A Measurement of the Complex Permittivity Tensor by a Standing-Wave Method in a Rectangular Waveguide

A rubber sheet manufactured by the rolling process strongly shows an anisotropic property, which is caused by carbon particles or carbon fibers aligned along the rolling direction. The measurement of the complex permittivity tensor in the rubber sheet is studied by a standing-wave method in a rectangular waveguide. The tensor elements, including nondiagonal and principal-direction ones, are measured and discussed. Errors in the measured tensor elements are evaluated.     

Spectral-domain analysis of open and shielded slotlines printed onvarious anisotropic substrates

A rigorous full-wave analysis based on the spectral domain approach for open and shielded slotline transmission lines is presented. The substrate materials under consideration are anisotropic, characterized by both their permittivity and permeability tensors. The formulation includes off-diagonal tensor elements to represent gyroelectric media, ferrites, or the misalignment between the principal axes of the substrate and the coordinate system of the waveguide. Dyadic admittance Green's functions for every structure are obtained with the help of differential matrix operators in the Fourier-transformed domain, and the Galerkin method is employed to find the propagation constants numerically     

Parameter reconstruction of materials with off-diagonal anisotropy using the state transition matrix method

An effective non-iterative method is developed for determination electromagnetic parameters of complex materials with anisotropy. Unlike the existing methods, the proposed method can extract the electromagnetic tensor parameters of materials with off-diagonal anisotropy using co- and cross-polarized reflection and transmission without using iterative procedures. Useful analytical expressions are derived for extracting the medium parameters of materials with off-diagonal anisotropy. The advantage of the method is that it uses state transition matrix and its properties in order to avoid nonlinearity and complexity of the problem. The method can work very well for dispersive materials since it is based on frequency-by-frequency extraction. The proposed method is validated by extraction of the complex permittivity and permeability tensors of two typical anisotropic materials.     

Transient analysis of microstrip line on anisotropic substrate inthree-dimensional space

The authors describe how anisotropy, with the permittivity tensor involving off-diagonal elements, may be generally formulated by Bergeron's method. The formulation is discussed for the propagation characteristics of single and parallel striplines on a sapphire substrate with tilted optical axis. To show the distinctive influence of anisotropy on the coupling property between lines, a parallel-line-type directional coupler on such a substrate is analyzed     

A Computer Simulation for the Analysis of Radar Echo-Sounding of Polar Ice Sheets

The goal of the work presented here is to model the timedomain reflected radar returns from polar ice sheets so that greater information can be gained from those returns. The results obtained by modeling the ice sheets as lossless and multilayered media are shown to be consistent with the measured results. They also provide insights into the mechanisms affecting the radar returns. In particular, the simulations suggest that the internal reflections in the polar ice sheet are due more to the variation in layer-to-layer permittivity rather than the conductivity. In addition, the best qualitative agreement between the simulations and the observed data were observed when the permittivity variations in each layer were varied randomly about the mean dielectric constant of the ice sheet.     

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides having a permittivity tensor with nonzero off-diagonal elements is described. In this approach, the nonphysical spurious solutions which are included in the solutions of the earlier vectorial finite-element method in an axial-components formulation do not appear. Numericaf examples On an anisotropic dielectric rectangular wave-guide composed of a uniaxial medium are given. Our results for the waveguide whose optic axis lies in the plane ( xy-plane) normal to the direction (z-axis) of propagation agree well with the results of the vectorial wave analysis using the variational method. We also demonstrate the application of this approach by analyzing the anisotropic dielectric rectangular waveguide whose optic axis lies in the xz - or yz -plane.     

