Maxwell-Garnett Effective Medium Theory Research Articles

Effective Dielectric Constant of Plasmonic Nanofluid Containing Core-Shell Nanoparticles

This paper focuses on the effective dielectric constant of water-based plasmonic nanofluid containing SiO2/Ag core/shell nanoparticles (NPs). Two effective models, based on S-parameter retrieval method and Maxwell-Garnett effective medium theory, are employed. The effective dielectric constants predicted by the two effective models are compared and the applicability is evaluated by comparing the reflectance and absorptance. Three influence factors, including volume fraction, core-shell ratio, and size of NPs, are considered. Results show both of the two effective models can predict reliable effective dielectric constants when the volume fraction, size, and core-shell ratio of nanoparticles are 5%, 25 nm, and 4:1 respectively. Only small deviations appear in the resonant region under this condition. With the increase of volume fraction, shell proportion, or size, deviations in the resonant region become larger for both of the two effective models. Therefore, the predicted effective dielectric constants are not suitable for the prediction of optical properties, because the resonant region is the key region of the solar conversion for plasmonic nanofluids. Hence, the parameters of NPs need to be changed to make the effective models applicable. Moreover, the effective model based on S-parameter retrieval can predict more reliable dielectric constant than the effective model based on Maxwell-Garnett theory.

Size and Concentration Effects on Surface Plasmon Resonance and Maxwell-Garnett Absorption in RF-Magnetron Sputtered Au/Al2O3 Nanocomposite Films

Au/Al 2 O 3 nanocomposite films, studied in this work, were prepared by RF-magnetron sputtering technique on glass substrate at room temperature under two different argon pressures, and subsequent heat treatment. Formation of gold nanoparticles was confirmed by X-ray diffraction patterns and UV-visible absorption spectroscopy. Au fill fraction f, changed from f=10.78% to f=25.45%, when argon pressure increased from 2x10 -3 mbar to 10x10 -3 mbar. For the as-deposited samples, reduction in volume fraction of gold particles causes a decrease in particle size, a lattice expansion and a blue-shift of the SPR peak position. An opposite trend is observed in the lattice parameter with respect to the gold volume fraction for the annealed samples. A small change in the sizes is observed and no significant shift of band absorption peak in samples of low Au content. However, at higher Au concentration, an appreciable red shift of the surface plasmon resonance with increasing temperature is observed. Experimental optical absorption spectra of all the samples were theoretically simulated by Maxwell–Garnett effective medium theory.

Terahertz Dispersion Characteristics of Super-aligned Multi-walled Carbon Nanotubes and Enhanced Transmission through Subwavelength Apertures

The terahertz (THz) dielectric properties of super-aligned multi-walled carbon nanotube (MWCNT) films were characterized in the frequency range from 0.1 to 2.5 THz with terahertz time-domain spectroscopy. The refractive index, effective permittivity, and conductivity were retrieved from the measured transmission spectra with THz incident wave polarized parallel and perpendicular to the orientation of carbon nanotubes (CNTs), and a high degree of polarization dependence was observed. The Drude-Lorentz model combined with Maxwell-Garnett effective medium theory was employed to explain the experimental results, revealing an obvious metallic behavior of the MWCNT films. Moreover, rectangular aperture arrays were patterned on the super-aligned MWCNT films with laser-machining techniques, and the transmission measurement demonstrated an extraordinarily enhanced transmission characteristic of the samples with incident wave polarized parallel to the orientation of the CNTs. Surface plasmon polaritons were employed to explain the extraordinarily enhanced transmission with high accuracy, and multi-order Fano profile was applied to model the transmission spectra. A high degree of agreement was exhibited among the experimental, numerical, and theoretical results.

