Effective Electromagnetic Properties Research Articles

Ultra-rapid microwave sintering employing thermal instability and resonant absorption

Abstract

Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions.

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

Analytical Formulas for Artificial Dielectrics With Nonaligned Layers

In this paper, we present analytical models to describe artificial dielectric layers (ADLs), when a lateral shift between layers is present. The alternate lateral displacement between layers is an important parameter to engineer the desired effective electromagnetic properties of the equivalent homogeneous material realized with the ADLs. More specifically, the equivalent dielectric constants that can be realized by alternatively shifting the layers are higher compared with the aligned case. Closed-form expressions are derived for the equivalent layer reactance that includes the higher order interaction between shifted layers. The given analytical formulas can be used to derive an equivalent circuit model that describes the scattering parameters of a plane wave impinging on a slab composed by an arbitrary finite number of metal layers. To aid the design of artificial dielectric slabs, the effective permittivity and permeability tensors are also retrieved from the scattering parameters.

Effective electromagnetic properties of microheterogeneous materials with surface phenomena

In this paper, we present an approach to calculate the complex dielectric permittivity of a micro-heterogeneous medium composed of non-conductive solid inclusions embedded into the conductive liquid continuous host. To take into account the surface effects, we approximate the inclusion by a layered ellipsoid consisting of a dielectric core and an infinitesimally thin outer shell corresponding to an electrical double layer (EDL). To predict the effective complex dielectric permittivity of materials with a high concentration of inclusions, we have modified the Effective Field Method (EFM) for the layered ellipsoidal particles with complex electrical properties. We present the results of complex permittivity calculations for the composites with randomly and parallel oriented ellipsoidal inclusions. To analyze the influence of surface polarization, we have accomplished modeling in a wide frequency range for different existing physic-chemical models of double electrical layer. The results obtained show that the tensor of effective complex permittivity of a micro-heterogeneous medium with surface effects has complicate dependences on the component electrical properties, spatial material texture, and the inclusion shape (ellipsoid aspect ratio) and size. The dispersion of dielectric permittivity corresponds to the frequency dependence for individual inclusion of given size, and does not depend on the inclusion concentration.

Ultralight polymer-derived ceramic aerogels with wide bandwidth and effective electromagnetic absorption properties

In this work, ultralight polymer-derived ceramic aerogels (PDCA) were prepared by a facile method of hydrosilylation crosslink and freeze drying. The electromagnetic absorption properties of ultralight PDCA were investigated for the first time. The PDCA pyrolyzed at 1000°C shows a uniform three-dimensional (3D) framework with a low bulk density of ∼0.19g/cm3 and high surface area of 134.48m2/g. The electromagnetic properties of PDCA were characterized by a vector network analyzer. The minimum reflection and absorption bandwidth of PDCA pyrolyzed at 1000°C, 1200°C and 1400°C are −43.37dB @ 7.6GHz, −42.01 dB@12.5GHz, and −31.69 dB@17.3GHz and 3.8GHz, 6.6GHz and 4.2GHz, respectively, at the frequency range of 2–18GHz. The strong electromagnetic absorption and wide bandwidth features of PDCA could be attributed to the multiple reflections of microwaves in the 3D framework, as well as the high dielectric loss and proper conductivity.

Modelling and Simulation of Rectangular Bundle of Single-Walled Carbon Nanotubes for Antenna Applications

This paper aims to present an effective electromagnetic (EM) modelling approach for rectangular bundle of single-walled carbon nanotubes (RB-SWCNTs), based on the electrical conductivity, relative complex permittivity and linear distribution impedance by applying General Ohm’s law for this bundle. The equivalent single conductor material (ESCM) model for personification the RB-SWCNTs is present in this paper. The main target of this modeling approach is to estimate and investigate the EM properties of RB-SWCNTs using common EM engineering tool solver CST (MWS). For this purpose, the RB-SWCNTs and ESCM dipole antennas will be designed and implemented using CST (MWS). The equivalent conductivity model, relative complex permittivity and other parameters of the RB-SWCNTs will be derived in this paper and considered as an equivalent material parameters for the ESCM. This modeling technique is expected to provide new avenues for designing different antenna structures.

