Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

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     

A novel bistatic scattering matrix measurement technique using amonostatic radar

Presents a new technique for measuring the bistatic scattering matrix of point targets using a monostatic radar. In this technique, the complexity of the traditional bistatic measurement setup and difficulties in retaining the phase coherence between the transmitter and the receiver are circumvented completely. The bistatic measurement is performed using a wideband, polarimetric, monostatic radar in conjunction with a rotatable ground plane positioned behind the target. Assuming that the distance between the target and the ground plane is larger than the radar resolution, the desired bistatic response (image contribution) can be isolated from the unwanted backscatter. Noting that the radar operates in the backscatter mode and using the reciprocity theorem, it is shown that the measured cross-polarized responses (σ_vhand σ_hv) cannot be determined uniquely. To rectify this problem, additional independent measurements are required. Additional equations for characterizing the cross-polarized components are obtained by placing an anisotropic lossless slab over the perfectly conducting flat surface. The validity and accuracy of the new bistatic measurement technique is demonstrated by measuring a number of point targets with known theoretical bistatic responses. Also, a new approach for determining the effective dielectric constant of dense random media based on the new bistatic measurement technique is developed     

Radar cross sections of dielectric or plasma coated conducting spheres and circular cylinders

Radar cross sections for a variety of spherical and cylindrical scatterers having homogeneous dielectric or plasma shells are obtained by using both the exact boundary value solutions and approximate, semi-empirical methods based on physical principles. The plasma is assumed to have the macroscopic properties of a lossless dielectric with a permittivity less than that of free space. A superposition approximation for the radar cross section of a dielectric coated conducting body is obtained by considering the scattered field to be the phasor sum of two principal components, the field scattered by the air-dielectric interface and the field scattered by an equivalent conducting body which differs from the actual body because of the lens action of the shell. This approximation yields very good agreement with the exact solutions for both spherical and cylindrical dielectric clad scatterers with radii in the Rayleigh region and in the resonant region, and for bistatic scattering as well as for backscatter. The echo area of a conducting sphere with nonconcentric spherical dielectric shell calculated by means of the superposition approximation is in excellent agreement with experimental measurements, thus demonstrating the validity of this method in a case for which the exact solution cannot be obtained.     

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     

Microwave imaging for a dielectric cylinder

The problem of reconstructing both the shape and the relative permittivity of a homogeneous dielectric cylinder from the measurement of scattered field is numerically simulated. The Newton-Kantorovitch algorithm and the moment method are used to solve a set of nonlinear integral equations. Numerical results show that, with multiple incident directions, good reconstruction is obtained. This algorithm can be applied at a single frequency without limitation on the value of dielectric constant. The effect of random noise on imaging reconstruction is also investigated     

Plane wave scattering by a corrugated conducting cylinder atoblique incidence

The problem of scattering from a corrugated conducting cylinder due to an obliquely incident plane wave is solved by a boundary-value method. The region between the corrugations is considered as a medium with tensor permeability and tensor permittivity, which is a valid assumption when the corrugation constant is much less than the free-space wavelength. By loading this region with a dielectric material, one of the components of the scattered electric field in the far-field region can be altered significantly with no change in the other component. These components, in turn, determine the bistatic scattering cross sections, and the dielectric loading of the corrugated region appears to have no effect on the cross section due to the polarized component, while showing significant changes in the cross section due to the depolarized component     

The bilocal approximation for the effective dielectric constant of an isotropic random medium

The bilocal approximation in strong fluctuation theory leads to an expression for the effective dielectric constant of a random medium. A detailed study of this expression is made for the case of a medium characterized by an isotropic correlation function. The effective dielectric constant is shown to obey an equation involving an integral containing the correlation function, the free space propagation constant, the quasistatic dielectric constant, and the effective dielectric constant itself, Numerical methods for solution are suggested. The low frequency behavior is also examined. The leading correction term to the quasistatic dielectric constant is shown to be different than previously deduced expressions.     

Slotted Line Measurements for Propagation Constant in Lossy Waveguide (Short Papers)

The propagation coefficient in a slotted waveguide partially loaded with a lossy dielectric can be determined accurately, in terms of the measured standing-wave pattern, by means of a computer program solving a set of transcendental equations. This determination is a necessary step in a permittivity measurement technique which was recently proposed by several authors.     

New method for complex permittivity measurement of dielectric materials

A novel technique for the measurement of dielectric properties of a homogeneous isotropic material is described. An accuracy better than 1% can be obtained on the permittivity and loss tangent values. The structure used is a cylindrical metallic cavity, carrying at its centre the circular cylindrical dielectric sample. The complex permittivity is deduced from the comparison between the experimental and the computed electromagnetic characteristics (frequencies, quality factors) of the resonant TE01? mode of the dielectric resonator.     

A Comprehensive Technique to Determine the Broadband Physically Consistent Material Characteristics of Microstrip Lines

This paper describes a method to extract the relative complex dielectric permittivity from propagation coefficient measurements on microstrip lines. The material characteristics of microstrip lines fabricated on two different types of substrates commonly used in microwave circuit and printed circuit boards are investigated. The mechanisms that cause the effective permittivity of microstrip lines to be dispersive are explored. The technique includes creating closed-form effective permittivity equations to relate the effective permittivity of the microstrip lines to the real part of the dielectric permittivity of the substrate. Curve-fitting methods are used to create causal dielectric material models that relate the imaginary part of the dielectric permittivity to its real part. The methods developed in this paper can be used to characterize low-loss dielectric materials whose polarization is dominantly dipolar within the microwave frequency range in high-speed packaging applications.      