A model study of aggregates composed of spherical soot monomers with an acentric carbon shell

Influences of morphology on the optical properties of soot particles have gained increasing attentions. However, studies on the effect of the way primary particles are coated on the optical properties is few. Aimed to understand how the primary particles are coated affect the optical properties of soot particles, the coated soot particle was simulated using the acentric core–shell monomers model (ACM), which was generated by randomly moving the cores of concentric core–shell monomers (CCM) model. Single scattering properties of the CCM model with identical fractal parameters were calculated 50 times at first to evaluate the optical diversities of different realizations of fractal aggregates with identical parameters. The results show that optical diversities of different realizations for fractal aggregates with identical parameters cannot be eliminated by averaging over ten random realizations. To preserve the fractal characteristics, 10 realizations of each model were generated based on the identical 10 parent fractal aggregates, and then the results were averaged over each 10 realizations, respectively. The single scattering properties of all models were calculated using the numerically exact multiple-sphere T-matrix (MSTM) method. It is found that the single scattering properties of randomly coated soot particles calculated using the ACM model are extremely close to those using CCM model and homogeneous aggregate (HA) model using Maxwell–Garnett effective medium theory. Our results are different from previous studies. The reason may be that the differences in previous studies were caused by fractal characteristics but not models. Our findings indicate that how the individual primary particles are coated has little effect on the single scattering properties of soot particles with acentric core–shell monomers. This work provides a suggestion for scattering model simplification and model selection.

Statistical Description of Inhomogeneous Samples by Scanning Microwave Microscopy

A quantitative analysis of the dielectric properties of a multiphase sample using a scanning microwave microscope (SMM) is proposed. The method is demonstrated using inhomogeneous samples composed of a resin containing micrometric inclusions of a known ceramic material. The SMM suitable for this task employs relatively large tips (tens of micrometers in diameter). Additionally, in order to make the instrument more suitable for high-throughput analysis, an original design for rapid tip changes is implemented. Single-point measurements of dielectric constant at random locations on the sample were performed, leading to histograms of dielectric constant values. These are related to the dielectric constants of the two phases using Maxwell–Garnett effective medium theory, taking into account the volume-of-interaction in the sample beneath the tip.

The influence of surfaces on the transient terahertz conductivity and electron mobility of GaAs nanowires

Bare unpassivated GaAs nanowires feature relatively high electron mobilities (400–2100 cm2 V−1 s−1) and ultrashort charge carrier lifetimes (1–5 ps) at room temperature. These two properties are highly desirable for high speed optoelectronic devices, including photoreceivers, modulators and switches operating at microwave and terahertz frequencies. When engineering these GaAs nanowire-based devices, it is important to have a quantitative understanding of how the charge carrier mobility and lifetime can be tuned. Here we use optical-pump–terahertz-probe spectroscopy to quantify how mobility and lifetime depend on the nanowire surfaces and on carrier density in unpassivated GaAs nanowires. We also present two alternative frameworks for the analysis of nanowire photoconductivity: one based on plasmon resonance and the other based on Maxwell–Garnett effective medium theory with the nanowires modelled as prolate ellipsoids. We find the electron mobility decreases significantly with decreasing nanowire diameter, as charge carriers experience increased scattering at nanowire surfaces. Reducing the diameter from 50 nm to 30 nm degrades the electron mobility by up to 47%. Photoconductivity dynamics were dominated by trapping at saturable states existing at the nanowire surface, and the trapping rate was highest for the nanowires of narrowest diameter. The maximum surface recombination velocity, which occurs in the limit of all traps being empty, was calculated as 1.3 × 106 cm s−1. We note that when selecting the optimum nanowire diameter for an ultrafast device, there is a trade-off between achieving a short lifetime and a high carrier mobility. To achieve high speed GaAs nanowire devices featuring the highest charge carrier mobilities and shortest lifetimes, we recommend operating the devices at low charge carrier densities.

