Effective Dielectric Permeability Research Articles

Система соосных дисковых диэлектрических резонаторов с азимутальными колебаниями

The own q-factor of a disk dielectric resonator (DDR) with azimuthal oscillations is determined by the radiation losses from the disk surface and dissipation in the dielectric. A change of disk parameters reducing the influence of one of these factors invariably causes an increased influence of the other parameter, whereas the own q-factor does not exceed 1/tgδ of the disk material. In a resonant structure made in the form of two coaxially arranged disks, the q-factor may be several times higher than this value. That the effect is in principle possible is obvious: in a multilayer structure with different dissipation in layers, it is possible to localize the electromagnetic field in an area with low dissipation. Preliminary experimental studies have shown that the effect does take place and depends on the choice of the working type of azimuthal oscillations and system parameters. The aim of this study is to justify the choice of the type of azimuthal oscillations and the region of structural parameters with which the highest levels of the own q-factor are obtained. For calculating the characteristics of azimuthal waves of the HE- and EH types producing oscillations in the DDR system, the phenomenological method of effective dielectric permeability was used. A system of distributed coupled planar dielectric waveguides and a dielectric cylinder were considered as the method’s first and second models, respectively. The results from an analysis of dispersion and energy characteristics of the own types of azimuthal resonators have shown that the highest levels of own q-factors are characteristic of an even EH-type and can be several times higher than 1/tgδ.

Spectral Dependence of the Refractive Index of Magneto-Optical Metamaterials

A new approach is proposed for determining the optical properties of metamaterials with a complex unit cell geometry. It is based on the concept of an effective dielectric constant eeff (ω) and magnetic permeability μeff (ω) as a sum of Lorentzian functions, each of which is responsible for a certain dipole or multipole resonance of the structure. It is found that for "fishnet" metamaterials the spectral dependences eeff (ω) and magnetic permeability μeff (ω) are determined by a small number of resonances. This approach is used to calculate the effective dielectric constant and magnetic permeability of metamaterials with ordered and disordered unit cells. The spectra obtained by this analytical model are in good agreement with numerical simulations.

Effective dielectric permeability of island metal films: Light scattering and absorption

It is shown that an island metal film could be characterized by nonlocal effective dielectric permeability described by simple algebraic equations, derived within the frame of this project. Based on this concept, elastic and inelastic light scattering was calculated in the vicinity to the dipole surface plasmon frequency on an isolated particle. In addition, the effective absorption due to the light localization in the island film consisting of nonabsorbing particles was explained.

ANISOTROPIC ZERO INDEX MATERIAL: A METHOD OF REDUCING THE FOOTPRINT OF VIVALDI ANTENNAS IN THE UHF RANGE

In this work, an anisotropic zero index material is designed for use in Vivaldi antennas. The metasurface structures are placed within the aperture of a Vivaldi antenna to improve the directivity and gain of the emitted radiation. The range of operation is in the ultrahigh frequency (UHF) range, between 300 MHz and 3 GHz. Two approaches are presented: a type of resonant metallic metamaterial that belongs to the larger class of anisotropic zero index metamaterials and a non-resonant material. A technique for lowering the dimensions of the resonant metamaterial unit cell is presented and applied. The work presented consists of simulation results obtained with HFSS modelling software from ANSYS. Metamaterials (1) are man-made materials, engineered such that they produce specific, well-defined interactions with the electromagnetic fields. While there exists a certain amount of ambiguity when defining metamaterials, for example when it comes to including photonic crystals in the metamaterials category, the particular class of materials used in this work is represented by a periodic array composed of the so-called meta-atoms. The meta-atoms are within the periodic unit cells of the material and are the substitute for atoms and molecules within natural materials. The physical size of the meta-atoms is much smaller than the wavelength of the electromagnetic wave that excites the material. The general consensus is that the unit cell should be approximately λ/10, where λ is the wavelength of the field. Just like natural materials are characterized by macroscopic material properties, metamaterials are characterized by effective material properties. In electromagnetics, the pertinent material properties are the dielectric permittivity and the magnetic permeability, therefore, when characterizing an electromagnetic metamaterial, one has to derive its effective dielectric permittivity and magnetic permeability. Zero index materials (ZIM) (2) are a class of materials for which one or both of the effective material parameters, dielectric permittivity and magnetic permeability can be zero. In certain applications, for instance antenna research, even though the effects of such ZIM materials are desired, they produce an unwanted impedance mismatch in the system. Another class of materials has evolved in order to address this problem: anisotropic zero index materials (AZIM). In this work, a design of such an AZIM is presented, as well as its application in antenna design. The application is a Vivaldi antenna with a coplanar design. Vivaldi antennas have a number of advantages that make them very attractive for many RF applications: they can be easily fabricated with PCB fabrication methods, and they have a high directivity and hence gain. These characteristics, along with their compact design makes them particularly suitable for antenna arrays (3). This antenna, also called notch antenna, was introduced by Gibson in 1979 (4).

