Effective Complex Permittivity Research Articles

A high Q factor sensor to measure the complex permittivity and effective permittivity based on a band stop frequency-selective surface

In this paper, a metamaterial sensor is proposed based on a band stop frequency-selective surface (FSS) with high Q factor of 421.9 at 8.032 GHz. The sensor consists of a square loop FSS and a F4B dielectric substrate. This is the first sensor based on a band stop FSS sensing the effective permittivity of 3D printed hollow structures. The equivalent circuit method is used to analyze the characteristics of the sensor, and the results agree well. Two materials under test and four different hole radii of 3D printed hollow structures are used to verify the sensing function. At the same time, the effective permittivity of the 3D printed hollow structure is analyzed, and the correctness of the effectiveness is verified by simulation inversion and Maxwell-Garnett formula. The sensor has the advantages of high Q factor, wide incidence angle and polarization angle insensitivity, which can provide some guidance in metamaterials sensing.

Tight bounds correlating peak absorption with Q-factor in composites and metallic clusters of particles

Resonances are fundamentally important in the field of nano-photonics and optics. Thus, it is of great interest to know what are the limits to which they can be tuned. The bandwidth of the resonances in materials is an important feature, which is commonly characterized by using the Q-factor. We present tight bounds correlating the peak absorption with the Q-factor of two-phase quasi-static metamaterials and plasmonic resonators evaluated at a given peak frequency by introducing an alternative definition for the Q-factor in terms of the complex effective permittivity of the composite material. This composite may consist of well-separated clusters of plasmonic particles, and, thus, we obtain bounds on the response of a single cluster as governed by the polarizability. Optimal metamaterial microstructure designs achieving points on the bounds are presented. The most interesting optimal microstructure is a limiting case of doubly coated ellipsoids that attains points on the lower bound. We also obtain bounds on Q for three dimensional, isotropic, and fixed volume fraction two-phase quasi-static metamaterials and particle clusters with an isotropic polarizability. Some almost optimal isotropic microstructure geometries are identified.

The difference in microwave loss mechanism between nano- and micron-sized Ag particles

Separated E/H-field heating in microwave cavities enables us to examine the microwave loss mechanisms. We prepared mixtures of SiO2 particles (having almost no microwave loss) and Ag particles with micrometer- and nano-sizes. Their average impedance and dielectric constants were measured. Electric conductivity exhibited percolation behavior at a specific threshold of Ag fraction. When the mixtures were heated in the separated fields, H-field heating was dominant in all the fraction ranges for the micrometer-sized Ag mixture. However, E-field heating was dominant below the percolation threshold for the nano-sized Ag mixture, and above the threshold, the H-field became dominant. This change in heating rates indicates the change in the energy loss mechanism. According to the size dependence of the induction current loss in a metallic sphere, the loss becomes less effective below the size of skin depth, namely, in the nano-size region. The permittivity of nano-sized Ag particles was estimated by an approximated Lindhard’s equation, which was input into the Maxwell–Garnett mixing model for predicting the effective complex permittivity of the mixture. It was possible to interpret the measured permittivity dependence on the Ag fraction.

링 공진기의 체배종속적 전류분포 해석을 통한 Molding Compound의 광대역 유전율 측정 방법 연구

In this study, we propose an algorithm that complements the frequency dependence of the relative permittivity conversion equation applied for the measurement of relative permittivity through a ring resonator. The broadband electrical characteristics of an epoxy molding compound (EMC) used in the fan-out wafer-level packaging (FOWLP) process were measured using our algorithm. By proposing a formula for calculating the permittivity that reflects the current distribution at the multiplied frequency of the microstrip ring resonator, the effective range of the permittivity of the sample was extended to the multiplied frequency region. Thus, a more sophisticated and effective complex permittivity was calculated over a wide band. The relative permittivity of the EMC measured by the proposed technique was 3.836 and the dielectric loss tangent was 0.022. This technique improved the relative permittivity measurement error rate by 3.95 % and the measurement error rate of the dielectric loss tangent by 8.4 %p compared to the conventional method.