Diameter-dependent shielding effectiveness and terahertz conductivity of multiwalled carbon nanotubes

In the present contribution we have experimentally demonstrated the diameter dependence of terahertz (THz) shielding and THz conductivity of multiwalled carbon nanotubes (MWNTs) and performed detailed theoretical analysis to extract the mechanism of shielding at different MWNT diameters. Self-standing films of three different types of MWNT having the same average length but different outer tube diameter (namely, MWNT_7, MWNT_25, and MWNT_40 nm) are prepared by the vacuum filtration technique. The shielding effectiveness (SE) of these films in the frequency range of 0.4–2.2 THz is measured at room temperature, and the results are analyzed using a theoretical model. Shielding due to absorption (SEA) turns out to be the dominant shielding mechanism for the MWNT_7 and MWNT_25 nm films, while the contribution of shielding due to reflection (SER) dominates for the MWNT_40 nm films in the smaller frequency region (<0.8 THz). Considering the films as a composite of MWNTs and air gaps, we have modeled the dielectric properties of the films using a combination of Maxwell–Garnett effective medium theory and the Drude–Lorentz model. THz conductivity is found to be increasing with increasing MWNT diameter due to the increasing number of Drude-like free electrons. No systematic dependence of the THz conductivity peak (TCP) frequency has been observed on the diameter of the tubes, which negates the idea of a curvature-induced bandgap as the sole origin of the much debated TCP in carbon nanotubes. Our results reveal intriguing aspects on THz response of MWNT films as a function of MWNT diameter.

The effect of solvent dependent local field factor in the optical properties of CdTe quantum dots

CdTe quantum dots (QDs) are synthesized at room temperature in aqueous solvents of different dielectric constants and characterized using optical spectroscopy. Absorption spectra of the QDs obtained is used to calculate the size dependent dielectric function of the QDs using Kramers–Kronig relation and iterative matrix inversion method. Effect of solvent dielectric constant on optical properties of QDs is studied theoretically using Maxwell–Garnett effective medium theory. Direct correlation between absorption intensity and solvent dielectric constant is explained on the basis of decreasing local field factor of the solvents. Emission rates of QDs is also found to have dependence on the dielectric constant of the solvent. Spontaneous emission rates of QDs in Ionic liquid environment is studied theoretically using Maxwell–Garnett effective medium theory. Our results show that variation in dielectric constant of Ionic liquids have a significant impact on spontaneous emission properties of the QDs.

Plasmonic properties of gold nanoparticles on silicon substrates: Understanding Fano-like spectra observed in reflection

Gold nanoparticles (AuNPs) are known for their localized surface plasmon resonance (LSPR) that can be measured with UV-visible spectroscopy. AuNPs are often deposited on silicon substrates for various applications, and the LSPR is measured in reflection. In this case, optical spectra are measured by surface differential reflectance spectroscopy (SDRS) and the absorbance exhibits a negative peak. This article studies both experimentally and theoretically on the single layers of 16 nm diameter spherical gold nanoparticles (AuNPs) grafted on silicon. The morphology and surface density of AuNPs were investigated by atomic force microscopy (AFM). The plasmon response in transmission on the glass substrate and in reflection on the silicon substrate is described by an analytical model based on the Fresnel equations and the Maxwell-Garnett effective medium theory (FMG). The FMG model shows a strong dependence to the incidence angle of the light. At low incident angles, the peak appears negatively with a shallow intensity, and at angles above 30°, the usual positive shape of the plasmon is retrieved. The relevance of the FMG model is compared to the Mie theory within the dipolar approximation. We conclude that no Fano effect is responsible for this derivative shape. An easy-to-use formula is derived that agrees with our experimental data.

Thermal conductivity enhancement of ethylene glycol and water with graphene nanoplatelets

In the present work, we report the effective thermal conductivity of ethylene glycol and water with graphene nanoplatelets. Sodium deoxycholate, a bile salt was used as the surfactant to prepare stable nanofluid dispersions. Stability tests were performed using UV–vis absorption spectrometry and zeta potential to monitor the stability of the prepared nanofluids as a function of time. Thermal conductivity measurements were carried out using transient hot wire technique. Thermal conductivity of the nanofluids significantly increases with respect to graphene loading. Maximum thermal conductivity enhancements of ∼21% and ∼16% at a loading of 0.5vol% was obtained for the nanofluids with graphene nanoplatelets seeded in ethylene glycol and water respectively. Analysis of experimental results with Maxwell-Garnett type effective medium theory reveal that despite the high thermal conductivity of graphene, interfacial thermal resistance between graphene and the surrounding base fluid limits the thermal conductivity enhancement significantly. The interfacial thermal resistance between graphene sheet and ethylene glycol was found to be 2.2×10−8m2KW−1 while between graphene sheet and water was found to be 1.5×10−8m2KW−1 respectively for the present nanofluids.

