Analysis of Inductive Dielectric Posts in Rectangular Waveguide

A rapidly converging moment solution for the complete analysis of homogeneous dielectric posts of the inductive type in rectangular waveguide is presented. The moment method approach uses filamentary currents to simulate both the field scattered by the post and the field inside the post and in turn point-matches the continuity conditions for the tangential components of the electric and magnetic fields across the post surface. The procedure is simple to execute and is general in that inductive posts of arbitrary smooth shape, size, location, and number, Iossless as well as lossy, can be handled effectively. Data are given and compared with the few cases for which approximate results are available. The technique is further appfied to other situations where no experimental data or other analytic results are available.     

Electromagnetic boundary conditions and uniqueness revisited

The formulation of the boundary conditions for electromagnetic problems is reexamined. It is shown that specifying a pair of two collinear field components on the boundary surface, one electric and one magnetic, ensures uniqueness, regardless of whether the pair is tangential or normal to the surface. Such boundary conditions, although not commonly used, are a possibility that the author may want to add to the well-known boundary conditions in terms of the tangential E field or the tangential H field. The treatment herein also provides an insight into the relation between the field-based analysis using Maxwell's equations and the potential-based analysis using the Helmholtz equation.     

The use of surface impedance concepts in the finite-differencetime-domain method

Surface impedance concepts are introduced into the finite-difference time-domain (FDTD) method. Lossy conductors are replaced by surface impedance boundary conditions (SIBC), reducing the solution space and producing significant computational savings. Specifically, a SIBC is developed to replace a lossy dielectric half-space. An efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented. Finally, three problems are studied to illustrate the accuracy of the FDTD-SIBC formulation: a plane wave incident on a lossy dielectric half-space, a line current over a lossy dielectric half-space, and wave propagation in a parallel-plate waveguide with lossy walls     

An absorber tip diffraction coefficient

The UTD corner diffraction solution for a perfectly conducting corner is empirically modified for the case of a dielectric corner. The dielectric may be lossless or lossy, but is assumed to be homogeneous. This modified solution is used to calculate the bistatic scattering from the tip of a dielectric pyramid. Sample calculations display some features of the scattering from a single lossy dielectric pyramid. To verify the solution, calculations are compared with backscatter measurements of a single pyramid that is cut from a homogeneous lossless dielectric (polyethylene). Calculations are then compared with measurements for the more pertinent case of bistatic scattering from a wall of pyramidal radar absorbing material     

Gaussian beam representation of aperture fields in layered, lossymedia: simulation and experiment

It is demonstrated that a three-dimensional electromagnetic field of a given linear polarization, emanating from an aperture source and propagating in a lossy medium, can be represented by an astigmatic Gaussian beam with complex source coefficients. The values of the coefficients can be determined experimentally by scans of the phase and amplitude of the field in the electric and magnetic principal planes near the aperture by means of a monopole probe and a liquid phantom (a phantom being a device that simulates the conditions encountered when radiation (e.g. microwaves) is deposited in biological tissues (e.g. human muscles) and permits a quantitative estimation of its effects). Once the source parameters are obtained, computations of the field everywhere else can be achieved rapidly. The theory is verified experimentally for bounded, homogeneous, and layered lossy media. Agreement is within 3% (relative to the maximum field at the aperture) over the entire scanned area     

Edge diffraction in the vicinity of the tip of a composite wedge

The electromagnetic field due to a line source radiating in the presence of a two-dimensional composite wedge composed of a number of conducting and dielectric materials is obtained. The Fourier transform path integral method (FTPI) is described and used to perform the numerical analysis. An important feature of the FTPI method is that it is based on a global solution to the Helmholtz scalar wave equation. As such the method avoids numerical enforcement of boundary conditions and the necessity of reformulating the analytical/numerical equations for each geometric configuration. The total scattered field is presented for several cases where one of the dielectric wedge sections is lossy, including examples of microwave scattering from a crested ocean surface and an air-ocean-sea ice interface     