同轴探头法测量片状介质材料的微波介电常数

提出了一种可用于测量片状介质材料微波复介电常数的同轴探头技术,该技术将同轴探头紧贴有导电衬底的片状介质,通过测量探头终端的矢量反射系数来确定介质的微波复介电常数。详细介绍了所采用的理论模型和测量系统。测量了一些常见介质材料的介电常数,测量值与理论值基本吻合。文章的同轴探头技术不仅可用于测量厚度较小的片状介质,而且可用测量样品量有限的液体。     

Microwave Dielectric Properties of Ceramic and Nanocomposite Titanates of Transition Metal

Ceramic and nanocomosite samples of the titanates of transition metals have been synthesized and their microwave dielectric properties have been investigated. Frequency and magnetic field dependences of the transmission and reflection coefficients in centimeter and millimeter wavebands were measured. It is established for most of studied ceramic titanates that transmission coefficient increases and reflection coefficient decreases when frequency increases. An absorption maximum has been found for ceramic sample made of Co_0.9Fe_0.1TiO₃. The real and imaginary parts of complex dielectric permittivity were determined from measurements of transmission and reflection coefficients. On the whole, real part of dielectric permittivity of nanocomposite titanates based on an opal matrix is less than for ceramic titanates.     

Finite-difference time-domain analysis of gyrotropic media. I.Magnetized plasma

When subjected to a constant magnetic field, both plasmas and ferrites exhibit anisotropic constitutive parameters. For electronic plasmas this anisotropy must be described by using a permittivity tensor in place of the usual scalar permittivity. Each member of this tensor is also very frequency dependent. A finite-difference time-domain formulation which incorporates both anisotropy and frequency dispersion, enabling the wideband transient analysis of magnetoactive plasma, is described. Results are shown for the reflection and transmission through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. A comparison to frequency-domain analytic results is included     

Transient response of microstrip step discontinuities on anisotropic substrate

In this paper, we present the numerical simulation of transient response of short pulse propagating through a microstrip step junction on anisotropic substrate having a tilted optical axis. In the simulation, the FD-TD method is extended to treat the cases having tilted optical axis expressed by a permittivity tensor with off-diagonal elements. The results show that the dispersion of transient signal caused by microstrip step discontinuities is quite significant and the dependence of transient characteristics of microstrip lines on the tilted angle of optical axis for anisotropic substrate can not be neglected.     

Practical aspects of complex permittivity reconstruction with neural-network-controlled FDTD modeling of a two-port fixture.

The paper discusses characteristics of a new modeling-based technique for determining dielectric properties of materials. Complex permittivity is found with an optimization algorithm designed to match complex S-parameters obtained from measurements and from 3D FDTD simulation. The method is developed on a two-port (waveguide-type) fixture and deals with complex reflection and transmission characteristics at the frequency of interest. A computational part is constructed as an inverse-RBF-network-based procedure that reconstructs dielectric constant and the loss factor of the sample from the FDTD modeling data sets and the measured reflection and transmission coefficients.As such, it is applicable to samples and cavities of arbitrary configurations provided that the geometry of the experimental setup is adequately represented by the FDTD model. The practical implementation of the method considered in this paper is a section of a WR975 waveguide containing a sample of a liquid in a cylindrical cutout of a rectangular Teflon cup. The method is run in two stages and employs two databases--first, built for a sparse grid on the complex permittivity plane, in order to locate a domain with an anticipated solution and, second, made as a denser grid covering the determined domain, for finding an exact location of the complex permittivity point. Numerical tests demonstrate that the computational part of the method is highly accurate even when the modeling data is represented by relatively small data sets. When working with reflection and transmission coefficients measured in an actual experimental fixture and reconstructing a low dielectric constant and the loss factor the technique may be less accurate. It is shown that the employed neural network is capable of finding complex permittivity of the sample when experimental data on the reflection and transmission coefficients are numerically dispersive (noise-contaminated). A special modeling test is proposed for validating the results; it confirms that the values of complex permittivity for several liquids (including salt water acetone and three types of alcohol) at 915 MHz are reconstructed with satisfactory accuracy.     

Approximate scalar finite-element beam-propagation method withperfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide     

Modal Analysis of Microstrip Antenna on Fiber Reinforced Anisotropic Substrates

In this communication, microstrip antenna on fiber reinforced anisotropic substrates has been considered in aerospace applications; however, the antenna's optical axis may not necessarily be colinear with any of the substrate's principal axes and that leads to a nondiagonal permittivity matrix (tensor). This work extends the studies of microstrip antenna on isotropic substrate and on uniaxial substrate to analyze antenna performance on fiber reinforced anisotropic substrates, where the permittivity matrix has five dielectric constants because of the substrate's fiber direction. The solution is based on modal analysis so that the wave immittance can be derived in a closed form. Analyses and experimental verification show that the antenna performance is strongly influenced not only by the permittivity along the principal axes but also by the fiber direction of the substrate.     