Effective Complex Permittivity of Random Composite Media: PVDF/(Na<sub>1/2</sub>Bi<sub>1/2</sub>)TiO<sub>3</sub>

The present study discusses the fabrication of non-lead ceramic/polymer composites employing (Na1/2Bi1/2)TiO3 (NBT) ceramic powder as a filler and poly(vinylidene fluoride); PVDF as a polymer matrix. The NBT (volume fraction, ϕ = 1) ceramics were synthesized using the conventional mixed-oxide method followed by the high-energy ball milling method whereas (1-ϕ)PVDF/ϕ(Na1/2Bi1/2)TiO3; 0 ≤ ϕ ≤ 0.3 composites were prepared from a melt-mixing process. It was observed that the real and imaginary parts of dielectric permittivity, ac conductivity, and longitudinal piezoelectric charge coefficient increase with the increase in NBT-content. Different dielectric mixing models were presented to determine the effective complex permittivity of the composites. Five dielectric mixture equations have been chosen to test the acceptability of experimental data. It was revealed that theoretical models as given by Bruggman, Rother-Lichtenecker, and modified Rother-Lichtenecker show good agreement with the experimental results of filler-concentration dependent alteration of effective relative permittivity and loss factor of the PVDF/NBT composite. A mathematical model of first-order exponential growth has also been proposed, which fitted excellently the experimental data (r2 > 0.998).

Thermoplasmonics Decontamination of Respirators Face Masks Using Silver Nanoparticles: A New Weapon in the Fight Against COVID-19 Pandemic.

The current COVID-19 pandemic has resulted in an urgent need for methods to decontaminate respirators masks for reuse while keeping them intact and functional. The severe shortage of professional masks such as N95 and FFP2 has necessitated their reuse over long periods. A very promising method is the pasteurization of these masks by thermoplasmonic heat generated by plasmonics nanoparticles when they are irradiated by light. Under illumination at its plasmonic resonance, a metal nanoparticle features enhanced light absorption, turning it into an ideal nano-source of heat, remotely controllable using light. In this work, we propose a numerical study based on the finite element method (FEM) of the thermoplasmonic properties of silver nanoparticles (AgNPs) decorating polypropylene (PP) fibers which is a basic material for the manufacture of these masks. The surface plasmon resonance (SPR) of these nanostructures was investigated through the computation of the complex effective dielectric permittivity and the absorption cross section in the near UV–visible (NUV-Vis) range. First, the SPR characteristics of AgNPs for different morphologies are determined from the absorption spectra, including the SPR-peak position λmax and the electric field enhancement. Second, we determine the power absorbed by an individual AgNP of different morphologies. From this, we calculate the internal temperature increase of the particle at the plasmonic resonance. The last step is devoted to the determination of the temperature profile in the surrounding medium in order to better understand and design the plasmon-assisted heating processes at the nanometric scale.

The influence of ambient temperature and X-band frequency on EMI shielding performance of graphene/silica nanocomposites

The electromagnetic interference (EMI) shielding devices fabricated by graphene-based nanocomposites are constantly exposed to high temperature and X-band frequency during service, but at present no theory can account for such environmental effects. In this work, a micromechanics-based theory is developed to address the influence of temperature and X-band frequency on EMI shielding of graphene/silica nanocomposites. First, the temperature-dependent electromagnetic constitutive relations are established for both graphene and silica, and then the temperature-dependent electromagnetic interface effects, including electron tunneling and hopping for the conductivity and dielectric polarization and relaxation for the permittivity, are introduced. With these constituent and interface properties, the effective complex permittivity and permeability of the nanocomposite are evaluated through the effective-medium approximation. The EMI shielding effectiveness (SE) in the X-band range is calculated from Maxwell's equations under the near-field wave source. The predicted complex permittivity and EMI SE are shown to agree with the experiments of rGO/silica nanocomposites over 320–480 K and 8–12 GHz. The X-band EMI SE enhances with the increase of temperature due to the increase of reflection loss, and the temperature influence increases with the sample thickness. Several other novel attributes are also discovered.

Integral effective medium approach for a metamaterial with radially-inhomogeneous spherical inclusions

In this study, a novel integral effective medium approach (IEMA) to obtain the complex effective permittivity and permeability tensors of 3-D metal-dielectric composite is developed. An infinite isotropic homogenous dielectric medium with periodically imbedded spherical inclusions with spherical inhomogeneity is considered here as an artificial dielectric in subwavelength. Within full-scattering theory, it is shown that such composite belongs to a general class of metamaterials with spherical inclusions.The obtained expressions for the elements of the effective tensors are valid in the entire subwavelength range. In order to test the proposed IEMA, the problem for metallic spherical particles coated by a layer of dielectric is solved analytically in greater detail by using the approach proposed earlier by the first author of the study.We were able to show that a metal-dielectric composite/metamaterial with spherical inhomogeneous inclusions can be considered as a quasi-periodic artificial crystal with a tunable band gap in the subwavelength range. In certain sub-ranges in subwavelength, such crystals can exhibit the properties of homogeneous ferrite material.