Impedance analysis of transmission line cells for EMC applications using Agros2D

When designing a TEM transmission line cell for electromagnetic compatibility susceptibility or immunity tests, its input impedance must be properly defined in order to deliver the maximum power to the device under test. The closed-form solution, relating the cell geometry with the characteristic impedance Zc, is possible only for the simplest “canonical” transmission line transverse cross-sections. The numerical methods must be used for arbitrary geometries instead. In this paper, we propose fast, robust, and accurate approach, based on fully hp-adaptive higher-order finite element electrostatic formulation. The approach is implemented in our in-house software Agros2D. The method applies for the impedance solution of an arbitrary TEM transmission line cell, any TEM transmission line with negligible losses, as well as for analyzing the effective electromagnetic properties of lossless complex stratified media.

Numerical estimation of effective electromagnetic properties for design of particulate composites

Most modern electromagnetic devices consist of dielectric and magnetic particulate composites. Predicting the effective electric permittivity and effective magnetic permeability of the envisioned composite is of great importance in validating the design for such applications. In this work, we propose a numerical method based on Yee's scheme and statistically generated representative volume element to estimate these effective electromagnetic properties for linear isotropic composites made with ellipsoidal particles. By considering particle geometry and composite microstructure precisely, it provides a more accurate tool for their design than available analytical bounds. Several numerical examples of composite microstructures are presented to demonstrate the capability of the proposed method. Comparison with analytical bounds and experimental results from literature is conducted to show validity.

A Layered Vegetation Model for GPR Full-Wave Inversion

The vegetation cover strongly affects microwave remote sensing backscattered signals and makes difficulties in retrieving the surface soil water content (SWC). In this paper, we developed a vegetation cover model for full-wave inversion of ground-penetrating radar (GPR) data assuming multiple layers with effective electrical properties. Measurements were performed in laboratory conditions over spelt wheat grown in a sandy soil. A stepped-frequency continuous-wave (SFCW) GPR system was set up using a vector network analyzer and a horn antenna operating in 1–4 GHz range in far-field conditions with different incidence angles and both VV and HH polarizations. In order to control the sand surface water content, a water table was fixed at 20 cm depth and 6 time-domain reflectometry (TDR) probes were horizontally placed at 2 and 20 cm depth. Measurements were performed and recorded hourly for about 1 month and the canopy height was measured daily. The effective electromagnetic properties of the vegetation layer were modeled using a complex refractive index model (CRIM) combined with a single Debye relaxation model. A scattering loss parameter was included in the electromagnetic full-wave GPR model for the vegetation layer. The proposed method was also applied in a $\sim 7$ ha agricultural field with a vegetation canopy height of $\sim 27$ cm (spring wheat). The laboratory measurements resulted in a strong link between the vegetation scattering losses parameter and canopy height (generally, the biomass structure), which cannot be retrieved directly from the GPR measurements. Applying this vegetation model to the GPR full-wave inversion led to a significant correction on GPR-derived SWC values from the field measurements.

Effective electromagnetic properties of honeycomb substrate coated with dielectric or magnetic layer

Effective electromagnetic properties of aramid honeycomb board coated with a layer of multi-wall carbon nanotube or iron flakes composites were measured with waveguide method from 4 to 12 GHz. It was proved that homogenization theory could predict the effective permittivity or permeability of the honeycomb composites with good accuracy. The coated honeycomb composites of relatively high permittivity and permeability could potentially be used to develop dielectric or magnetic substrate for shielding layer or absorbing structures working at microwave frequencies.

Polarization properties of a one dimensional metamaterial lens

ABSTRACTThe control of microwave (MW) radiation transmission through the polarization state of the incident beam is the basis for many applications in sensors and optics. Altering the polarization state of electromagnetic radiation by transmission through a metamaterial (MTM) lens could lead to novel devices and sensors. The polarization properties of 1D split ring resonator and rod type MTM structures were investigated and compared to a previously reported corresponding 2D MTM lens. Unlike the 2D lens, the 1D MTM did not contribute to a change in polarization state of transmitted MWs. The transmission response, however, was found to be determined by the coupling mechanisms between the MTMs constituent elements and orientation of the incident MW polarization. For the 1D lens, changing incident polarization from alignment parallel to the MTMs rod elements to alignment perpendicular to the rods, at resonance frequency, changes the effective index of refraction from net negative to positive. For a MTM structure, facing perpendicular to the incident radiation, the effective electromagnetic properties change from negative permittivity and positive permeability (for polarization parallel to the rod elements) to positive permittivity and negative permeability (for polarization perpendicular to the rod elements). © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1218–1222, 2014