Localization of electromagnetic field on the “Brouwer-island” and liquid metal embrittlement

Liquid metal embrittlement (LME) manifests itself as a sudden destruction of a metal sample if it is covered by a thin liquid film of eutectic mixture of specially selected metals. The proposed theoretical model of this phenomenon is based on an assumption related to the possibility of electromagnetic field localization in folds of interface between the phases or components of eutectic mixture filling cracks in solid metal surface (the typical example is In–Ga eutectic on Al-surface). Based on simultaneous presence of three different components in each space point of eutectic mixture (homogeneous In + Ga melt, solid In, and solid Ga), the system of interface folds could be simulated by the Brouwer surface – well known in topology. This surface separates three different components presented at each of its point. Such fractal surfaces posses by a finite volume. The volume occupied by the surface is defined as a difference between the eutectic mixture volume and the sum of volumes of its components. We investigate localization of external electromagnetic radiation in this system of folds. Due to very large magnitude of effective dielectric permeability of the considered system, at relative small volume change and fractal dimension of interface close to the value 3, the wave length of incident radiation inside the system is considerably decreased and multiscale folds are filled with localized photons. A probability of this process and the life time of the localized photons are calculated. The localized photons play crucial role in destruction of primary cracks in the metal surface. They are capable “to switch of” the Coulomb attraction of charge fluctuations on opposite “banks” of the crack filled with the eutectic. As a result, the crack could break down.

Flexible microwave absorbers based on barium hexaferrite, carbon black, and nitrile rubber for 2–12 GHz applications

Flexile single layer electromagnetic wave absorbers were designed by incorporating appropriate amounts of carbon black in a nitrile butadiene rubber matrix along with an optimized amount of magnetic counterpart, namely, barium hexaferrite for applications in S, C, and X-bands. Effective dielectric permittivity and magnetic permeability were measured using cavity perturbation method in the frequency range of 2–12 GHz. The microwave absorbing characteristics of the composites were studied in the S, C, and X-bands employing a model in which an electromagnetic wave is incident normally on a metal terminated single layer. Reflection loss exceeding −20 dB is obtained for all the samples in a wide frequency range of 2–12 GHz when an appropriate absorber thickness between 5 and 9 mm is chosen. The impact of carbon black is clearly observed in the optimized composites on the mechanical strength, thickness, band width of absorption, dielectric properties, and absorptivity.

Electrodynamic properties of fractal clusters

An influence of interference on a character of light interaction both with individual fractal cluster (FC) consisting of nanoparticles and with agglomerates of such clusters is investigated. Using methods of the multiple scattering theory, effective dielectric permeability of a micron-size FC composed of non-absorbing nanoparticles is calculated. The cluster could be characterized by a set of effective dielectric permeabilities. Their number coincides with the number of particles, where space arrangement in the cluster is correlated. If the fractal dimension is less than some critical value and frequency corresponds to the frequency of the visible spectrum, then the absolute value of effective dielectric permeability becomes very large. This results in strong renormalization (decrease) of the incident radiation wavelength inside the cluster. The renormalized photons are cycled or trapped inside the system of multi-scaled cavities inside the cluster. A lifetime of a photon localized inside an agglomerate of FCs is a macroscopic value allowing to observe the stimulated emission of the localized light. The latter opens up a possibility for creation of lasers without inverse population of energy levels. Moreover, this allows to reconsider problems of optical cloaking of macroscopic objects. One more feature of fractal structures is a possibility of unimpeded propagation of light when any resistance associated with scattering disappears.