Graphene Based Wideband Electromagnetic Absorbing Textiles at Microwave Bands

The design and realization of graphene based wideband electromagnetic (EM) absorbing textiles are becoming of primary interest. Hence, the development of new conductive coatings to be cast onto commercial textiles is crucial. In this article, we propose new graphene based absorbing textiles that conjugate outstanding EM absorbing properties at radiofrequency with low-weight, flexibility, cost-effectiveness, and washability. With this purpose, an innovative production process of polyvinylidene fluoride (PVDF) coatings filled with graphene nanoplatelets (GNPs) is developed for the production of radar-absorbing coated textiles, which are fully characterized in terms of morphological, electrical, and EM absorbing properties. In particular, the complex dielectric permittivity of the coated textiles including different amounts of GNPs is assessed through the measurement of the complex permittivity of a benchmark sample, the consequent estimation of the average GNP size and the prediction by simulations of the effective complex permittivity of graphene based coatings loaded with different GNP amounts. Such predicted data are crucial to design radar absorbing textiles with minimum bandwidths at −10 dB of 5 GHz and reflection coefficients below −5 dB over all the frequency range from 8 up to 18 GHz. These textiles are then produced and characterized in terms of reflection coefficient in free space against a plane wave with normal incidence. The obtained results demonstrate the full satisfaction of the design requirements. In fact, the produced samples show a reflection coefficient with a bandwidth at −10 dB up to 77% of the resonant frequency.

Test tube dedicated microwave liquid dielectric sensor for non-contact properties change monitoring and material characterization with tube exchange capability

The paper presents a novel measurement technique for non-contact properties change monitoring and material characterization which is suitable for in-progress monitoring of processes, especially ones using corrosive reagents or reactive materials. The method relies on sensing of dielectric properties of liquids contained inside a test tube at microwave frequencies by a quasi-parallel-plate transmission line type sensor. The theoretical study is validated with experimental data in terms of extracting complex effective permittivity and response reproducibility on an example of various alcohols. This is followed by measurements of ethanol-water and water-sodium persulfate solutions. The determined concentration-normalized differential reflection coefficient transfer curves for a discrete set of frequencies up to 2 GHz indicated sensitivity up to 14 dB/ml and −172 °/ml with a resolution in the range of 6–7 µl for the former solution and up to −17 dB/g and −31 °/g. The obtained results prove the usability of the developed method.

Study of the Optical and Thermoplasmonics Properties of Gold Nanoparticle Embedded in Al2O3 Matrix.

In this paper, the optical and thermoplasmonics properties of nanocomposites consisting of spherical gold nanoparticles (AuNPs) integrated in {Al}_{2}{O}_{3} matrix are determined using the Finite Element Method (FEM). Firstly, the refractive index (n), extinction coefficient (kappa ), absorption coefficient {(mu }_{a}), and optical conductivity (sigma ) are calculated from the effective complex permittivity obtained by solving the Laplace’s equation for different size and concentration of nanoparticles. The surface plasmon resonance (SPR) properties of AuNPs are optimized from the peak presented in the absorption coefficient spectrum. The results show that the optical parameters n, kappa , {mu }_{a}, and sigma undergo a strong variation around the wavelength {lambda }_{max} corresponding to the SPR phenomenon. The value of {lambda }_{max} increases from 560 to 600 nm when the radius of the particles varies between r=5 and r=30 nm. The effect of the AuNP concentration on the band gap energy {E}_{g}(eV) of Au-{Al}_{2}{O}_{3} nanocomposites is also studied, a shift from Eg=5.34 to Eg=5.49 eV is observed when the concentration of the AuNPs increases from 0 to 0.82mathrm{%}. The electric field enhancement induced by the AuNPs at plasmonic resonance is also determined depending to the particle size; the results show that the enhancement factor increases from g=4.71 to g=6.95 when the radius of the AuNPs increases from r=5 to 30 nm. The thermal dissipation of the plasmonic energy of spherical of our system dispersed in the {Al}_{2}{O}_{3} matrix is determined considering the Joule effect which occurs by the oscillation of the charges at the plasmonic resonance. The generated thermal power by particles is calculated for different sizes, which allows to calculate the thermal power per gram of particles depending on the intensity of the incident electric field. The results show that the plasmonic thermal power is almost identical for small particles when the radius is less than r=15 nm and increases considerably when the size increases from r=15 to 30 nm. For a fixed size and incident field amplitude, we calculated the temperature change in the nanocomposites Au-{Al}_{2}{O}_{3} depending of time for different particle concentrations; the temperature variation curves obtained are linear as a function of time.