Electromagnetic absorbing properties of graphene–polymer composite shields

A graphene-based composite, consisting of a thermosetting polymeric matrix filled with multilayer graphene microsheets (MLGs), is developed for application in thin radar absorbing materials. An innovative simulation model is proposed for the calculation of the effective permittivity and electrical conductivity of the composite, and used for the electromagnetic design of thin radar absorbing screens. The model takes into account the effects of the MLG morphology and of the fabrication process on the effective electromagnetic properties of the composite. Experimental tests demonstrate the validity of the proposed approach and the accuracy of the developed simulation models, which allow to understand the interaction mechanism between the incident electromagnetic field radiation and the MLG-based composite. Two dielectric Salisbury screen prototypes with resonant frequency at 12GHz or 12.5GHz and total thickness of 1.8mm and 1.7mm, respectively, are fabricated and tested. The results and technique proposed represent a simple and effective approach to produce thin absorbing screens for application in stealth technology or electromagnetic interference suppression.

Influence of direct bias current on the electromagnetic properties of melt-extracted microwires and their composites

We study the influence of a direct bias current on the magnetoimpedance (MI) in melt-extracted amorphous CoFeSiB microwires and the effective electromagnetic properties of epoxy composites filled with these microwires. Our analysis reveals two remarkable features of the current dependence of MI in the range of gigahertz frequencies: a redshift of the dielectric resonance frequency and a decrease of the peak resonance of the effective permittivity as the bias current increases. Both effects are intrinsically linked to the influence of the polymer matrix on the magnetic structure and properties of the microwires. A discussion of these results is proposed in terms of two competing effects of the bias current, i.e., the induced additional effective field in the plane normal to the wire axis and the stress relief from Joule heating.

Effective Permittivity of Shielding Composite Materials for Microwave Frequencies

Due to mass constraints, composite materials are possible candidates to replace metal alloys for electromagnetic shielding applications. The design of standard metallic shielding enclosures often relies on finite-element calculations. But in the case of composite materials, the strong dependence on the shielding properties to the microstructure makes the finite-element approach almost impossible. Indeed meshing the microstructure would imply a huge number of elements, incompatible with usual computational resources. We propose in this paper to develop homogenization tools to define the effective electromagnetic properties of composite materials at microwave frequencies. The ratio between the characteristic size of the microstructure and the wavelength is shown to be a key parameter in the homogenization process. The effective properties can then be used as an input for electromagnetic compatibility standard tools, designed for homogeneous media.

Numerical computation of effective electromagnetic properties for dielectric honeycombs

The finite element numerical computation and the retrieval technique are adopted to evaluate the effective electromagnetic properties of the regular periodic dielectric honeycomb cores under the periodic boundary conditions. And then we compare the effective permittivities of dielectric honeycomb unit cells with the different configurations and the same dielectric materials. The size effect of dielectric honeycomb unit cells on the effective permittivity is pointed out. To simulate the periodic boundary conditions, the PEC (Perfect Electric Conductor) and PMC (Perfect Magnetic Conductor) are imposed on the unit cells in the different periodic dielectric honeycombs. Moreover, the requirement of effective media theory is satisfied that the unit cell dimension is the factor 6 smaller than the center wavelength at least. So the refractive index and the wave impedance are obtained by the scattering parameter retrieval method. On this basis, the effective permittivity and permeability of periodic electric honeycombs are calculated. Numerical results show that the configuration and size of dielectric honeycomb unit cells have the obvious influences on the effective electromagnetic properties. And the effective electromagnetic properties of the periodic dielectric honeycomb cores have the obvious in-plane size effect. With increasing infinitely the number of unit cells, the effective permittivity of dielectric honeycombs trends to the homogenization value. The research demonstrates that the size effect has the same action on the effective electromagnetic and mechanical properties of periodic honeycomb structures. It provides the analyzing foundation for the multifunctional design and application of honeycomb sandwich structures in the special fields (radomes, stealth structures and so on).

From Maxwell Garnett to Debye Model for Electromagnetic Simulation of Composite Dielectrics—Part II: Random Cylindrical Inclusions

A mixing rule in the theory of composites is intended to describe an inhomogeneous composite medium containing inclusions of one or several types in a host matrix as an equivalent homogeneous medium. The Maxwell Garnett mixing rule is widely used to describe effective electromagnetic properties (permittivity and permeability) of composites, in particular, biphasic materials, containing inclusions of canonical shapes (spherical, cylindrical, or ellipsoidal). This paper presents a procedure for deriving an equivalent Debye model that approximates the geometry-based Maxwell Garnett model for randomly distributed cylindrical inclusions. The derived Debye model makes the equivalent dielectric material suitable for any time-domain electromagnetic simulations.