Scattering by arbitrarily cross-sectioned layered, lossy dielectric cylinders

The scattering properties of TM or TE illuminated lossy dielectric cylinders of arbitrary cross section are analyzed by the surface integral equation techniques. The surface integral equations are formulated via Maxwell's equations, Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by flat-pulse expansion and point matching. Once the surface fields are found, scattered field in the far-zone and radar cross section (RCS) are readily determined. RCS thus obtained for circular homogeneous dielectric cylinders and dielectric coated conducting cylinders are found to have excellent agreements with the exact eigenfunction expansion results. Extension to arbitrary cross-sectioned cylinders are also obtained for homogeneous lossy elliptical cylinders and wedge-semicircle cross-sectioned cylinders, with and without a conducting cylinder in its center. RCS dependences on frequency and conductivity as well as the matrix stability problem of this surface integral equation method are also examined.     

Eigenvalues of a dielectric-coated conducting cone

The general problem of radiation/scattering from a dielectric coated semi-infinite conical structure excited by an arbitrary surface current distribution on the dielectric layer is formulated. Since the angular eigenfunction expansion is not suitable for this problem, the radial eigenfunction expansion is employed. The boundary value method is applied to obtain the fields in the form of infinite double series over the appropriate eigenfunctions in terms of spherical Hankel and associated Legendre functions. The conical dielectric shell may be lossy or lossless and the series solution generally involves complex eigenvalues which are calculated numerically. Using a small conducting sphere at the tip of the cone, the singularity of the Hankel functions at the origin is overcome, thus permitting the use of the orthogonality relations of Sommerfeld's complex-order wave functions to solve the problem and construct sets of infinite simultaneous linear equations which are presented in matrix form.     

A moment method solution for TMz and TEzwaves illuminating two-dimensional objects above a lossy half space

A moment method (MM) solution for analyzing the electromagnetic shielding and scattering properties of two-dimensional (2-D) objects over a lossy half space is presented. The materials of the objects can be metal, dielectric, or magnetic. Also, the lossy half space is included to simulate the effects of the earth ground or any flat homogeneous lossy surface. An MM based on a volume formulation and a special Green's function in the spectral domain is developed. Both TM _z and TE_z waves incident upon 2-D metal or lossy material structures are demonstrated for the shielding effects of those bodies in the presence of the lossy ground. Besides, the echo widths of a composite object either in free space or above the lossy half space are determined by using the MM. Some of the results are compared with those by other methods, and good agreements are obtained. The MM solution can be used to study the shielding and scattering problems for cylindrical structures located over a lossy ground     

Scattering from loaded grooves

Electromagnetic scattering from a two-dimensional groove recessed in an arbitrarily thick conducting screen is studied. The groove may be empty or loaded with a lossy material which may or may not completely fill the cavity. For the partially loaded groove, the filling material is assumed electrically dense so that the standard impedance boundary condition is applicable at the top surface of the material. Employing a full-wave analysis, integral equations are derived for the tangential components of the electric field over the aperture. It is shown that the equations are identical for both partially loaded and completely loaded (or empty) cases provided that the aperture admittance of the groove is treated as the equivalent admittance of the internal medium looking into the aperture, thus simplifying the integral equations. When the groove is completely filled by a dense material, the formulation reduces to that corresponding to a direct application of the impedance boundary condition over the aperture.     

Two-dimensional hybrid element image reconstruction for TMillumination

A Newton's iterative scheme for electromagnetic imaging is proposed for reconstruction of the dielectric properties of inhomogeneous, lossy bodies with arbitrary shape. The algorithm is based on a finite element (FE) representation which is coupled to a boundary element (BE) formulation for the forward solution of the electric fields; together these are termed the hybrid element method. It utilizes FE discretization of only the area of interest while incorporating the RE method to match the conditions of the homogeneous background region extending to infinity. This paper presents image reconstruction for the 2D TM polarization case where two classes of dielectric distributions are studied which demonstrate the flexibility of this method along with some of the difficulties associated with larger imaging problems     

Derivation and application of a class of generalized boundaryconditions [electromagnetic scattering]