Модели искажений сигналов при распространении в лесных массивах

Models of signal propagation in forests are presented, based on the representation of forests as a continuous quasi-homogeneous medium and characterized by an effective complex permittivity. The values of the effective permittivity are a functional of the total volumetric concentration of the components of vegetation relative to the main medium - the atmosphere, of the frequency of signals, of the electrical and taxometric characteristics of forests. It is shown that when propagating along the lines under consideration, the spectral components of digital signals acquire partial phase and amplitude shifts, which causes distortions of the complex envelopes of signals and energy losses during reception with respect to propagation in free space. Modeling was carried out using models of signal propagation in forests with typical characteristics to estimate the probabilistic characteristics of receiving digital signals with 4-level phase shift keying with frequency band extension. It is shown that for these signals with a frequency band of 10...20 MHz with a center frequency of the P-band with horizontal polarization, the energy loss with respect to propagation in free space with equivalent attenuation exceeds 1.2 dB due to the distortion of the complex envelopes of the signals. A smaller effect on the probabilistic characteristics of receiving signals with vertical polarization is also shown - the energy loss in this case reaches 0.5 dB.

A Microwave Sensor of Moisture Content and Salinity of Soil

A new method dedicated to the measurement of the moisture content and salinity of soil is proposed in this paper. The method takes the advantage of the most accurate permittivity sensor available at microwave frequencies based on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {TE}}_{01\delta }$ </tex-math></inline-formula> mode dielectric resonator providing the effective complex permittivity of the measured mixture. The measurement has been undertaken mostly at 1 GHz due to the fact that conductive losses of liquids are substantially varying with salinity at low microwaves, thus, increasing measurement sensitivity. At first, intrinsic properties of the major components of the soil, such as sand, salt and saline water, are extracted from the effective parameters measured at microwave frequencies and compared with the Maxwell-Garnett mixing rule to extract their intrinsic properties. In case of the soil, the unknown moisture content and salinity are extracted from raw measurement results using an empirical permittivity model of a conductive mixture which, unlike to analytical dielectric mixing rules, accounts for a percolation threshold.

Tunable physical effects in Bi-mica hyperbolic structures

Recent years, the need to create tunable THz devices emerged due to rapid development of THz photonics. As a rule, such devices are based on semiconductors and phase change materials, and the use of hyperbolic media based on these materials is a promising approach to realize terahertz wave near-field control. In this work, the dispersion of complex effective permittivity tensor of a layered structure consisting of 40 nm, 70 nm and 120 nm semimetallic Bi films on a top of 21 μm mica dielectric substrate, calculated on the basis of THz time-domain spectroscopy method, is used to theoretically estimate such effects as Purcell enhancement, Van Hove singularity, and Compton effect. The influence of continuous-wave optical pumping onto the optical properties of Bi-based hyperbolic medium and related effects is also studied in this work. The studied effects may be used in THz radiation enhancement, thermoelectric engineering and thermophotovoltaics, optical and electronic detection, molecular sensing, and even in development of spasers. The obtained results prove the possibility of application of Bi-mica composite in a development of fast-acting terahertz hyperbolic materials which are easy to produce due to their simple structure.

Laboratory study of the electrical properties of Lutetian limestones in the 100 Hz to 10 MHz frequency range

ABSTRACTLutetian limestones have been widely used in historical monuments within the Paris Basin during the course of the medieval and modern periods. Among the physical properties that can be used to assess the evolution of the limestonesin situin the buildings and their present health, the complex effective permittivity in the 10–100 kHz frequency range is easy to measure and reflects the internal structure of the stone along with the dependence on the water content. To improve our knowledge about this property, a laboratory study on four samples collected in the relevant quarries has been undertaken using measurements in the 100 Hz–10 MHz frequency range. Except close to zero water content, the observed results exhibit a quasi‐absence of variation of the real effective permittivity with the water content. The frequency variation fits fairly well with a model taking into account a Jonscher's decrease, a direct current conductivity, a high‐frequency dielectric permittivity and losses, and a relaxation phenomenon. When fitted by a Cole–Cole model, the magnitude of the corresponding relative permittivity change always stays close to 30, but the time constant varies from 1.0 μs to 0.1 μs as the water content increases.

