Space-time integral equation approach to dielectric targets

A time-domain integral equation technique is presented for computing the response of arbitrarily shaped three-dimensional nondispersive homogeneous dielectric solids. The method is an extension of the previously reported space-time integral equation (STIE) approach to scattering from conducting solids. It consists of the simultaneous solution of four integral equations by a procedure of marching in time. The incident pulse-width is of the order of a target dimension. The result is a "smoothed impulse response," or, after deconvolution, a frequency response valid from dc through the resonance region. While applicable to arbitrary shapes, the numerical solution was implemented for smooth solids with plane symmetry. Results for a sphere and a sphere-capped cylinder are given and verified, respectively, by comparison with the Mie series solution and with measurements.     

An integral equation for electromagnetic scattering from homogeneous dielectric bodies

A single surface integral equation for problems involving electromagnetic scattering from homogeneous dielectric bodies illuminated by time-harmonic sources is developed via the equivalence principle. The equation is formulated in terms of an equivalent electric current defined at the body surface. When allowed to radiate in a homogeneous medium having the material parameters of the exterior medium of the original problem, the electric current solution to the integral equation produces the correct scattered electric and magnetic fields external to the body.     

An integral equation solution to the scattering of electromagnetic radiation by dielectric spheroids and ellipsoids

A new approach to the scattering of electromagnetic radiation by dielectric scatterers and application of it to the case of scattering by homogeneous spheroidal and ellipsoidal raindrops is presented. We transform the (singular) integral equation for the scattering into an integral equation for the Fourier transform of the internal field, which has a nonsingular kernel. This equation is solved by reducing it by quadrature into a set of algebraic equations. The scattering amplitude so obtained is shown to satisfy the Schwinger variational principle, and the method is thus both numerically stable and known to be convergent. We present sample calculations for spheres, for spheroids, and for ellipsoids.     

Resonant solutions involved in the integral equation approach to scattering from conducting and dielectric cylinders

Resonant solutions involved in the integral equation formulation for analyzing the scattering problems and the elimination of these erroneous solutions are investigated. The parameter ranges where the resonant solutions are mixed into the correct ones and the degree of errors caused by the resonant solutions are checked on through numerical computation of matrix condition numbers and scattering cross sections for dielectric cylinders of square cross section with side width/wavelength ratio being less than about 1.27. As a method of removing the resonant solutions, the method taking some lower order equations of the so-called "extended boundary condition (EBC) method" into consideration is proposed.     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

An integral equation approach to electrical conductance tomography

A reconstruction procedure for electrical conductance tomography developed by solving a linear Fredholm integral equation of the first kind is discussed. The integral equation is obtained from a linearized Poisson's equations. Properties of the integral equation are discussed, and problems associated with numerical solution of the equation are treated. The reconstruction requires only one matrix multiplication and therefore can be computed in a short time. Test results of the algorithm using both simulated and measured data are presented.     

Electromagnetic scattering from a dielectric wedge and the singlehypersingular integral equation

Electromagnetic fields scattered by a finite dielectric wedge are computed using a hypersingular integral equation (HIE). The results are compared with those obtained previously using a singular integral equation (SIE) and with the theory that predicts that the fields near the edge of the wedge behave like static fields. The HIE produces more consistent results than the SIE, probably because the unknown boundary function tends to a constant near the edge instead of diverging. The two numerical methods agree reasonably well, and these results agree only in part with the static field behavior     

A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies

The problem of electromagnetic wave scattering by heterogeneous dielectric bodies is formulated in a recursive manner by organizing their homogeneous subregions into hierarchical multiply-nested structures. The inner details of each multiply-nested body are completely accounted for by an equivalent surface representation that yields the electric and magnetic fields tangent to the body only in terms of a single unknown electric surface current density distributed on its outer surface. In this manner, the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density. For a large number N of different homogeneous dielectric subregions within such a heterogeneous body, the proposed method has a computational complexity of O(N/sup 1.5/) and storage requirements that increase in proportion to O(N). Furthermore, the equivalent surface representation derived for a particular subregion is invariant under rotation and translation and may, therefore, be applied to identical subregions without repeating the computation. The fields at any interior points are calculated by a fast backward recursion.     

An integral equation and its application to spiral antennas onsemi-infinite dielectric materials

This paper presents an integral equation that can handle wire antennas on a semi-infinite dielectric material. The integral equation is reduced to a set of linear equations by the method of moments. For efficiency, the impedance matrix element Z_m,n is divided into two parts on the basis of weighted Green's function extractions. The far-zone radiation field, which is formulated using the stationary phase method, is also described. After the validity of the presented numerical techniques is checked using a bow-tie antenna, a spiral antenna is analyzed. The current distribution, radiation pattern, axial ratio, power gain, and input impedance are discussed. It is found that the radiation field inside a dielectric material is circularly polarized. As the relative permittivity of the dielectric material increases, the angle coverage over which the axial ratio is less than 3 dB becomes narrower     

Integral equation for scattering by a dielectric

The determination of the scattered and transmitted transient electromagnetic waves produced by a uniform dielectric body is reduced to the solution of a singular integral equation of the first kind for one tangential vector field defined on the surface. All derivations are carried out within the heuristic approach to Green functions and delta functions. The electric and magnetic fields are expressed in terms of the sources, initial values, and the boundary values by means of the Green function for the scalar wave equation. The appropriate integral equation is derived, and the integrals for the scattered and transmitted fields are given. The simpler problem of scattering of scalar waves is developed first. Formulas for the scattering of monochromatic fields are also given in the scalar and electromagnetic cases when transmitted fields do not vanish.     