Boundary conditions involving higher order derivatives are presented for simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to nonplanar surfaces. As an illustration, a metal-backed uniform dielectric layer is simulated. It is shown that fourth-order conditions are capable of providing an accurate simulation for layers at least a quarter of a wavelength in thickness     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Field Solution for Radial Waveguides with Annular Discontinuities

A method is established which gives the internal field of a radial waveguide in the presence of annular-type slots on the conducting walls or metallic scatterers inside the guide. The exciting field can have a general form, and the dielectric constant of the region could be lossy or lossless. To obtain a solution, the induced currents (magnetic current in case of slot-type discontinuity) over the scattering bodies are expanded into a finite series of suitable basis functions with unknown coefficients. The total number of these functions is directly related to the electrical dimensions of the scatterers. The complex coefficients are then obtained by employing the appropriate Green's functions and an application of the boundary conditions over the scattering bodies. The method is then applied to the probIem of coupling between two radials waveguides by annular slots on the common boundary. It is shown that in general, higher order modes have significant effect on the solution, and for a precise evaluation of the field their contribution must also be included.     

Analysis of waveguide antenna arrays with protruding dielectricelements

The two-dimensional problem of radiation of TE and TM waves from a waveguide array with protruding smooth dielectric elements of arbitrary shape is considered, and solution algorithms are suggested. The algorithms are based on applying the method of auxiliary sources for the representation of electromagnetic fields outside and inside the protrusions in combination with the method of integral equations for the electric field at the waveguide aperture. The point matching of the field tangential components on the protrusion-to-free-space boundary and at the waveguide aperture is used to reduce the problem to a system of linear algebraic equations for the amplitudes of the auxiliary filamentary currents and of the waveguide aperture electric field, which is assumed to be piecewise constant. The amplitudes obtained from the solution of the system are used for computing the array reflection coefficient and element pattern, which are shown in some cases to be significantly dependent on the protrusion shape. Examples of arrays with flat-topped element patterns resulting from array geometry numerical optimization are also presented     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

Analysis of TE scattering from dielectric cylinders using amultifilament magnetic current model

A moment solution is presented for the problem of transverse electric (TE) scattering from homogeneous dielectric cylinders. The moment solution uses fictitious filamentary magnetic currents to simulate both the field scattered by the cylinder and the field inside the cylinder and in turn point-matches the continuity conditions for the tangential components of the electric and magnetic fields across the cylinder surface. The procedure is simple to execute and is general in that cylinders of arbitrary shape and complex permittivity can be handled effectively. Metallic cylinders are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure     

Analysis of electromagnetic scattering from dielectrically coatedconducting cylinders using a multifilament current model

A method of moments solution is presented for the problem of transverse magnetic scattering from dielectrically coated conducting cylinders. The solution uses fictitious filamentary electric sources of yet unknown currents to simulate both the field scattered by the cylinder and the field inside the dielectric coating. The simulated fields obey the boundary conditions, namely, the continuity of the tangential components of the electric and magnetic fields across the air-dielectric interface and the vanishing of the tangential component of the electric field at the perfect conductor, at selected sets of points on these respective surfaces. The result is a matrix equation that is readily solved for the unknown current. The currents can be used to determine approximate values for the fields and field-related parameters of interest. The procedure is simple to implement and is general in that cylinders of smooth but otherwise arbitrary shape and coating of arbitrary complex permittivity can be handled. Illustrative examples are considered and compared with available data, demonstrating the efficiency of the solution     

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.     

Wave tilt sounding of a linearly inhomogeneous layered half-space

The wave tilt of a transverse electric (TE) electromagnetic wave over a linearly inhomogeneous lossy layer overlying a homogeneous half-space is studied. Two approaches are used: an exact formulation using solutions of Airy's equation and an approximate numerical solution using a large number of homogeneous layers with a linearly increasing dielectric constant. The numerical results of both solutions are practically identical as long as the thickness of the layers in the approximate model are somewhat smaller than a quarter-wavelength.