Electric Surface Current Densities Research Articles

A Directional Borehole Radar System

In this paper we present the simulation and design of a directional borehole radar. In addition we discuss an imaging method for the radar system. The antenna system contains an electric dipole which is in one direction shielded by a cylindrical perfectly conducting reflector. The radiation pattern of the reflected wavefield is computed by first solving the integral equation. This equation combines the unknown electric surface current density on the reflector and the known incident field from the electric dipole. Once the electric surface current density is known, the radiation pattern of the system is computed using the integral representation over the reflector and the dipole. The radiation patterns for various configurations have been computed in order to find an optimal configuration. A prototype of the antenna system based on an optimal configuration has been built, and the directional radiation pattern has been measured in the plane perpendicular to the antenna system. The measurements were in good agreement with the computations. Subsequently a three dimensional imaging method for the borehole radar is presented. Here a deconvolution is carried out in the angular direction, making use of the computed radiation pattern. Some imaging results will be shown.

Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns.

Moment-method analysis of arbitrary 3-D metallic N-port waveguide structures

Moment-method analysis of arbitrarily shaped perfectly conducting (metallic) waveguide structures with N waveguide ports is presented that is based on the free-space Green's function. Utilizing the Kirchhoff-Huygens principle, the problem is formulated in terms of the electric-field integral equation. The eigenvectors of the waveguide port sections and the Rao-Wilton-Glisson functions for triangular patches are used as basis functions for the magnetic and electric surface current densities, respectively. The accuracy of the method is verified by measurements or reference values. Its versatility is demonstrated at several design examples of practical interest, such as a lateral coax-fed waveguide, a twisted waveguide, and a waffle-iron filter with round teeth.

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.

Rigorous combined mode-matching integral equation analysis of horn antennas with arbitrary cross section

A combined rigorous method is presented for the analysis of horn antennas with arbitrary cross section and general outer surface. The horn taper is described by the mode-matching (MM) method where the cross-section eigenvalue problem is solved by a two-dimensional (2-D) finite element (FE) technique. For the exterior horn surface including the radiating aperture, the application of the Kirchhoff-Huygens principle yields two expressions for the admittance matrix which are based on the electric (EFIE) and the magnetic (MFIE) field integral equation, respectively. The equations are solved numerically by the method of moments (MoM). For the preferred EFIE formulation, the eigenvectors of the last waveguide taper section and RWG functions for triangular patches are utilized as basis-functions for the magnetic or electric surface current densities, respectively. The presented method is verified by available reference values or measurements for a waveguide radiator with a peripheral choke, a conical and a rectangular horn. Its flexibility is demonstrated at the example of a conical ridged waveguide horn.

A fictitious domain method for conformal modeling of the perfect electric conductors in the FDTD method

We present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors (PEC) in the finite-difference time-domain (FDTD) method. The idea is to extend the electromagnetic field inside the PEC and to introduce a new unknown, the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the PEC. This requires the use of two independent meshes: a regular three-dimensional (3-D) cubic lattice for the electromagnetic field and a triangular surface-patching for the surface electric current density. The intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density. An interesting property of this method is that it provides the surface electric current density at each time step. Furthermore, this method looks like FDTD with a special model for the PEC. Numerical results for several objects are presented.

Very compact double C-patch antenna

A miniaturised C-patch antenna excited by means of a coaxial probe is described. The antenna consists of two stacked C-shaped elements connected together with a vertical conducting plane. The antenna is designed on an air substrate and offers attractive dimensions, being five times lower than those of a conventional half wavelength microstrip patch antenna operating at the same frequency. A 10 dB bandwidth of 3% is obtained. The voltage standing wave ratio, radiation patterns, and electric surface current density are presented.