导体-介质组合体散射分析两种积分方程法比较

采用耦合积分方程和单积分方程两种方法,分析了三维导体-介质组合体目标的电磁散射问题.与传统的耦合积分方程法相比,单积分方程法使介质体表面的未知量数目减少一半,并且能获得更快的迭代解.讨论了导体-介质交界线上RWG基函数的正确处理问题.对介质锥-导体柱组合体、导体-介质组合球和某导弹模型的雷达截面(RCS)进行了计算和比较,验证了两种积分方程方法的正确性,且数值结果表明单积分方程法更加有效.     

A surface integral equation approach to the scattering andabsorption of doubly periodic lossy structures

The scattering and absorption of a doubly periodic array of absorbers, either placed in free space, backed by a perfect conductor or by a half-infinite space with the same material properties as the elements forming the array, is analyzed with a surface integral equation approach (SIE). The use of a suitable periodic Green's function as kernel of the SIE reduces the formulation of the problem to a single absorber. A set of equivalent electric and magnetic currents on the surface of the absorber is discretised using Glisson functions and the SIE is solved with Galerkin's method. The validity and flexibility of the SIE approach is exemplified by comparing numerical results with measurement data for a family of commercially available absorbers     

A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability

A fast solution to the combined field volume integral equation (CFVIE) for electromagnetic scattering by large three-dimensional dielectric bodies of arbitrary permittivity and permeability is presented. The CFVIE is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents. The resultant integral equation is solved using the method of moments (MoM). Then the precorrected fast Fourier transform (P-FFT) method is applied to reduce the memory requirement and accelerate the matrix-vector multiplication in the MoM solution. In the implementation of the P-FFT method, two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources. In addition, two sets of interpolation operators are also applied respectively for the computation of the vector/scalar potentials and the curl of the vector potentials in the support of the testing functions. The resultant method has a memory requirement of O(N) and a computational complexity of O(NlogN) respectively, where N denotes the number of unknowns.     

A boundary integral equation approach to oxidation modeling

Thermal oxidation of silicon involves the diffusion of oxidant molecules from the gas-oxide interface to the oxide-silicon interface, and the transport of newly formed oxide away from the latter. Under suitable formulations these two processes can be shown to be boundary-value problems of harmonic and biharmonic nature. Based on these properties, a boundary integral equation method (BIEM) has been developed for modeling oxidation. This method achieves simplicity and efficiency by solving a two-dimensional problem using line integrals on the boundaries. The use of source distributions as intermediary solutions facilitates direct calculations of a wide variety of boundary parameters.     

Iterative integral equation solution for cylindrical dielectric resonator

An exact integral equation describing the substrate-mounted open cylindrical dielectric resonator is derived, and a first approximate solution for the fundamental resonant mode is calculated. Results are presented and are compared with both experiment and another theoretical approach.     

An integral equation formulation of the direct scattering problem for an inhomogeneous slab

A numerical technique based on an integral equation scheme is developed for solving the direct scattering problem for an inhomogeneous slab. The integral equation is derived, using the induced current concept and the Green's function technique. The numerical method of solving the integral equation is presented. The method is proved to be numerically satisfactory and is applied to the slab of specific profiles. Numerical results for several cases are also included.     

Surface integral representations for electromagnetic scattering from dielectric cylinders

The surface integral representations are derived for electromagnetic wave scattering from dielectric bodies. Several kinds of integral equations are given for dielectric cylinders immersed in an obliquely incident wave. The interior resonant solutions, the cause of erroneous solutions, accompanied with the equations presented here and the removal of these solutions are briefly discussed.     

An Integral approach to measurement of surface roughness parameters from light scattering in dielectric waveguides

An integral approach to measurement of the mean square deviation of a rough surface from light scattering in planar dielectric waveguides is proposed. A relationship between the attenuation coefficient of waveguide modes, waveguide parameters, and surface roughness is established. The limiting sensitivity of the method is estimated, and the simplicity of the method implementation and the high sensitivity of measurements are experimentally demonstrated.     

An integral equation approach to the analysis of finite microstripantennas: volume/surface formulation

An E-field integral equation for the analysis of finite printed circuit antennas with multiple dielectric regions is developed. In this analysis, the ground plane is considered to be finite. The dielectric substrates may be either lossless or lossy, and they may be inhomogeneous but must be finite. The equivalence principle is used to replace all conducting bodies by equivalent surface electric currents and all dielectrics by equivalent volume polarization currents. The respective boundary conditions on the dielectrics and the conductors are utilized to solve for the electric current on the entire structure. Typical results are presented to illustrate the potential of this method