Toy model to describe the effect of positional blocklike disorder in metamaterials composites

We study theoretically the effect of a new type of blocklike positional disorder on the effective electromagnetic properties of one-dimensional chains of resonant, high-permittivity dielectric particles, where particles are arranged into perfectly well-ordered blocks whose relative position is a random variable. This creates a finite order correlation length that mimics the situation encountered in metamaterials fabricated through self-assembled techniques, whose structures often display short-range order between near neighbors but long-range disorder, due to stacking defects. Using a spectral theory approach combined with a principal component statistical analysis, we study, in the long-wavelength regime, the evolution of the electromagnetic response when the composite filling fraction and the block size are changed. Modifications in key features of the resonant response (amplitude, width, etc.) are investigated, showing a regime transition for a filling fraction around 50%.

Magnetic properties of Sn–Mg substituted strontium hexaferrite nanoparticles synthesized via coprecipitation method

Nanoparticles of Sn–Mg substituted strontium hexaferrite with the composition of SrFe 12− x (Sn 0.5 Mg 0.5) x O 19 ( x = 0.0–1.0) were synthesized by chemical coprecipitation method. Deionized water/ethanol (50/50) was used as the solvent. The single phase strontium hexaferrites were obtained at pH 13 and Fe 3+/Sr 2+ molar ratio of 9 after calcination at 800 °C. The mean particle size of samples was decreased from 82 to 56 nm with increasing the Sn–Mg content from x = 0.0 to x = 0.8. The effect of Sn–Mg substitution on magnetic properties of hexaferrites was studied using vibrating-sample magnetometer. It was found that increasing the Sn–Mg from x = 0.0 to x = 0.8 reduced the coercivity from 4728.9 to 1455.5 Oe and increased the saturation magnetization from 51.34 to 65.49 emu/g. A vector network analyzer was used to investigate the microwave absorption properties. According to microwave measurements, doped strontium hexaferrite composites had much more effective electromagnetic absorption properties than undoped strontium hexaferrite composite.

Measurements of Planar Metal–Dielectric Structures Using Split-Post Dielectric Resonators

Split-post dielectric resonators were used for the measurement of the complex permittivity and the complex permeability of planar, uniaxialy anisotropic, low- and medium-loss metamaterials at microwave frequencies. Several metamaterials with different metal patterns deposited on dielectric substrates by plasma deposition were investigated, including edge-coupled and broadside-coupled split-rings and circles. It has been shown that, depending on the type of metal pattern and their surface resistance, the metamaterials may exhibit various magnetic and dielectric properties. Several small metamaterial samples were scanned in the cavity electromagnetic field by moving them inside the split-post dielectric resonator. This allowed us to identify loss mechanisms in the samples and to distinguish between their electric and magnetic properties. Our measurements were confirmed by modeling the transmission/reflection characteristics of virtual waveguides containing real metamaterial samples and homogenous samples with the same effective electromagnetic properties as those obtained from the split-post dielectric resonator method using a finite-difference time-domain electromagnetic simulator software package.

Spectral analysis and connectivity of porous microstructures in bone

Cancellous bone is a porous composite of calcified tissue interspersed with soft marrow. Sea ice is also a porous composite, consisting of pure ice with brine, air, and salt inclusions. Interestingly, the microstructures of bone and sea ice exhibit notable similarities. In recent years, we have developed mathematical and experimental techniques for imaging and characterizing the brine microstructure of sea ice, such as its volume fraction and connectivity, as well as a range of theoretical approaches for studying fluid, thermal, and electromagnetic transport in sea ice. Here we explore the application of our sea ice techniques to investigate trabecular bone. For example, percolation theory that quantifies brine connectivity and its thermal evolution can also help assess the impact of osteoporosis on trabecular structure. Central to our approach is the spectral measure of a composite material, which contains detailed information about the mixture geometry, and can be used in powerful integral representations to compute the effective properties. The spectral measure is obtained from the eigenvalues and eigenvectors of a self-adjoint operator determined exclusively by the composite microgeometry. Here we compute the spectral measures for discretizations of images of healthy and osteoporotic bone. The measures are used to compute the effective electromagnetic properties of the bone specimens. These data are then inverted to reconstruct the porosity of the original specimens, with excellent agreement.