Finite Element Modeling of Heat Transfer in a Nanofluid Filled Transformer

In order to investigate the heat transfer characteristics of transformer oil containing nanoparticles, an electric-thermal-fluidic analysis using the FEM is carried out in this paper. The temperature and velocity distribution of oil and density of nanoparticles in a nanofluid filled transformer under natural and forced convections are obtained. The results show that generally the heat transfer efficiency is better under the forced convection. In addition, the distribution of nanoparticles in the oil depends on the temperature and velocity of the oil. This indicates that the local density and electrophoresis of nanoparticles must be considered for nanofluid application in transformers because of their potential influence on the temperature and velocity of the oil. Therefore, improvement of the simulation model taking into account of the local density of nanoparticles using the effective thermal conductivity had been carried out. Furthermore, electrophoretic force term had been implemented in Navier-Stokes equation, whereas the effective dielectric permeability was obtained by a homogenization technique using FEM.

Influence of temperature and fiber structure on the dielectric properties of polypropylene fibrous structures

In this work, dielectric spectroscopy was conducted on five commercial woven polypropylene-based fabrics. Measurements of dielectric loss tangent, the effective relative dielectric permeability and ac electrical conductivity were performed over a wide range of temperature and frequency. The results in temperature range from 250 K to 355 K showed that the samples with lower value of volume fraction whose yarn is made from a short fiber have a lower value of the above mentioned dielectric parameters than the samples with bigger value of volume fraction and filament yarn along the weft and the warp lines. Based on the results gained from the measurements in the vacuum and ambient conditions, it can be concluded that the samples with a lower value of volume fraction, whose yarn is made from a short fiber, showed stability of dielectric properties in the measurement interval. Copyright © 2014 John Wiley & Sons, Ltd.

Computer simulation of dissociative equilibrium in aqueous NaCl electrolyte with account for polarization and ion recharging. Ionization mechanism

The Monte Carlo method in a system with periodic boundary conditions was used within the model with explicit account for many-bod interactions to calculate ion-water correlation functions and the mean force ion-ion potential for extremely dilute aqueous electrolyte. Many-body interactions result in a decrease in the first coordination number of ions by approximately one molecule. The same effect is observed in the case of hydration in water vapors. Partial displacement of molecules from the lower layer into the higher hydrate layers occurs mainly by means of interactions of dipoles induced on molecules. Many-body interactions enhance the stability of unrecombined ion pairs separated by solvent molecules (SSIP states). The depth of the minimum in the dependence of the ion-ion mean force potential with account for many-body interaction forces is several times higher than in primitive interaction models. The value of effective relative dielectric permeability of the solvent at short distances from the ions grows faster than 1/R. Due to solvent polarization, counterions are strongly repelled at distances corresponding to overlapping of their hydrate shells and are weakly attracted at large distances. Stability of ion pair SSIP states in liquid electrolyte is due to rearrangement of the molecular structure of the solvent in the interion space and is an entropy effect. This mechanism differs qualitatively from that observed under hydration in water vapor and the depth of the minimum corresponding to SSIP states is by an order of magnitude lower in liquid electrolyte as compared to that in saturated water vapor.

Electrostatic stratification of the global cloud system by the self-consistent field of the metastable electronion subsystem of the atmosphere

Analysis of frequency distribution of the heights of clouds formation has been conducted by the data of airplane sounding for compatibility to the structure of surface and highaltitude electrostatic field. Coincidence of maximal sites of frequency distribution of cloud heights with zero values of distribution of threedimensional charges of atmosphere has been found. Correspondence does not depend on the type of cloudiness, though cloud distributions by themselves differ essentially for the different types. It has been shown that frequency distribution of the heights of clouds formation is related to gravity polarization of the active atmospheric medium — metastable undercooled coulomb plasma of thermalizing atmospheric electrons. Effective dielectric permeability of such a medium varies within the limits of 104—106 CGSE. Approximate solution of self consistent Poisson equation for medium field of atmospheric electrons corresponding to Landau equation for the firstorder phase transitions has been given. Exact solution has been found for the equation depending on boundary conditions. Parameters of solution, module of elliptic function and effective length of screening have been chosen in accordance with the experiment and reproduce altitude run of potential correctly. Module dependence has a critical character of firstorder phase transitions. The nature of dependence is related to heavy mode of lengmure vibrations of ionicelectronic atmosphere subsystem.

