are applied to analyze ellipsometric Mueller matrix spectra acquired in the visible and near-infrared spectral region from metal and semiconductor slanted columnar thin films. Furthermore, the effective dielectric function tensor generated by the two Bruggeman formalisms is compared to effective major axes dielectric functions individually determined with a homogeneous biaxial layer approach. Best-match model parameters of all three model approaches are discussed and compared to estimates from scanning electron microscope images. The structural parameters obtained from all three optical modeling approaches agree well with the electron microscopy technique. A comparative discussion is given for the validity and applicability of the three model approaches for analysis of future devices structures that may require optical readout using generalized ellipsometry methods.

Optical and microstructural characterisation of Au–Sn and Cu–Sn diffusive layers

Phase composition, crystallinity, optical and electrical properties were determined for Au–Sn and Cu–Sn ultra-thin films produced by sequential evaporating and co-depositing of metals on glass plates in a vacuum. Thickness of Sn films grown on top of Au(Cu) nanolayers (dAu(Cu)=20nm) was varied to obtain different atomic concentration ratios of Au(Cu)-rich diffusive samples up to 1:1. The samples were characterised using the XRD, SEM, spectroscopic ellipsometry and transmittance measurements. The XRD patterns indicated creation of AuSn and AuSn2 intermetallic phases at room temperature in both types of Au–Sn samples, formation of Cu6Sn5 compound in bilayer Sn/Cu samples and Cu10Sn3 intermetallic in the co-deposited Sn–Cu film. There was observed a substantial influence of morphology and phase composition on the effective complex dielectric functions and optical conductivity of the multiphase films, determined using the transmittance and variable angle spectroscopic ellipsometry measurements in the photon energy range of 0.6–6.5eV. Adopting the Drude–Lorentz parameterisation approach to optical spectra enabled to extract contributions related to the free-carriers, interband transitions and plasmonic effects. The optical resistivity agreed reasonably with the dc-resistivity results, which changed approximately from 17.5μΩcm to 26μΩcm and from 24μΩcm to 96μΩcm for investigated Au–Sn and Cu–Sn systems, respectively.

Fano interference in supported gold nanosandwiches with weakly coupled nanodisks

We studied the far-field optical response of supported gold-silica-gold nanosandwiches using spectroscopic ellipsometry, reflectance and transmittance measurements. Although transmittance data clearly shows that the gold nanodisks in the sandwich structure interact very weakly, oblique reflectance spectra of s- and p-polarized light show clearly asymmetric line-shapes of the Fano type. However, all experimental results are very well described by modeling the gold nanodisks as oblate spheroids and by employing a 2 × 2 scattering matrix formulation of the Fresnel coefficients provided by an island film theory. In particular, the Fano asymmetry can be explained in terms of interference between the scattered waves from the decoupled nanodisks in the spectral range limited by their respective plasmon resonances. We also show that the reflectance and ellipsometry spectra can be described by a three-layer system with uniaxial effective dielectric functions.