Parameter Optimization of Frequency Selective Surfaces Made of Composite Materials

Debye model is used for approximating the frequency dependent complex effective permittivity of the composite structures in filter and shielding applications at microwave frequencies. In debye model, desired shielding effectiveness (SE) is obtained by determining the Debye parameters using trial and error method. But this may result in wasting time or not converging to an optimum solution. In this work to overcome this problem Debye parameters were optimized by using Differential Evolution (DE) algorithm. A Maxwell Garnett (MG) mixing rule was applied to these optimized parameters to obtain frequency selective surface (FSS) parameters. 12dB shielding threshold was chosen between 0.05 – 5GHz frequency range. In accordance with the obtained parameters of FSS, a structure was designed in CST simulation software and simulations had been conducted to obtain SE results. It was seen that the results obtained from analytical computations agree with those obtained from simulations.

Broadband Applications of a Tunable Nano-Rod Metaferrite

The rigorous analytical model of broadband effective electromagnetic response of the two-component metaferrite is presented in this study in the range up to THz frequencies. The metaferrite is a square array of ferric or ferromagnetic infinitely long cylinders of circular cross section symmetrically imbedded into homogenous isotropic dielectric host medium. It is assumed that the cylinders are fully or partially magnetized by a dc biasing magnetic field directed along the cylinder axes. Expressions of the complex effective permeability and permittivity tensors are obtained in the study. Expressions of the complex effective relative permeability and permittivity transverse to the direction of magnetization are derived and analyzed as functions of the frequency of incident electromagnetic wave and constitutive parameters of the metaferrite.It is shown that tuning a dc biasing magnetic field enables to effectively change the transmittivity and reflectivity of the metaferrites in the considered frequency range. We were also able to show that a layer of the metaferrite can be used for exciting surface plasmons at GHz frequencies. Finally, we have discussed the principal possibility of usage of the considered metaferrite for fabricating the substrates of miniaturized patch antennas with improved performance.

Tight Bounds on the Effective Complex Permittivity of Isotropic Composites and Related Problems

Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the complex plane that are bounded by two circular arcs. An implication of particular significance is a set of limits to the maximum and minimum absorption of an isotropic composite material at a given frequency. Here, after giving a short summary of the underlying theory, we show that the bound corresponding to one of the circular arcs is at least almost optimal by introducing a certain class of hierarchical laminates. In regard to the second arc, we show that a tighter bound can be derived using variational methods. This tighter bound is optimal as it corresponds to assemblages of doubly coated spheres, which can be easily approximated by more realistic microstructures. We briefly discuss the implications for related problems, including bounds on the complex polarizability.

Complex Effective Dielectric Permittivity and Characteristic Impedance of Tunable Coplanar Line

An analysis of complex dielectric permittivity and characteristic impedance of micromechanically tunable coplanar line is presented. The coplanar line parameters tuning is achieved by signal line electrode movement above the substrate or the dielectric plate above the surface of line electrodes. A reconfiguration of electromagnetic field with complex nature occurs as a result of such movement in the line. It is described in terms of effective permittivity and characteristic impedance. We studied an influence of physical and geometrical parameters of the line on characteristics of effective permittivity tuning and change in characteristic impedance and line loss. It is found that proposed method for line tuning parameters allows us to obtain a high sensitivity to movement for effective parameters, wherein the level of losses in the line is not deteriorated, and under certain conditions are reduced. These results make it possible to design high-quality tunable resonant elements and phase shifters based on micromechanically controlled coplanar line.

Computational Study and Experimental Verification of the Effective EM Properties of a Particle-Matrix Composite

We present a simulation of the effective electromagnetic (EM) parameters of a carbonyl iron (CI) powder - polyurethane (PU) composite based on a realistic micrometer-level 3-dimensional model by fractions. CI particles, 10 × 10 × 10, were randomly modeled in a PU matrix, and the optimized meshing condition was adapted to simulation. The calculated effective complex permittivity and permeability were compared with the classical mixing formulas and measurements of prepared CI-PU samples to verify the simulation results. Studies of the local EM field distribution and a parametric analysis of the composite revealed how the randomly distributed particles behaved differently than periodic particles. This study shows the possibility of designing a composite material based on a full-wave simulation.