Quasi-static effective permittivity of periodic compositescontaining complex shaped dielectric particles

A methodology is described for computing the quasi-static effective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) lattice of dielectric particles. The particles in this composite material may have complicated shapes. This methodology uses a moment method based technique to determine the electric dipole moments of the particles immersed in a uniform electric field. The effective permittivity is then obtained using an appropriate macroscopic model. With this methodology, the mutual interaction between particles can be accounted for accurately. The computed effective permittivity for round cylinders and spheres suspended in a host are compared with our previous T-matrix method results as well as the Maxwell Garnett (MG) formula predictions. Three additional examples involving square (2-D), rounded square (2-D), and spherical (3-D) dielectric inclusions are also given, illustrating the shape effects on the computation of the quasi-static effective permittivity. While the square- and cubic-shaped particles can possess great mutual interaction, surprisingly their effective permittivity is well predicted for all volume fractions by the simple MG formula in both 2-D and 3-D problems     

A multiple scattering solution for the effective permittivity of asphere mixture

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N² algorithm rather than the normal N³ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible     

Numerical scattering analysis for two-dimensional dense randommedia: characterization of effective permittivity

A new numerical method for determining effective permittivity of dense random media in two dimensions is presented. The core of the method is to compare the average scattered field of a random collection of scatterers confined within an imaginary boundary with the scattered field from a homogeneous dielectric of the same shape as the imaginary boundary. The two-dimensional (2-D) problem is aggressively studied to provide insight into the dependence of the method's convergence on particle size, boundary shape, and boundary dimension. A novel inverse scattering method is introduced based on the method of moments (MoM), which greatly reduces the computation time and increases the flexibility of the procedure to analyze a variety of geometries. Results from this 2-D method may be used directly to compare with theoretical methods for determining effective permittivity such as the Polder-Van Santen (1946) mixing formula or field techniques such as the quasi-crystalline approximation     

The inclusion of fringing capacitance and inductance in FDTD forthe robust accurate treatment of material discontinuities

The analysis of structures, which contain sharp material discontinuities using the finite-difference time domain method (but without resorting to a very fine mesh) although much researched, has not yet been definitively solved. In this paper, the fringing fields associated with the discontinuities are dealt with by adjusting the permittivity and permeability assigned to the field nodes that are immediately adjacent to the discontinuities. This method is shown to be effective for a variety of structures and to be without the problems of violating energy or divergence conservation     

3mm涂层隐身材料的天线温度模型

根据电磁场理论导出了3mm涂层隐身材料的辐射率．在此基础上建立了涂层隐身材料的辐射计天线温度模型．给出了天线温度与涂层材料的厚度、相对介电常数、相对磁导率之间的定量关系．并将数值计算结果与实际测量值进行了比较,其结果的一致性说明了该模型的有效性．     

Effects of particle shape on the effective permittivity ofcomposite materials with measurements for lattices of cubes

The effects of inclusion shape on the quasi-static effective permittivity of a two-phase periodic composite material are discussed in this paper. The lattice is formed from complex-shaped conducting inclusions suspended in a host medium. The effective permittivity is computed using an accurate moment-method-based technique. Numerical results are presented for a variety of particle shapes including circular, square, and "rounded square" cylinders (two dimensional) as well as lattices of spheres and cubes (three dimensional). It was found that among these shapes, lattices of square cylinders and cubes produced nearly the minimal polarization per unit volume possible (a` la Maxwell/Maxwell Garnett). It appears that the strong mutual interaction between edges and corners of these particles is responsible for this effect. That is, it was observed that the mutual interaction between square cylinders and cubes caused a decrease in their dipole moments and, hence, the effective permittivity, which is opposite to the usual expectation from mutual interaction between circular cylinders and spheres. Experimental verification of this effect is provided by quasi-static conductivity measurements     

The far-zone scattering calculation of frequency-dependent materials objects using the TLM method

The transmission-line matrix method is used for the calculation of the far scattered field and radar cross section of frequency dependent materials objects. Three different materials have been considered, namely, Debye, plasma, and Lorentz for which the electric susceptibility is complex. The proposed model is based on the computation of the equivalent currents and on a time domain near-to-far-field transformation technique. To illustrate this study, the far-zone scattering results for different spheres using the three materials indicated above are presented.     