Finite-Element Formulation in Terms of the Electric-Field Vector for Electromagnetic Waveguide Problems

A vector finite-element method for the analysis of anisotropic waveguides with off-diagonal elements in the permeability tensor is formulated in terms of all three components of the electric field. In this approach, spurious, nonphysical solutions do not appear anywhere above the "air-line." The application of this finite-element method to waveguides with an abrupt discontinuity in the permittivity is discussed. In particular, we discuss how to use the boundary conditions of the electic field at the interface between two media with different permittivities. To show the validity and usefulness of this formulation, examples are computed for dielectric-loaded waveguides and ferrite-loaded waveguides.     

Full vectorial finite element formalism for lossy anisotropicwaveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures containing lossy, anisotropic materials. In this procedure a formulation in terms of the transverse magnetic field component is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus one avoids the unnecessary iterations which arise when using complex frequencies. To demonstrate the strength of the presented method, numerical results are shown for a rectangular waveguide filled with lossy anisotropic dielectric with off-diagonal elements in a permittivity tensor and compared with those obtained by the telegrapher equation method. The results are in excellent agreement both for phase and for attenuation     

Improved coupled-mode theory for reciprocal anisotropic waveguides

An improved coupled-mode theory for a reciprocal anisotropic multiwaveguide system is derived. The general reciprocal anisotropic medium is described by a symmetric permittivity tensor that can have nonzero off-diagonal elements. The derivation is based on the generalized reciprocity relation. The coupled-mode equations are applicable to both lossy (gain) and lossless systems. For the special case of lossless systems, it is shown that the matrices in the coupled-mode equation are Hermitian, so that energy conservation is observed exactly. For the special case of a single anisotropic waveguide, the results also reduce to the previously derived solutions by D. Marcuse (1975). The improved coupled-mode theory in an anisotropic multiwaveguide system is illustrated with numerical examples     

微波频率下乙酸乙酯皂化反应等效介电系数的实验研究

微波化学研究中的关键问题之一是对化学反应过程中的介电系数进行跟踪和测量.本文采用开槽同轴谐振探头首次测量了乙酸乙酯皂化反应对微波的反射系数,并用遗传算法获得了微波频率下该反应的等效介电系数.结果发现等效介电系数实部随温度的变化趋势符合L Onsager和Debye理论对极性混合溶液的描述;等效介电系数虚部因极化损耗和欧姆损耗随温度变化而相应变化;而等效介电系数实部随时间的变化与L Onsager极性混合溶液等效介电系数理论的描述相反.     

聚合物薄片的复介电常数微波测量方法

提出了一种在微波频域测量聚合物样品薄片复介电常数的方法,它利用自动测量线测试系统测量出电压驻波比和相角,然后采用级数各阶次展开方法,由反射系数推导出复介电常数.级数低阶次方法求解厚度较大的被测样品复介电常数时,为确保结果具有较高的精确度,要求测量频率不超过1.5GHz.为了克服这种测量频域的局限性,可采用级数高阶次展开方法来求解复介电常数.用级数展开方法测量聚苯乙烯、多乙酸乙烯酯和聚亚胺酯的复介电常数值,结果与真实值相近,可以和传输/反射法相媲美.     

Inverse scattering of inhomogeneous biaxial materials coated on aconductor

The inverse scattering of inhomogeneous biaxial materials coated on a perfectly conducting cylinder with known cross section is investigated. A group of unrelated incident waves is used to illuminate the cylinder. By properly arranging the direction and polarization of various unrelated incident waves, the difficulties of ill-posedness and nonlinearity were circumvented and the permittivity tensor distribution can be reconstructed through simple matrix operations. For theoretical formulation based on the boundary condition, a set of integral equations is derived and solved by the moment method as well as the unrelated illumination method. Numerical results show that the permittivity tensor distribution of the materials can be successfully reconstructed even when the permittivity is fairly large. Good reconstruction has been obtained both with and without Gaussian noise in measured data. In addition, the effect of noise contamination on imaging is also examined     

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.