A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials

Some electromagnetic materials exhibit, in a given frequency range, effective dielectric permittivity and/or magnetic permeability which are negative. In the literature, they are called negative index materials, left-handed materials or meta-materials. We propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta-material. The method we investigate can be considered as an alternative method compared to the method presented by the second author and co-workers. In particular, we shall use the abstract framework they developed to prove well-posedness of the exact problem. We recast this problem to fit later discretization by the staggered discontinuous Galerkin method developed by the first author and co-worker, a method which relies on introducing an auxiliary unknown. Convergence of the numerical method is proven, with the help of explicit inf–sup operators, and numerical examples are provided to show the efficiency of the method.

Resonant magnetic response of TiO2 microspheres at terahertz frequencies

Spray-drying technique is used to fabricate spherical microparticles out of dissolved TiO2 nanoparticles. We show both experimentally and through numerical calculations that the microspheres support a Mie resonance, leading to an effective magnetic response. For this purpose, nearly single layers of microspheres were prepared and characterized by time-domain terahertz spectroscopy. We developed an experimental approach allowing simultaneous measurement of complex transmittance and reflectance of a thin layer, which in turn enables evaluation of its effective dielectric permittivity and effective magnetic permeability. Numerical finite-element-method calculations of the electromagnetic response show that the prepared microparticles are suitable for preparing a metamaterial with negative effective magnetic permeability.

Magnetic-type resonance in nonmagnetic line wire excited by surface plasmons in microwave range

A magnetic resonance microwave response has been detected and identified in a structure of parallel nonmagnetic wires or a single line wire perpendicular to the electric field of a plane electromagnetic wave in the case where the wires are arranged near an array (grating) of resonant surface-plasmon-generating elements and oriented along the direction of wave propagation. A giant resonance is observed for a definite (resonance) length of the wire(s) in a certain frequency range corresponding to the existence of surface plasmons (below the resonance frequency of the plasmon-generating array). It is suggested that the magnetic response of the wire(s) is due to the excitation of resonance currents by the magnetic field of surface plasmons. Using the observed phenomena, it is possible to obtain new magnetic metamaterials (in particular, those possessing simultaneously negative effective dielectric permittivity and magnetic permeability) tunable in a broad frequency range.

Metamaterials: Characteristics, Design and Microwave Applications

We present an overview of unique properties of metamaterials, especially negative index materials. These have allowed novel applications, concepts and devices to be developed in the past decade. A review of the progress made in this field is presented with a focus on microwave devices and applications in wireless communications. Since a metamaterial can be regarded as a continuous medium with effective dielectric permittivity and effective magnetic permeability, we present the procedure for the extraction of effective electromagnetic parameters for a guided wave structure with split-ring resonators. As examples, our own designs of bandpass and triple-band filters, which are constructed using metamaterial-inspired resonator elements, are presented and discussed.

Tunable double negative band structure from non-magnetic coated rods

A system of periodic poly-disperse-coated nano-rods is considered. Both the coated nano-rods and the host material are non-magnetic. The exterior nano-coating has a frequency-dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods, while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the subwavelength limit. Tunable pass bands exhibiting negative group velocity are generated and correspond to simultaneously negative effective dielectric permittivity and magnetic permeability. These can be explicitly controlled by adjusting the distance between the rods, the coating thickness and the rod diameters.

Metamaterials and the homogenization of composite materials

Metamaterials and photonic crystals are often distinguished by the requirement that the former have features fine compared with the wavelength, and thus be homogenizable. We discuss the assumption implicit in this: that the metamaterial microstructure have well defined effective dielectric constant and magnetic permeability (concentrating on the former case). We illustrate subtleties in the calculation of effective dielectric constant in the particular case of square prisms composed of dielectric arranged in a square array in a host medium of another dielectric constant, commenting on poles, zeros, essential singularities and branch cuts of the effective dielectric constant function.