Tailoring double-negative metamaterial responses to achieve anomalous propagation effects along microstrip transmission lines

The design of a double-negative metamaterial loaded microstrip transmission line (DNG MTM-TL) to tailor the propagation characteristics at S- and C-band frequencies is presented. Guided-wave propagation along this DNG MTM-TL was studied numerically. The scattering parameters of the DNG MTM-TL were obtained with Ansoft's High Frequency Structure Simulator. A two-port network realization of the DNG MTM-TL is established. The effective permittivity and permeability for the DNG MTM-TL is extracted using this two-port network representation. It is shown that both a negative permittivity and a negative permeability and, hence, a negative index of refraction exist in the design frequency range. These material parameters are dispersive and conform to a two-time derivative Lorentz material model type of resonance behavior. This form of the index of refraction may be very suitable for applications dealing with phase and dispersion compensation along a microstrip transmission line.     

Experimental characterization of the effective propagation constantof dense random media

A new technique for measuring the effective propagation constant of dense random media is presented. This technique involves two major steps: (1) measurement of the mean bistatic scattered field of a cluster of the random medium confined in a spherical boundary and (2) characterization of the complex permittivity for a homogeneous dielectric sphere having identical radius and bistatic scattered field as those of the spherical cluster of the random medium. Using this measurement technique, not only the effective propagation constant of complex dense random media for which an analytical solution does not exist can be characterized, but it can also be used to establish the validity region of the existing models. The sensitivity analyses of the proposed algorithm show that the imaginary part of the effective propagation constant can be measured very accurately. It is also shown that the effective complex permittivity of media with very low dielectric contrast or volume fractions can be characterized accurately. Measurements of the effective propagation constant of different dense random media comprised of homogeneous spherical particles of different packing densities are reported and compared with the existing analytical models     

Open-Ended Waveguide Measurement and Numerical Simulation of the Reflectivity of Petri Dish Supported Skin Cell Monolayers in the mm-wave Range

Open-ended waveguide reflectometry is a promising tool for permittivity and other material properties calculation at mm-waves (30–300 GHz). Measurement of the reflection coefficient does not require sample manipulation, allowing in vivo and in vitro non destructive studies on cells. Here we used this technique for measuring the power reflection coefficient (reflectivity) of water and Petri dish supported human skin melanoma and keratinocyte cell cultures, in the 53–72 GHz frequency range. The dependence of the reflectivity on polystyrene or glass thickness of the Petri base plate and on the cell layer thickness was analyzed. Permittivity data were then easily retrieved by using a plane wave-dominant mode approach for formulating the reflectivity at the aperture of the flange-mounted open-ended rectangular waveguide probe. Limits and validity of such an approximate approach were analyzed and compared with full-wave near field formulations for which magnitude and phase of the reflection coefficient must be measured and solved using complicated systems of integral equations and extensive numerical calculation. Finally, Petri dish reflectivity measured by the open-ended waveguide method was compared with that numerically simulated under far-field exposure conditions used in a large number of in vitro studies. Such an analysis showed that, under certain conditions, open-ended reflectivity values approach the far field ones.     

Estimation of Incoherent Scattered Field by Multiple Scatterers in Random Media

This paper proposes a method to estimate directly the incoherent scattered intensity and radar cross section (RCS) from the effective permittivity of a random media. The proposed method is derived from the original concept of incoherent scattering. The incoherent scattered field is expressed as a simple formula. Therefore, to reduce computation time, the proposed method can estimate the incoherent scattered intensity and RCS of a random media. To verify the potential of the proposed method for the desired applications, we conducted a Monte‐Carlo analysis using the method of moments; we characterized the accuracy of the proposed method using the normalized mean square error (NMSE). In addition, several medium parameters, such as the density of scatterers and analysis volume, were studied to understand their effect on the scattering characteristics of a random media. The results of the Monte‐Carlo analysis show good agreement with those of the proposed method, and the NMSE values of the proposed method and Monte‐Carlo analysis are relatively small at less than 0.05.     

Electromagnetic logging technique based on borehole radar

An electromagnetic logging technique based on borehole radar is introduced in this paper. The tool consists of one transmitter and two receivers, which can be used to cancel the effect of the antenna characteristics by taking the ratio of two receiver signals. Since receiver signals measured in the time domain can be converted into the frequency domain by Fourier transformation, the amplitude ratio and the phase difference between two receiver signals in a wide-frequency band are obtainable. The response of the tool to different formations is investigated, and the algorithm that converts the amplitude and the phase information to the conductivity and the relative permittivity of the surrounding medium is given by a three-dimensional finite-difference time domain. The effect of the borehole on measurement and the response of the tool to a formation interface are simulated and analyzed numerically. The validity of this technique is confirmed by experiment. This technique can be applied to detect physical properties, including the conductivity and the relative permittivity, of the surrounding medium and the locations of the fractures intersecting the borehole.     