3-D FEM/BEM-hybrid approach based on a general formulation of Huygens' principle for planar layered media

Huygens' principle is used to exclude inhomogeneous regions and ideal conducting regions from planar layered structures. The fields in the inhomogeneous regions are modeled by the finite-element method (FEM) with tetrahedral edge elements in terms of the electric-field strength E/spl I.oarr/. The fields in the layered structure are described by an integral representation of the electric-field strength E/spl I.oarr/ in terms of equivalent electric and magnetic Huygens' surface current densities for the inhomogeneous regions, and in terms of electric Huygens' surface current densities for ideal conducting regions. It is formulated with the help of electromagnetic (EM) potentials resulting in low-order singular integral kernels to facilitate the numerical handling of the integral representation. A general formulation of the integral representation is given for observation points lying in the Huygens' surface. As compared to the homogeneous-space case, additional terms in the integral representation have to be considered if parts of the Huygens' surface lie in an interface of layers with different material properties. An integral equation is formulated and discretized by a Galerkin testing procedure (boundary-element method), together with the finite-element (FE) system resulting in an unequivocal discretized description of the entire field problem. The method is validated with the help of a canonical test problem. Further numerical results are presented for dielectric resonators coupled to microstrip circuits.

Application of modal expansion and method of moments to study electromagnetic scattering from a rectangular cavity recessed in a three‐dimensional conducting surface

The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three‐dimensional (3‐D) conducting body is analyzed using the modal expansion inside and the integral equation method outside the cavity. Assuming (1) an equivalent electric surface current density flowing on the 3‐D conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture, only the scattered fields outside the cavity are determined . The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting 3‐D surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the method of moments (MoM). The numerical results on scattering from rectangular cavities embedded in various 3‐D objects are compared with the results obtained by other numerical techniques.

Electromagnetic interaction between two parallel circular cylinders on a planar interface

Multiple interaction between two parallel and infinitely long circular cylinders on a planar interface separating two different media is analyzed theoretically. The scattering equations are derived from the so-called extinction theorem applied to this particular geometry. For simplicity, the surface is considered to be perfectly conducting although the method can be extended for any material. The equations, solved numerically by means of an appropriate discretization of the surface, provide the electric surface current density from which the scattered intensity can easily be calculated. Scattering of the transversal-magnetic and transversal-electric incident wave is studied as a function of the cylinder separation for cylinder diameters from 0.2/spl lambda/ to 4/spl lambda/ (/spl lambda/ being the incident wavelength). The effects of the interaction between cylinders are shown in the scattering cross section and in the surface current density of the planar substrate and of the cylinders.

Variational aspects of the reaction in the method of moments

The reaction R(J/sub 1/, J/sub 2/) between two electric surface current densities J/sub 1/ and J/sub 2/ is the integral of the dot product of J/sub 1/ with the electric field produced by J/sub 2/. Jack H. Richmond (see ibid., vol.39, no.4, p.473-479, 1991) has correctly shown that the reaction is variational (a formula is variational if it has a stationary point at the quantity of interest) with Galerkin's method but is not necessarily variational when the non-Galerkin element method is applied in the manner where one set of functions is used to expand both J/sub 1/ and J/sub 2/ and another set of functions is used to test both the integral equation for J/sub 1/ and that for J/sub 2/. In this paper, the reaction R(J/sub 1/, J/sub 2/) is shown to be variational when the non-Galerkin method is applied in the manner of operation where the set of functions used to expand J/sub 2/ is the set of functions used to test the integral equation for J/sub 1/ and the set of functions used to test the integral equation for J/sub 2/ is the set of functions used to expand J/sub 1/. Hence, the manner of operation just described may be more appropriate than Richmond's if a variational result is desired. A few numerical results are included to compare the performance of both manners of operation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Novel basis function for the equivalent magnetic current in the method of moments solution of dielectric scattering problems

In the method of moments surface formulation of dielectric scattering problems, two sets of basis functions are required for the equivalent electric and magnetic surface current density. In the Letter a novel simple basis function for the magnetic current is presented which is approximately spatially orthogonal to the widely used basis function developed by Rao et al.

Electric surface current model for the analysis of microstrip antennas with application to rectangular elements

An approach to the analysis of microstrip antennas which is applicable also to relatively thick substrates using the relevant Green's function is presented. The Green's function is derived and closed form expressions for various antenna characteristics which explicitly take into account the presence of the dielectric material are obtained in terms of the electric surface current density. For rectangular microstrip elements near resonance the current distribution is approximated using lossless transmission line analysis, thus enabling the complete evaluation of the characteristics of the element near resonance. The results obtained in this approach for the radiation resistance, surface wave resistance, radiation pattern, directivity, and bandwidth are presented in a detailed set of graphs for a representative set of parameters.