Effect of deposition time on surface plasmon resonance and Maxwell-Garnett absorption in RF-magnetron sputtered carbon-nickel films

Abstract In this work, carbon-nickel films were grown during four deposition times (50 s, 90 s, 180 s and 600 s) at room temperature on glass substrates by radio frequency magnetron sputtering. The optical absorption spectra of the films were investigated with a special emphasis on the surface plasmon resonance (SPR) of Ni nanoparticles. The optical absorption peaks caused by the surface plasmon resonance of Ni nanoparticles were observed in the wavelength range of 300 nm to 330 nm. It has been shown that the surface plasmon resonance peaks exhibit a red shift and a blue shift depending on the deposition time. The red and blue shifts of the surface plasmon resonance in the absorption spectra of the films were observed with the increase and decrease of Ni nanoparticle size, respectively. The Ni nanoparticle size, dielectric function of carbon matrix εm and plasma frequency of free electrons ωp for the films deposited at deposition time of 180 s have maximum values of 80 nm, 0.401 and 7.25 × 1015 s–1, respectively. These observations are in a good agreement with the electrical resistivity measurements and Maxwell-Garnett (M-G) effective medium theory (EMT).

Nonlinear thickness and oxidation-dependent transparency and conductance of sputtered titanium suboxide nanofilms

Optically transparent and electrically conductive semiconducting titanium suboxide nanometer thick films, which are technologically important in a wide variety of applications, show a nonlinear dependency of optical and electrical properties on film thickness and oxidation time. The optical, electrical, chemical, and structural properties of the sputter-deposited titanium suboxide nanofilms on fused quartz glass at room temperature are investigated by varying the film thickness, and the additional oxidation is controlled by the duration of air exposure. The optical properties of the nanofilms are simulated by considering them as both a homogeneous film as well as an inhomogeneous film with the combination of the Lorentz Drude model and the Maxwell Garnett effective medium theory (MG-EMT). Their electrical properties are simulated with the MG-EMT. The optical transmittance, electrical conductivity, secondary ion mass spectroscopy, x-ray photoemission spectroscopy analysis, and simulation of titanium suboxide nanofilms indicate that inhomogeneous film growth and oxidation are responsible for the nonlinear dependency. The oxygen atomic ratios to titanium for the as-deposited films depend on the deposition time and vary in 1.60–1.73, while those exposed to air for seven days increase to 1.79–1.99.

Fractal morphology of black carbon aerosol enhances absorption in the thermal infrared wavelengths.

In this Letter, we numerically calculate the mass absorption cross sections (MACs) of black carbon fractal aggregates in the thermal infrared solar spectrum. Compared to equivalent-size spheres, the MAC values of aggregates show a percent enhancement of ≈150 and 400 at small and large length scales, respectively. The absorption properties of aggregates with size parameters >1 surprisingly continued to remain in the Rayleigh optics regime. We explain this phenomenon using the Maxwell-Garnett effective medium theory and the concept of phase shift parameter.

Interband-transition-modified third-order nonlinear optical properties of Al nanoshells in carbon disulfide

Al nanoshell geometry and the defined parameters used for simulations of linear and nonlinear optical properties.

Induced Magnetic Anisotropy in Liquid Crystals Doped with Resonant Semiconductor Nanoparticles

Currently, there are many efforts to improve the electrooptical properties of liquid crystals by means of doping them with different types of nanoparticles. In addition, liquid crystals may be used as active media to dynamically control other interesting phenomena, such as light scattering resonances. In this sense, mixtures of resonant nanoparticles hosted in a liquid crystal could be a potential metamaterial with interesting properties. In this work, the artificial magnetism induced in a mixture of semiconductor nanoparticles surrounded by a liquid crystal is analyzed. Effective magnetic permeability of mixtures has been obtained using the Maxwell-Garnett effective medium theory. Furthermore, permeability variations with nanoparticles size and their concentration in the liquid crystal, as well as the magnetic anisotropy, have been studied.