A General Three-Dimensional Tensor FDTD-Formulation for Electrically Inhomogeneous Lossy Media Using the Z-Transform

A general three-dimensional tensor finite-difference time-domain (TFDTD) formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes. The time domain representation of electric losses is achieved using Z-transforms. The regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3-D face-fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the (known) average flux density vector and the (unknown) local electric field vector. For electrically lossy media, this tensor is complex in the frequency domain. However, it can be modified for use with the Z-transform. Only this modified real form is inverted, then transformed from the frequency into the Z-domain, and finally into the time domain. Furthermore, a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface. This matrix is complex in the frequency domain for lossy media. By applying the Z-transform, this matrix can also be transformed into the time domain using only real modified matrix elements. The accuracy of the method is confirmed by comparisons with analytical solutions.     

An effective medium description for a random uniaxial anisotropic medium with small-scale fluctuations

Some properties of the electromagnetic field are determined for an unbounded medium characterized by a permittivity tensor whose elements can be expressed as the sum of two terms, one deterministic and the other random. The deterministic and random parts of the permittivity tensor are considered to be uniaxial anisotropic; thus it is a diagonal tensor where two of the three elments are equal. Starting from the bilocal approximation to Dyson's equation, an effective permittivity tensor and mean dyadic Green's function are obtained for small-scale fluctuations. Some important properties of the ordinary and extraordinary waves are also made known.     

低有效介电常数复合材料的聚波特性研究

该文通过建立结构模型,分析了辐射源辐射功率密度与有效介电常数和有效磁导率的关系,然后分析了辐射功率密度与此种属性材料介电常数、厚度、辐射源位置及工作频率的关系。结果表明,辐射源辐射功率密度与有效介电常数和有效磁导率的比值成正比关系,相对低的介电常数可以显著改善辐射源前向辐射功率密度,最大辐射功率密度是厚度的周期函数,而与辐射源位置关系不大;获得较大辐射功率密度的工作频带是非常窄的。理论上解释了人工构造的低介电常数材料作为天线覆层提高增益的原因。     

Full-wave analysis of circular microstrip resonators inmultilayered media containing uniaxial anisotropic dielectrics,magnetized ferrites, and chiral materials

In this paper, Galerkin's method in the Hankel transform domain is applied to the determination of the resonant frequencies, quality factors, and radiation patterns of circular microstrip patch resonators. The metallic patches are assumed to be embedded in a multilayered substrate, which may contain uniaxial anisotropic dielectrics, magnetized ferrites, and/or chiral materials. The numerical results obtained show that important errors can be made in the computation of the resonant frequencies of the resonators when substrate dielectric anisotropy, substrate magnetic anisotropy and/or substrate chirality are ignored. Also, it is shown that the resonant frequencies of circular microstrip resonators on magnetized ferrites can be tuned over a wide frequency range by varying the applied bias magnetic field. Finally, the computed results show that the resonance and radiation properties of a circular microstrip patch on a chiral material is very similar to those of a circular patch of the same size printed on a nonchiral material of lower permittivity     

Method of moments evaluation of the two-dimensionalquasi-crystalline approximation

In remote sensing, the propagation of electromagnetic fields through random media is often of concern. We may wish to characterize the effects of clouds or water droplets along the line of sight between an airplane and a radar installation, or we may be interested in using radar to probe the random medium itself, such as in determining snow depth and particle size. In all of these problems it is necessary to predict the propagation constant in the “random” medium. The purpose of this paper is to characterize the accuracy of the quasi-crystalline approximation and other associated methods of determining the effective permittivity for two-dimensional (2-D) random media. A numerical method based on the method of moments is used as a gauge for comparison with the theoretical methods. After deriving the 2-D quasi-crystalline approximation and presenting the numerical method, the behavior of the effective permittivity is analyzed for a range of particle sizes, volume fractions and dielectric losses. From this analysis, regions of validity for the theoretical methods are determined. An investigation is also given which explores the effect of particle arrangement methods on the pair distribution function which, in turn, is shown to have a significant effect on the imaginary component of the effective permittivity     

On a Method to Reduce Uncertainties in Bulk Property Measurements of Two-Component Composites

For two-component composites, we address the inverse problem of estimating the structural parameters and decrease measurement errors in bulk property measurements. A measurement of the effective permittivity at one frequency gives microstructural information about the composite that is used in cross-property bounds to estimate the effective permittivity at other frequencies. We use this information and inverse bounds on microstructural parameters to tighten error bars on permittivity measurements at microwave frequencies. The method can be used in the design of random and periodic composite materials for a large variety of applications. We apply the method to a composite material used in radar applications.      

Polarizability of gyrotropic sphere

The polarizability of gyrotropic spheres is studied in this short article. Gyrotropic media are anisotropic in two respects: the symmetric part of the permittivity dyadic is uniaxial, and furthermore, there is also antisymmetric part in the permittivity. The polarizability is also dyadic with its components depending on the relations of the permittivity components of the material.