Propagation constant and the velocity of the coherent wave in adense strongly scattering medium

Frequency- and time-domain experiments are conducted to study the effective propagation constant of the coherent wave in a dense strongly scattering medium. A wide-band microwave signal (10-40 GHz) is propagated through randomly distributed glass spheres with a 5.73 mm average diameter and separated into incoherent and coherent fields. The real and imaginary parts of the propagation constant are obtained from the coherent field. The narrow size distribution of the particles enables the authors to study scattering from the Rayleigh region through the Mie resonance scattering region. The results of the experiments are compared to independent scattering, effective-field approximation (Foldy's), and the higher order quasi-crystalline approximation (QCA) using Mie scattering coefficients and the Percus-Yevick approximation for the pair-distribution function. The phase and group velocities of the coherent wave are obtained from the effective propagation constant and compared with theory. In addition, the velocity of the coherent wave in random media is measured using the time-domain technique. It is shown that the velocity of the coherent wave in random media is neither phase nor group velocity     

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.     

Space-charge waves in partially depleted negative-mobility media

Space-charge waves in a two-dimensional negative-mobility medium are described by a relatively simple and easy-touse expression for the complex propagation constant. Attention is focused on the dominant mode in the most important limit of low growth rate. Diffusion is included in the analysis. Whereas most previous workers imposed a stiff lateral-motion constraint at the surfaces of the drifting electron stream, we allow the electrons to move freely in the transverse direction at the lateral boundaries of the stream. This free-surface assumption corresponds to the partially depleted condition which prevails in many experiments. It has the effect of reducing diffusion damping and hence enhancing the growth of space-charge waves at high frequencies. The enhanced high-frequency growth rate makes the free-surface theory agree better with experimental data on thin-layer reflection and traveling-wave amplifiers than the stiff-surface theory does. Our results are cast in a form which allows heterogeneous dielectric media to be characterized by a single "effective dielectric constant." Dielectric configurations considered include symmetrical and unsymmetrical combinations of simple dielectric media, multilayered dielectric media, and simple or multilayered dielectric media with metal backing.     

In situ measurements of the complex propagation constant in rocks for frequencies from 1 MHz to 10 MHz

The complex propagation constant for frequencies between 1 MHz and 10 MHz has been measured for propagation between bore holes in granite rock at a site near Raymond, Colo., USA. The measurement technique consisted in Comparisons of the phase and amplitude of signals received on two identical dipole antennas spaced at different distances on a radial from an isolated transmitter. The conductivity and permittivity of the medium calculated from the propagation constant are compared with laboratory measurements of samples from the same boreholes, and reasonably good agreement is obtained.     

Acoustic and electromagnetic wave interaction: analyticalformulation for acousto-electromagnetic scattering behavior of adielectric cylinder

An analytical solution for the bistatic electromagnetic (EM) scattering from an acoustically excited vibrating dielectric circular cylinder is presented. The incident acoustic wave causes a boundary deformation as well as a dielectric inhomogeneity within the dielectric cylinder. First, a perturbation method is developed to calculate the EM scattering from a slightly deformed and inhomogeneous dielectric cylinder. Then, assuming the vibration frequency is much smaller than the frequency of the incident EM wave, a closed form expression for the time-frequency response of the bistatic scattered field is obtained. The solution for acoustic scattering from an elastic cylinder is applied to give the displacement on the surface as well as the compression and dilation within the cylinder. Both the surface displacement and the variation in material density (dielectric constant fluctuation) within the cylinder contribute to the Doppler component of the EM scattered field. Results indicate that the Doppler frequencies correspond to the mechanical vibration frequencies of the cylinder and that the Doppler components only become sizeable near frequencies corresponding to the natural modes of free vibration in the cylinder. These resonances depend only on the object properties and are independent of the surrounding medium. Thus, utilizing the information in the Doppler spectrum scattered by an acoustically excited object vibrating at resonance could provide a means for buried object identification     

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     

传输／反射法测量材料电磁参数的研究

分析了材料样品填充的矩形波导或同轴线等效网络的归一化通用矩阵,提出了一种求解材料电磁参数（εr,μr)的解析方法。分析表明,行性阻抗Zc与传播常数数γ均可直接由传/反射参数确定。同时应用特性阻抗与传播常数得到了磁性材料的电磁参数（εr,μr)。利用特性阻抗Zc、传播常数γ以及同时利用二者分别得到了三个确提高测量精度并确定测量误差;同时,可用于解决复介电常数测量的多值性问题与π模糊性问题。实际测试结果证明本文方法的有效的且有实用意义。     

Velocity Modulation of Electromagnetic Waves

This paper deals with electromagnetic wave propagation through dielectric media whose propagation constants vary as a function of time. If the parameters of the medium cannot respond to changes in the electric and magnetic fields of the propagating wave, the fields within such media will be linear. Maxwell's equations are solved for cases in which the scalar permittivity and permeability vary independently with time. When the impedance is constant, an exact solution is obtained. When the impedance varies, a closed form approximation is found since an exact solution is not always possible. The field energy and electromagnetic momentum are derived for a velocity transient and it is seen that, in general, the energy changes and the momentum remains constant. The frequency deviation that results when a monochromatic wave is passed through a section of dielectric with nonconstant velocity of propagation is discussed in detail. An approximate solution is obtained for the case in which the electrical length of such a section is small; it is found that essentially linear phase modulation occurs. The general solution is found for the case in wtilch the electrical length of section is long and the permittivity of the medium sinusoidally modulated. The optimum length found to give the greatest frequency deviation is shown to be generally impracticable. It appears that ferroelectric or ferrimagnetic velocity-modulated dielectrics are feasible, at least for low-power modulators.