Linear Optical Properties of Gold Colloid

Gold colloid was prepared by reducing HAuCl 4 ·4H 2 O with Na 3 C 6 H 5 O 7 ·2H 2 O. The morphology, size of gold nanoparticles and the optical property of colloid were characterized by transmission electron microscope and UV-Vis spectrophotometer, respectively. It shows that the gold nanoparticles are in the shape of spheres with diameters less than 8 nm, and the surface plasmon resonance absorption peak is located at about 438 nm. As the volume fraction of gold particles increases, the intensity of absorption peak strengthens. The optical property of gold colloid was analyzed by Maxwell-Garnett (MG) effective medium theory in the company of Drude dispersion model. The results show that the matrix dielectric constant is a main factor, which influences the optical property of gold colloid. DOI: http://dx.doi.org/10.5755/j01.ms.21.4.9558

Study of energy transfer between molecules placed in the vicinity of a bimetal composite nanoparticle

In this study, the problem of energy transfer between two molecules near a bimetallic composite nanoparticle is investigated. The influence of the interaction between metal particles on the intermolecular energy is studied, because when two metal nanoparticles are placed close to each other, their plasmons coupling giving rise to new features. On the other hand, we discuss the transfer of resonance energy between donor and acceptor molecules (a single donor and a single acceptor) in the presence of a nanocomposite containing gold and silver nanoparticles based on the Maxwell-Garnett effective medium theory and within the quasistatic limit. We show that the interaction energy strongly depends on the particle size, the filling factor of metal particles, the intermolecular distance (the distance between the donor and acceptor molecules), and the dielectric constant of host matrix.

Tunable Localized Resonances of Spherical Composite Particles at Optical and Near-Infrared Frequencies

We report on the design of spherical composite particles (SCPs) which consist of a homogeneous distribution of metal nano-particles (Ag) in a dielectric matrix. The effective dielectric function of SCPs is described by Maxwell–Garnett effective medium theory. Within the context of Mie scattering, the extinction efficiency of SCPs in air can be specified which exhibits two different kinds of resonances;localized surface plasmon resonances (LSPRs) and dielectric resonances (DRs). Both kinds of resonances can be tuned through the permittivity of the dielectric matrix, filling fraction of the metal nano-particles, and the radius of SCPs. The special features of the localized resonances of SCPs have the potential to be used in a wide variety of applications.

Optical properties of left-handed metamaterial involving coated nano-spheres

We present theoretical results of a left-handed metamaterial engineered by a combination of coated and solid nano-spheres. The structure is a binary composite of CdS–TiO2 core–shell and Au solid nano-spheres which simultaneously dispersed in the air matrix. The effective medium parameters derived by extended Maxwell-Garnett (EMG) effective medium theory. It is shown the possibility of fine-tuning the metamaterial in order to observe left-handed behavior. The results are supplemented with transmittance curves, calculated by layer-multiple-scattering (LMS) method. The predictions of the EMG theory are in good agreement with those of LMS method; thus the (CdS–TiO2)/Au nano-composite is an appropriate choice as a three-dimensional left-handed metamaterial.

Optical properties of SiC/AZO plasmonic nano composite at infrared frequencies

We report a study of the optical properties of a mixture of spherical inclusions within a host continuum. The structure of the designed SiC/AZO material is a binary composite of two different kinds of nano spheres, one made from a semiconductor material (SiC) and the other from a plasmonic material (AZO). Its electromagnetic response is studied using the extended Maxwell–Garnett effective medium theory and a rigorous method based on layer-multiple-scattering theory. A very nice agreement between both treatments is established, rendering the effective medium approximation a useful guide for the experimentalist in the field.