고차모드 시간영역 유한차분법을 이용한 원통형 메타물질 Slab의 해석

본 논문에서는 고차모드 시간영역 유한차분법(FDTD)을 이용하여 원통형 메타물질 Slab의 주파수 영역 특성을 정확하게 구하는 방법을 연구하였다. 메타물질의 해석방법에는 분산매질 FDTD방정식이 가장 광범위하게 사용되는데 주파수 분산특성을 갖는 유전율과 투자율 모델을 가정하기 때문에, 주파수 응답특성을 구하기 위해서는 주파수 영역에서 차분방정 식을 전개해야 한다. 본 논문에서는 고차모드 FDTD 방법을 유도하여 기존의 분산매질 FDTD 방법과 비교하여 유전체물질에서는 동일한 결과를 얻을 수 있지만 메타물질 해석에서는 오차가 발생을 한다는 것을 확인하였다. 원통형 메타물질 Slab을 해석하기 위해서 고차모드 FDTD 방법을 이용하면 계산오차를 줄일 수 있고 정확한 주파수 특성을 얻을 수 있다. 본 논문에서 제안한 방법을 사용하면 메타물질을 이용한 다양한 회로구조에 대하여 정 확한 주파수 특성을 얻을 수 있다. In this paper, the higher order FDTD(Finite-Difference Time-Domain) method is used to obtain the frequency response characteristics of the cylindrical metamaterial slab. FDTD method is one of strongest electromagnetic numerical method which is widely used to analyze the metamaterial structure because of its simplicity and the dispersive FDTD equation which has the dispersive effective dielectric constant and permeability are derived to analyze the metamaterials. This derived dispersive FDTD equation has no errors in analyzing the dielectric materials but there are some time and frequency errors in case of analyzing the metamaterials. We used the higher order FDTD method to obtain the accurate frequency response of the metamaterials. Comparisons between the dispersive FDTD method and the higher order FDTD method are performed in this paper also. From the results, we concluded that more accurate frequency response for various metamaterials applications can be obtained using the proposed method in this paper.

Effective permittivity and permeability of coated metal powders at microwave frequency

Abstract Recent developments of the microwave heating of compacted metal powders bring a demand on calculation of corresponding effective optical parameters. Since the existing models cannot be applied to such powders, in this paper new effective dielectric permittivity and magnetic permeability are introduced by means of the combination of Mie theory and Bruggeman's effective medium. It is demonstrated that both an insulating shell and the skin effect should be taken into account. The shell drastically modifies the effective permittivity, while ignoring the skin effect brings to the permittivity an error as large as 30% at 30 GHz for copper powder with grains of 50 μ m radius. The induced currents are shown to affect the magnetic properties of the powders. The strong skin effect substantially reduces the permeability of magnetic grains, and thus the intrinsic permeability measured in experiments can be much less than the real one. The strong dependence of the effective parameters on the microstructure of powders suggests a variety of possible heating scenarios in experiments.

Time harmonic wave diffraction problems in materials with sign-shifting coefficients

Some electromagnetic materials present, in a given frequency range, an effective dielectric permittivity and/or magnetic permeability which are negative. We are interested in the reunion of such a “negative” material and a classical one. More precisely, we consider here a scalar model problem for the simulation of a wave transmission between two such materials. This model is governed by a Helmholtz equation with a weight function in the Δ principal part which takes positive and negative real values. Introducing additional unknowns, we have already proposed in Bonnet-Ben Dhia et al. (2006) [1] some new variational formulations of this problem, which are of Fredholm type provided the absolute value of the contrast of permittivities is large enough, and therefore suitable for a finite element discretization. We prove here that, under similar conditions on the contrast, the natural variational formulation of the problem, although not “coercive plus compact”, is nonetheless suitable for a finite element discretization. This leads to a numerical approach which is straightforward, less costly than the previous ones, and very accurate.